Structural Geology: Principles, Concepts, and Problems - Third Edition

Structural Geology Structural Geology Principles, Concepts, and Problems Third Edition Robert D. Hatcher, Jr University of Tennessee Christopher M. Bailey College of William & Mary New York Oxford OXFORD UNIVERSITY PRESS Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and certain other countries. Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America. Copyright © 2020 by Oxford University Press Copyright © 1995 by MacMillan/Prentice-Hall Copyright © 1990 by Merrill For titles covered by Section 112 of the US Higher Education Opportunity Act, please visit www.oup.com/us/he for the latest information about pricing and alternate formats. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by license, or under terms agreed with the appropriate reproduction rights organization. Inquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above. You must not circulate this work in any other form and you must impose this same condition on any acquirer. Library of Congress Cataloging-in-Publication Data Names: Hatcher, Robert D., 1940– author. | Bailey, Christopher M., author. Title: Structural geology / Robert Hatcher (University of Tennessee, Knoxville), Chuck Bailey (College of William & Mary). Description: Third edition. | New York : Oxford University Press, [2020] | Includes bibliographical references. Identifiers: LCCN 2018059976| ISBN 9780190601928 (hardcover : acid-free paper) | ISBN 9780190601966 (ebook) Subjects: LCSH: Geology, Structural. | Geology, Structural—Textbooks. Classification: LCC QE601 .H35 2020 | DDC 551.8—dc23 LC record available at https:// lccn.loc.gov/2018059976 COVER: Bighorn River water gap through Sheep Mountain anticline, north of Greybull, Wyoming. Photo by Michael Collier. Printing number: 9 8 7 6 5 4 3 2 1 Printed by LSC Communications, Inc. United States of America We dedicate this book to our parents, teachers, and other mentors. Brief Contents Preface xviii PART ONE Introduction 1 1 Introduction 2 2 Fundamental Concepts and Nontectonic Structures 19 3 Geochronology in Structural Geology 44 4 Geophysical Techniques and Earth Structure 65 PART TWO Mechanics: How Rocks Deform 111 5 Stress 112 6 Strain and Strain Measurement 131 7 Mechanical Behavior of Rock Materials 8 Microstructures and Deformation Mechanisms 181 PART THREE Fractures and Faults 217 9 Joints and Shear Fractures 10 Faults and Shear Zones 11 Fault Mechanics 12 Thrust Faults 269 283 13 Strike-Slip Faults 14 Normal Faults 315 331 218 247 165 PART FOUR Folds and Folding 355 15 Anatomy of Folds 356 16 Fold Mechanics 381 17 Complex Folds 408 PART FIVE Fabrics and Structural Analysis 427 18 Cleavage and Foliations 19 Linear Structures 428 458 20 Structural Geology of Plutons 21 Structural Analysis 473 501 PART SIX Appendices 539 Appendix 1 Structural Measurements and Observations 540 Appendix 2 Stereographic Projections and Fabric Diagrams 549 Appendix 3 Structural Cross Sections—Methods for Cross-Section Construction 558 Appendix 4 Woodall Shoals Fabric Data Glossary 576 | References Cited 597 569 | Index 619 Contents Preface xviii Acknowledgments xx PART 1: Introduction 1 Introduction 2 Plate Tectonics 7 Equilibrium 11 Geologic Cycles 15 Chapter Highlights 17 Questions 17 Further Reading 17 2 Fundamental Concepts and Nontectonic Structures 19 Fundamental Concepts 19 Primary Sedimentary Structures 22 Bedding 22 Mud Cracks 25 Ripple Marks 27 Rain Imprints 27 Tracks and Trails 28 Sole Marks, Scour Marks, Flute Casts 28 Dewatering Structures 28 Fossils 29 Reduction Spots 29 Sedimentary Facies 30 Unconformities 30 Primary Igneous Structures 32 Gravity-Related Features 35 Landslides and Submarine Flows 35 ESSAY: Deciphering a Major Structure in the Southern Highlands of Scotland 36 Salt Structures 37 Impact Structures 39 viii Chapter Highlights 42 Questions 42 Further Reading 43 Contents 3 Geochronology in Structural Geology 44 Geochronology 44 Radioactivity and Isotope Geochronology 45 Closure Temperature 46 Assumptions 47 Radioisotopic Dating Techniques 48 Cosmogenic Surface Exposure Dating 58 The Vital Role of Geochronology in Structural Geology 59 Stable Isotopes 60 ESSAY: Rock Bodies That Appear to Be the Same in the Field May Not Turn Out to Be When Their Ages Are Determined 60 Chapter Highlights 63 Questions 64 Further Reading 64 4 Geophysical Techniques and Earth Structure 65 Seismic Reflection 65 Seismic Refraction 71 Earthquakes and Seismic Waves 71 Earthquake Waves and Whole-Earth Structure 71 Locating Earthquakes 73 Earthquake Magnitude and Intensity 75 Seismic Tomography 77 Focal Mechanisms and “Beach Balls” 78 Potential Field Methods 78 Terrestrial Magnetism 79 Remanent Magnetism 81 Magnetic Reversals 82 Induced Magnetism 82 Applications Using Magnetism 82 Gravity 83 Applications Using Gravity 89 Electrical Methods 90 Borehole Geophysics 90 Natural Gamma-Ray Log 95 ESSAY: Geophysical Data and the Structure of Mountain Chains 96 Electrical Logs 98 Photoelectric Logs 101 Neutron Logs 102 Temperature, Caliper, and Sonic Logs 102 Utility of Conventional Geophysical Logs—Geology from Wiggly Lines Borehole Imaging Logs 103 Suspension Logging 106 Vertical Seismic Profiles 106 Chapter Highlights 107 Questions 108 Further Reading 108 103 ix x Contents PART 2 5 Mechanics: How Rocks Deform 111 Stress 112 Definitions 113 Stress on a Plane 115 Mohr Circle Derivation 116 Mohr Construction 119 Amontons’ Law and the Coulomb–Mohr Hypothesis 121 Stress Ellipsoid 123 Stress at a Point 123 Measuring Present-Day Stress in the Earth 124 ESSAY: The Earthquake Cycle 127 Chapter Highlights 129 Questions 129 Further Reading 130 6 Strain and Strain Measurement 131 Definitions 132 Measures of Strain 133 Strain Ellipse and Ellipsoid 134 Simple, General, and Pure Shear 137 ESSAY: Daubrée and Mead Experiment 138 Progressive Deformation, Strain Symmetry, and Strain Path 139 Mohr Circle for Strain 141 Tensor Operations for Strain 142 Measuring Strain in Rocks 143 Strain Measurement Techniques 146 Linear Markers 146 Initially Elliptical Markers 148 From Two to Three Dimensions 153 The Utility of Strain Analysis 154 Concluding Thoughts 157 ESSAY: Finite Strain from Deformed Pebbles 159 Chapter Highlights 161 Questions 162 Further Reading 163 7 Mechanical Behavior of Rock Materials Definitions 166 Elastic (Hookean) Behavior 167 Permanent Deformation—Ductility 169 165 Contents Viscous Behavior 169 Plastic (Saint-Venant) Behavior 170 Elasticoviscous (Maxwell) Behavior 172 Controlling Factors 173 Behavior of Crustal Rocks Ductile-Brittle Transition 173 173 ESSAY: Jelly Sandwiches, Crème Brûlée, and the Mechanical Behavior of the Lithosphere 175 Strain Partitioning 177 Chapter Highlights 179 Questions 179 Further Reading 180 8 Microstructures and Deformation Mechanisms 181 Lattice Defects and Dislocations 182 Point Defects 183 Line Defects—Dislocations 183 Planar Defects—Stacking Faults 187 Translation (Dislocation) and Twin Gliding 188 Deformation Mechanisms 188 Cataclasis 188 Creep Processes 189 Superplastic Flow 195 Geochemical Processes 196 Mass-Transfer Processes 196 Factors That Influence the Rates of Chemical Reactions 200 Microstructures 200 Inclusion Trails and Deformation Lamellae 200 Unrecovered Strain, Recovery, and Recrystallization 200 Crystallographic Preferred Orientations 202 Laboratory Models of Deformation Processes 206 Final Thoughts 210 ESSAY: Fault Rocks—A Fourth Class of Rocks 211 Chapter Highlights 214 Questions 215 Further Reading 216 PART 3 9 Fractures and Faults 217 Joints and Shear Fractures 218 ESSAY: Fracking 221 Fracture Analysis 226 Significance of Orientation 226 Fracture Formation in the Present-Day Stress Field Fold- and Fault-Related Joints 229 Fracture Mechanics: Griffith Theory 229 Joints and Fracture Mechanics 232 228 xi xii Contents Fracture Surface Morphology 234 Joints in Plutons 238 Nontectonic and Quasitectonic Fractures 239 Sheeting 239 Columnar Joints and Mud Cracks 239 ESSAY: Mesozoic Fracturing of Eastern North American Crust—Product of Extension or Shear? 241 Chapter Highlights 245 Questions 245 Further Reading 245 10 Faults and Shear Zones 247 Fault Anatomy 248 Anderson’s Classification 250 Recognizing Faults 252 ESSAY: Seismic Risk Associated with Tectonic Structures 254 Shear Zones 255 Shear-Sense Indicators 256 Composite Foliations 260 Strain in Ductile Shear Zones 260 Brittle Shear Zones 263 ESSAY: Existence and Displacement Sense of Large Faults 264 Chapter Highlights 267 Questions 267 Further Reading 268 11 Fault Mechanics 269 Anderson’s Mechanics and Fundamental Assumptions 270 Anderson’s Fault Types 271 Type 1. Thrust Faults 271 Type 2. Strike-Slip Faults 271 Type 3. Normal Faults 271 Role of Fluids 273 Frictional Sliding Mechanisms 274 Movement Mechanisms 274 Fault Surfaces and Frictional Sliding 275 Shear (Frictional) Heating In Fault Zones 276 Reality of Fault Mechanics 278 ESSAY: Artificial Earthquakes 280 Chapter Highlights 281 Questions 282 Further Reading 282 Contents 12 Thrust Faults 283 Nature of Thrust Faults 284 Detachment Within a Sedimentary Sequence 286 Propagation and Termination of Thrusts 290 Features Produced by Erosion 293 ESSAY: Debate About Thrust Faults 295 Crystalline Thrusts 301 ESSAY: Gravity Model Foldbelt 303 Cross-Section Construction and the Room Problem 305 Thrust Mechanics 308 Mechanics of Crystalline Thrusts 311 Chapter Highlights 312 Questions 313 Further Reading 313 13 Strike-Slip Faults 315 Properties and Geometry 315 Tectonic Setting of Strike-Slip Faulting 319 Geometry Related to Other Fault Types 319 Terminations of Strike-Slip Faults 321 Releasing and Restraining Bends 324 Transtension and Transpression 324 Transforms 325 Mechanics of Strike-Slip Faulting 326 ESSAY: Rigid Indenters and Escape Tectonics 326 Chapter Highlights 329 Questions 329 Further Reading 329 14 Normal Faults 331 Properties and Geometry 332 Environments and Mechanics 336 Growth Faults 337 Rift Zones 343 Regional Crustal Extension 343 Hyperextension of Continental Crust and Mantle Oceanic Core Complexes 348 Collapse Structures and Related Features 349 Relationship to Strike-Slip Faults 349 Final Thoughts 349 347 ESSAY: Inverted Faults and Tectonic Inheritance 350 Chapter Highlights 353 Questions 353 Further Reading 353 xiii xiv Contents PART 4 Folds and Folding 355 15 Anatomy of Folds 356 Descriptive Anatomy of Folds 357 Fold Anatomy 357 Kinds of Folds 359 Fold Shape 364 Use of Parasitic Folds in Determining Position in a Fold 366 ESSAY: Gravity–Driven Soft-Sediment Folds and Faults 368 Folds at Map and Cross Section Scale 370 Fold Classifications 373 Ramsay’s Classification 374 Donath and Parker Classification 374 Which Classification to Use? 378 ESSAY: Folds and the Development of the Petroleum Industry 378 Chapter Highlights 379 Questions 380 Further Reading 380 16 Fold Mechanics 381 Fold Mechanisms and Accompanying Phenomena 382 Bending 383 Buckling 384 Flexural Slip 389 Parallel and Similar Folds 389 Passive Slip—A Problematical Mechanism 390 Kink Folding 390 Flexural Flow 394 Passive Flow (Passive Amplification) 394 Combined Mechanisms 395 Deformation Mechanisms and Strain 396 Discussion 400 Nucleation and Growth of Folds 400 ESSAY: A Tale of Two Folds: Deciphering the Fold Mechanisms of Two Small Folds 403 Chapter Highlights 406 Questions 406 Further Reading 407 17 Complex Folds 408 Occurrence and Recognition 409 Superposed Folds and Fold Interference Patterns 409 Type 0 410 Type 1 411 Type 2 411 Type 3 412 Modifications 412 Recognition of Multiple Fold Phases 412 Noncylindrical and Sheath Folds 414 Contents Formation of Complex Folds 418 Mechanical Implications of Complex Folding 418 ESSAY: The Value of Rosetta Stones 422 Chapter Highlights 424 Questions 424 Further Reading 425 PART 5 Fabrics and Structural Analysis 427 18 Cleavage and Foliations 428 Definitions 428 Cleavage-Bedding Relationships 438 Cleavage Refraction 439 Mechanics of Slaty Cleavage Formation 441 ESSAY: Early Ideas on the Origin of Slaty Cleavage 441 Progressive Cleavage Development in Fine-Grained Sediment 443 Strain and Formation of Slaty Cleavage 447 Crenulation Cleavage 449 Cleavage Fans and Transecting Cleavages 449 Transposition 451 ESSAY: Cleavage Formation and the Identification of Elephants 455 Chapter Highlights 456 Questions 456 Further Reading 457 19 Linear Structures 458 Definitions 458 Nonpenetrative Linear Structures 458 Penetrative Linear Structures 460 Boudinage 464 Lineations as Flow and Transport Indicators 464 Folds and Lineations 465 Folded Lineations 466 Interpretation of Linear Structures 468 ESSAY: Pitfalls in Interpreting Linear Structures 469 Chapter Highlights 471 Questions 471 Further Reading 472 20 Structural Geology of Plutons 473 The Nature of Magma 475 Distinguishing Magmatic from Solid-State Tectonic Structures 475 The Enigma of Tabular Pluton Emplacement 477 xv xvi Contents Emplacement of Stocks and Batholiths 484 ESSAY: A Tale of Two Plutons 494 Chapter Highlights 498 Questions 499 Further Reading 499 21 Structural Analysis 501 Cross-Section Analysis 502 Deformation Plan in an Orogen 502 Structural Analysis Procedures 505 Geologic Mapping 505 Mesoscopic Structural Analysis 506 Domain Analysis 507 Microtextural Studies 507 Finite- and Incremental-Strain Studies 509 Fracture Analysis 509 Chronology of Development of Structures 510 Structural Analysis in Foreland Fold-Thrust Belts (FFTBs) 510 Structural Analysis of Multiply Deformed Rocks in the Cores of Orogens 512 ESSAY: Historical Development of Structural Analysis Methods in Metamorphic Rocks 516 Structural Analysis of Multiply Deformed and Transposed Rocks 517 Pitfalls in Using Style and Orientation in Polyphase-Deformed Rocks ESSAY: Structural Analysis at Woodall Shoals 518 Analysis of Salt Structures 524 Structural Analysis in Continental Interiors 531 Structural Analysis in Seismically Active Regions—Insight into Paleoseismology 532 Background 532 Structural Analysis of the Lima Reservoir Fault Chapter Highlights 537 Questions 537 Further Reading 538 PART 6 532 Appendices Appendix 1: Structural Measurements and Observations 540 Directional Reference Frame and Location 540 Orientation of Planes: Strike and Dip 543 Orientation of Lines: Trend and Plunge; Rake 544 Recording Data 546 517 Contents Appendix 2: Stereographic Projections and Fabric Diagrams 549 How to Begin Plotting Manually 551 Plotting Planar Structures 552 Plotting Linear Structures 553 Locating Fold Axes Using Equal-Area Plots: β and π Diagrams 554 β Diagrams 554 π Diagrams 554 Contouring Data 554 Appendix 3: Structural Cross Sections—Methods for Cross-Section Construction 558 Introduction 558 Rules of Cross-Section Construction 560 1. Surface Topography 560 2. Transferring Geologic Contacts from Map to the Section 561 3. Transfer of Dip Orientations from the Geologic Map to the Cross Section 561 4. Maintaining Constant Thickness 562 5. Thickness of Rock Units Related to Dip Angle 562 6. Vertical Exaggeration and Scale 562 7. Section Location and Map Name 562 8. Explanation of Rock Unit Symbols 562 9. Use of and Projection of Data from the Section Line 562 10. Calculation of Dip of All Contacts from Outcrop Patterns 564 Editorial Tips for Constructing Cross Sections 564 Taking Cross Sections to the Next Level—Cross-Section Balancing 566 Introduction 566 Balanced Section Construction Limitations 567 567 Appendix 4: Woodall Shoals Fabric Data Glossary 576 References Cited Index 619 597 569 xvii Preface to the Third Edition The third edition of Structural Geology: Principles, Concepts, and Problems is a complete revision from the first two editions. Each chapter has been rewritten with many new figures and color added to numerous illustrations throughout the book. We have added a new chapter on geochronology, and the 3rd edition integrates many new and exciting developments in structural geology and tectonics from the past two decades. Chuck Bailey joined as co-author; this will be evident in chapters where his expertise has had a major impact on improvement of the technical quality, but also on the overall quality of the book. Our numerous meetings, e-mail, and phone conversations proved especially valuable in that they enabled us to work through issues that arose and helped with incorporation of review comments. We feel, however, that the basic thread woven through the first two editions has carried into the third: to present a balanced coverage of all topics in modern structural geology at a level appropriate for students in junior-senior-level structural geology courses offered today in most geology programs in North America. To the Users of This Book The arrangement of chapters in the book follows the same outline as previous editions, with no major organizational changes. One thing that may be noticeable is that much of the discussion of the historical basis of concepts and ideas has been moved to essays. This permits students who are interested in the historical development of structural geology to explore further, but it does not interrupt the overall flow of chapters. One of the pedagogical tenets we have followed in this and previous editions is including more information in each chapter than can be covered in one or two class periods. This makes the book both a text and a reference document, which we consider a positive attribute of our book. Another is the use of different letter styles throughout the book for terms we consider to be most important for students to remember (in bold italic), important but not imperative to be learned (in italic), or for information only (regular type). The Glossary at the end of the book contains all of the first two categories and many of the last. The 21 chapters are arranged in five parts. The introductory section is intended for review and to present information not usually included in structural geology texts. One of our goals was to provide an initial section of four chapters that reviews basic concepts, and presents two topics rarely covered in the courses most students have taken before taking structural geology: geochronology and geophysics. These two chapters are not intended to be exhaustive summaries of these subjects, but to present a basic understanding of geochronology and geophysics that bears on the subject of structural geology. They are intended to form an integral part of understanding the basis of processes related to rock deformation, timing of deformation, and geometry of structures. A section introducing down-hole geophysics was included in the geophysics chapter, because so many students receive bachelors and masters degrees and then become employed in the engineering/environmental, seismic hazard assessment, and petroleum industries where down-hole geophysical data are commonly utilized. The four introductory chapters can be presented as an integral part of the course, or assigned as collateral reading. We feel that they belong at the front of the book so they can be covered—or xviii Preface to the Third Edition not—at the beginning of the course to review existing concepts like plate tectonics and nontectonic structures, then introduce the basis of radiometric age determinations and the principal topics from geophysics that are useful in structural geology—and afterward move on to the basic subject matter of structural geology. The section on mechanics introduces stress, strain, material behavior, and microstructures. In discussing the order of presentation in this section, we feel that the presentation of strain should follow the discussion of stress, recognizing that some structural geologists advocate presenting strain early with stress toward the end of the course. Our feeling is that these subjects belong together early in the course, and should be covered sequentially with stress first. The chapters on stress, strain, and material behavior present some of the topics found in the basic strength of materials courses in engineering curricula—with a geologic bias—and with less mathematics. The microstructures chapter provides an introduction to deformation processes that occur on a micro-scale. It lays a foundation for presentation of microstructures later in the book. The section dealing with fractures and faults begins by introducing the most pervasive geologic structures on the Earth’s surface: joints. This is followed by a chapter describing the basic properties of faults and shear zones, and introduces shear-sense indicators that permit us to determine the movement sense on a fault at the outcrop- or micro-scale. It also emphasizes that not all faults are simple brittle structures confined to the upper crust, but may be broad, ductile shear zones that form along faults in the deep crust. The chapter on fault mechanics presents the mechanical basis for faulting. The following three chapters discuss the three primary fault types and their nature in greater detail. The section on folds and folding contains three chapters: a chapter dealing with the fundamental properties of folds, another dealing with fold mechanics, and a third deals with complex folds. This section also serves to bring out the fact that folds are not all ductile structures as frequently presented—they form in the brittle realm as well. The last section in the text dealing with rock fabrics and structural analysis contains four chapters. The chapter on cleavage and foliations introduces the most common planar structure in metamorphic rocks, and discusses the mechanics of how these structures form. The chapter on lineations (not lineaments) discusses the different kinds of linear structures in rocks. The chapter on structures in plutons discusses the wide variety of plutons and their associated structures. The structural analysis chapter outlines various ways to analyze geologic structures that can be brought to bear for structures that formed at different scales in different geologic environments. It involves integration of different techniques and many of the structures discussed in earlier chapters. Our wish beginning with the first edition remains the same: as teachers, we want students to enjoy their structural geology course. Earth’s structures and the tectonic processes that form them are both important and intriguing. We view the world around us with a sense of wonder, and hope this book provides a scientific framework to help understand it. The learning process need not be difficult or painful, but it should be challenging and can be approached as a game: the rules of the game should be spelled out by your instructor at the beginning of the course. The degree to which your instructor becomes involved in the course from the beginning largely determines the quality of the course and how much students derive from it. The text chosen helps to determine the level at which the course is taught and the kinds of material to be covered. The balanced coverage in this text is intended to enhance the involvement of both students and instructors in structural geology. Finally, we hope this book will kindle the interests of students who use it and some will choose to become structural geologists—a measure of success for any structural geology course. xix Acknowledgments The late Nancy L. Meadows, in the Tectonics and Structural Geology Research Group at the University of Tennessee, played a critical role in quality control of pre-publisher editing and proofing chapters, checking references, compiling the glossary and references, and, in the first two editions, constructing and checking the indexes. We are eternally grateful for her longterm contributions to the quality of this book. Andrew L. Wunderlich, also in our research group, made a major contribution to this third edition by providing outstanding graphics and ArcGIS support, constructing preliminary layouts of each chapter and appendices in InDesign prior to review, compiling the spreadsheet with old and new glossary terms, and conducting the final check of references against the text. Rebecca J. Christ did some editing and particularly compiled a massive spreadsheet containing the information on permissions for figures. The Science Alliance Center of Excellence at the University of Tennessee has provided both salary and stipend support for RDH (and many graduate and undergraduate students) for the past three-plus decades. This has permitted travel to many places, particularly mountain chains and continental shields, which would have otherwise been inaccessible, to better understand the structure and evolution of continental crust. Many of the photos published in this textbook could not have been made without this support. We have benefitted from the many outstanding undergraduate and graduate research students that we’ve worked with during the past several decades. These students enabled us to become better structural geologists, and challenged us to provide cogent explanations of sometime complex mechanics and processes. They also have encouraged us to learn along with them, so that we benefitted from their questions and persistence to understand our subject. Both of us have led and participated in numerous field trips where professionals and students are presented with possible solutions to complex structures and tectonic histories. Many times, the additional sets of eyes have pointed out critical—previously unseen—features that facilitated the understanding of the structural and tectonic histories of poorly known areas. Gilles Allard (University of Georgia, Emeritus) kindly provided contact with Réal Daigneault (Québec Geological Survey and Université du Québec à Chicoutimi), who gave us two illustrations for Chapter 6. Rick Law (Virginia Tech) patiently listened to and answered numerous questions about quartz deformation by RDH and contributed an illustration that was incorporated into Chapter 8. We are grateful to former University of Tennessee undergrad and M.S. student Ching Tu (Schlumberger Corp.), and Walter Wunderlich (TVA design engineer, retired), who offered useful improvements to some of the mathematics in Chapter 5. Our third edition has benefited enormously from constructive reviews of chapters commissioned by Oxford University Press. A few of the reviewers disagreed with our pedagogical philosophy, but their comments were constructive and quite useful in improving our book. These reviewers are: two anonymous reviewers, Joseph Allen (Concord University), Andy Bobyarchick (University of North Carolina–Charlotte), Maria Brunhart-Lupo (Colorado School of Mines), Gabriele Casale (Appalachian State University), Robert Cicerone (Bridgewater State University), Randy Cox (University of Memphis), Anna Crowell (University of North Dakota), Ernest Duebendorfer (Northern Arizona University), Eric Ferré (Southern Illinois University), Mary Hubbard (Montana State University), Kristin Huysken (Indiana University Northwest), Jamie Levine (Appalachian State University), Ryan Mathur (Juniata College), Melanie Michalak (Humboldt State University), Devon Orme (Montana State University), Terry Panhorst (University of Mississippi), Mitchell Scharman (Marshall University), xx Acknowledgments Christian Schrader (Bowdoin College), John Singleton (Colorado State University), Jaime Toro (West Virginia University), Frederick Vollmer (SUNY–New Paltz), David West (Middlebury College), Paul Wetmore (University of South Florida), Laura Wetzel (Eckerd College), Michael Williams (University of Massachusetts), and Martin Wong (Colgate University). Earlier constructive reviews of third-edition chapters commissioned by Pearson/Prentice Hall were also beneficial in the evolution of this edition of our book, and are much a ppreciated. These reviewers are: Jeffrey Amato (New Mexico State University), Cynthia Coron (Southern Connecticut State University), David Foster (University of Florida), Ron Harris (Brigham Young University), Eric Horsman (East Carolina University), Eric Jerde (Morehead State University), Paul Karabinos (Williams College), and John Weber (Grand Valley State University). We also express our deep appreciation to our most recent Pearson/Prentice Hall editor Andrew Dunaway and our Oxford editors, Dan Kaveny and Dan Sayre, for their encouragement and enthusiastic support of our efforts to complete the third edition of this textbook. Bob Hatcher Chuck Bailey xxi PART 1 Introduction OUTLINE 2 1 Introduction 2 Fundamental Concepts and Nontectonic Structures 3 Geochronology in Structural Geology 44 4 Geophysical Techniques and Earth Structure 65 19 1 Introduction 15° LT A stone, when it is examined, will be P of continents and ocean basins, the linearity of For centuries the shapes er u mountain ranges, the distribution of volcanoes, and the cause of earth– C (Figure 1–1). Today we know that most of quakes have fascinated humans these features are produced by deep-seated processes operating since the Earth formed; these processes have shaped both past and present configurations of tectonic plates (Figure 1–2). The effects of earthquake and volcanic activity are constant reminders that the Earth is a dynamic planet and that tectonic plates PACIFIC are driven by awesome forces. Most of Earth’s human OCEAN population is influenced by tectonic activity; unfortunately, earthquakes and volcanic eruptions threaten many people (Figure 1–1). A found a mountain in miniature. h l t ile i p o Trench l a n JOHN RUSKIN, 1858, Modern Painters 500 0 25° S kilometers 60° W 72° W (a) PERU 15° 15° P P LT – PARAGUAY o 72° W Trench kilometers 60° W l a n ile o 500 0 25° S i p h l a n PACIFIC OCEAN Holocene volcano l t i p Trench PACIFIC OCEAN BOLIVIA LT ru C l t ile C h – e A u A er Earthquake focal depth (km) 0 – 70 71 – 150 151 – 300 301 – 500 >501 CHILE ARGENTINA 0 25° S 72° W 500 kilometers 60° W (b) (a) Earthquake focal PERU FIGURE 1–1 (a) Shaded relief map of part of western South America. The Andes Mountains stand out in strong relief. As the Nazca Plate is depth (km) A subducted along the Peru-Chile Trench, South America undergoes crustal thickening, uplift, and volcanism. The Altiplano is a high plateau 0 – 70 15° – 150 created from Shuttle Radar Topography Mission [SRTM] image PIA03388.) with an average elevation LT over 3,300 m. LT—Lake Titicaca.71(Map BOLIVIA 151 – 300 P (b) Locations 1973 and distribution of Holocene volcanoes. Notice that earthquake focal e and focal depths of earthquakes (Mw ≥ 6) since 301 – 500 ru depths generally increase with distance inland from the Peru-Chile Trench. (Data from U.S. Geological Survey National Earthquake Informa>501 – the Smithsonian Institution’s Global Volcanism Program.) tion Center and Holocene l t C T l a n ile i p h 2 volcano Introduction Eurasian Plate North American Plate Juan de Fuca Plate Australian Plate Antarctic Plate Eurasian Plate Iranian Plate Caribbean Plate San Andreas fault Philippine Sea Plate Arabian Plate Cocos Plate Pacific Plate 3 | Nazca Plate South American Plate African Plate Antarctic Plate (a) Elevation (meters) 8,000 5,000 3,000 1,000 500 250 100 0 –1,500 –3,000 –4,000 –5,000 –6,000 –10,000 (b) FIGURE 1–2 (a) Names and distribution of Earth’s tectonic plates. Arrows indicate plate motion direction, and length of arrows indicate rate of motion. (U.S. Geological Survey.) (b) Shaded relief map of continents and ocean basins illustrating their relationship to plates and plate boundaries. Relief map generated from U.S. Geological Survey Global 30 Arc-Second Elevation (GTOPO30) and Intergovernmental Oceanographic Commission/International Hydrographic Organization General Bathymetric Chart of the Oceans (GEBCO) digital elevation models. 4 | Introduction Aside from the imminent danger and practical need to comprehend and mitigate the dangers associated with these hazards, most geologists feel a basic scientific urge to understand these processes. Structural geologists are concerned with deformation of rocks and why parts of the Earth’s crust are bent into smoothly curved shapes— producing folds—but others, sometimes in the same regions, are broken by faults. We also want to understand both the processes that produce structures and the history of how the structures formed. The opening quote by Ruskin is applicable to the structural geologist as we consider the nature and origin of structures from regional scale down to grain scale. Structural geology is the study of rock deformation. It considers the geometry, dynamics, kinematics, and mechanics of earth structures and has great relevance to society and the world economy. It is readily applied to engineering problems that involve the foundations of bridges, dams, buildings, and power plants where large excavations are necessary, as well as highways where excavations extend for long distances. Studies of geologic structures beneath buildings, dams, and highway cuts are of great importance because of the potential for renewed motion along faults and other fractures, as well as concern for the stability of slopes and geologic materials. Siting large engineered structures in active fault zones, like the U.S. West Coast, is not desirable, but sometimes it is impossible to build them in tectonically quiet areas. Therefore, geologists and engineers must work together from the design stage through construction to evaluate which structures are still active and might affect engineering works, as well as to minimize cost. Environmental problems and land-use planning—such as earthquake hazards, waste isolation and disposal, and controls on the distribution of ground water—provide additional applicability for structural geology. Documenting the antiquity or recent movement of faults is an important aspect that requires understanding of structural geology. Location of sites for disposal of municipal, industrial, and radioactive waste requires application of structural and tectonic principles. Understanding the controls of large structures, such as folded layers of permeable and impermeable rocks that contain ground water, and small structures, such as fractures, on the distribution of ground water provides additional applications for this discipline. The proposed (now shelved) Yucca Mountain Repository in southern Nevada (Figure 1–3) is a controversial underground storage facility intended to safely house the United States’ spent nuclear fuel and radioactive waste for at least 25,000 years. Over the past two decades the structural geology, mechanical characteristics, seismic history, and ground water flow paths were extensively studied in order to characterize the (b) (a) WEST 5,000 FIGURE 1–3 (a) Oblique aerial view to feet above sea level the south of Yucca Mountain crest showing coring activities. (b) Oblique aerial view of the south portal into Yucca Mountain; note 25 ft diameter tunnel boring machine. (a and b 3,000 retrieved from University of North Texas Web Archive, http://www.ymp.gov.) (c) Geologic cross section through Yucca Mountain illustrating gently tilted volcanic rocks cut 1,000 by a series of steeply dipping normal faults. (c) (Modified from Day et al., 1998.) Yucca Crest EAST Repository tunnel Topopah Spring Tuff Introduction site; key questions include recurrence interval and magnitude of seismic and volcanic activity, and permeability associated with fractures in the volcanic bedrock. Structural geology has long had a close working relationship with petroleum and mining geology. The ability to project fault surfaces, geologic contacts, and other structures to depth is used to great advantage by geologists who explore for valuable minerals and petroleum. Tectonic principles have been applied to understanding larger trends and regional processes that control the concentration of mineral deposits and hydrocarbons. Structural geology considers the geometry, dynamics, kinematics, and mechanics of earth structures. Geometry refers to the shape and orientation of structures on any scale. A first-order, and non-trivial, task for structural geologists is to accurately describe the geometry of Earth structures. Geometric understanding occurs over a wide range of scales, from field mapping of regional-scale structures to measuring the orientation of crystal axes in individual mineral grains under the microscope. Dynamics deals with the study of motion of bodies in response to forces that produced the motion. In contrast, kinematics deals with the motion of materials independent of the forces that caused the motion. Rock masses can be uplifted from great depths in the crust, rotated between fault blocks, and translated hundreds to thousands of kilometers from their place of origin. Rock structures provide important kinematic clues, and this evidence is observable over a wide range of scales. Mechanics focuses on the effects of forces or stresses on materials. Understanding the geometry and mechanical properties of a rock mass provides information related to how it will behave when put under stress. It is important to remember that we typically study structures after they form, frequently millions to billions of years later; thus we must infer the nature and magnitude of forces that affected the rocks as well as the physical conditions (pressure, temperature, fluid content) present when the structures formed. Some structural geologists conduct experiments deforming rocks under controlled conditions in the laboratory; this mechanical understanding is valuable for interpreting natural structures. Structural geology is similar to architecture in that both disciplines require an ability to visualize objects in three dimensions. Visualizing objects in three dimensions can be difficult. Perhaps begin by thinking about familiar objects such as the room where you live, the decorations on the wall, and the locations of furniture; and then move on to less familiar geologic structures (Figure 1–4). Keep in mind that most of us also had difficulty with 3-D visualization when we began studying structural geology, but learning to visualize objects in three dimensions comes through practice. The shapes of geologic structures change through time, along with the physical conditions that formed them. In particular, the contrast in shape and type | 5 (a) (b) FIGURE 1–4 Structures are three-dimensional. Consider the famed Sydney Opera House (a) and its distinctive shell roof, and then think about the shapes of folds such as the Sheep Mountain anticline in Wyoming (b). This oblique aerial view (U.S. Department of Agriculture) nicely illustrates the three-dimensionality of the anticline. It is cored with Precambrian crystalline rocks and flanked by Paleozoic and Mesozoic sedimentary rocks of differing resistance to erosion that hold up flanking ridges and underlie valleys. Note the small folds in the lower left-hand part of the photo that mimic the shape of the main fold. between structures formed near the Earth’s surface and those formed at great depth under the weight of overlying rocks and at high temperatures indicates profound differences in physical conditions. As the elevation of a mountain range is reduced by erosion, physical conditions affecting the crust change both near the surface and at depth. An appreciation of structural geometry thus permits us to make better interpretations of kinematics and mechanics, and ultimately of the origins of earth structures. Tectonic structures are produced in response to stresses generated, for the most part, by plate motion within the Earth, and include faults and folds, along with other structures. They make up the tectonic framework of the Earth. 6 | Introduction (a) (b) FIGURE 1–5 Continuous (ductile) and discontinuous brittle structures in rocks. (a) Folded gneissic layering produced by ductile flow in metasedimentary rocks along Long Island Sound near Lyme, Connecticut. (b) Brittle deformation produced several sets of fractures in Precambrian metasedimentary rocks near Central City, Colorado. Scale is indicated by 3 to 5 m tall trees in foreground. (RDH photos.) The kinds of structures that form in different parts of the crust are determined by: (1) prevailing temperature and pressure; (2) rock composition; (3) the nature of layering; (4) contrast in properties with direction between and within individual layers (anisotropy) or the lack of contrast (isotropy); and (5) amount and character of fluids within the rock mass. How rapidly the mass is deformed and the orientations of stresses applied to it also influence the kinds of structures produced. These factors determine whether deformation will be continuous (ductile deformation) or discontinuous (brittle deformation), producing a great variety of structures both in the Earth and on other planets (Figure 1–5). Structures may also form as products of nontectonic processes, such as extraterrestrial impacts, landslides, and other features formed by gravity. It is useful to distinguish between tectonic and nontectonic structures (Chapter 2), because some nontectonic structures closely resemble— even mimic—structures formed by tectonic processes. Much knowledge about geologic structures is derived from observing and attempting to understand structures in the field; thus, one of our goals is to improve our abilities to recognize, describe, measure, and interpret both subtle and obvious geologic structures in rocks. Also, a better understanding of physical and chemical principles and the ability to use mathematics and computers are needed to bridge the gaps between field, laboratory, and theoretical studies. The link between field and laboratory studies is both essential and supportive, for structural geology is divisible into subdisciplines of scale, structures, and processes, most of which overlap in geologic time. For example, laboratory studies determining fluid pressure that facilitates movement on faults are supported by field observations of evidence that fluid was present when a fault was active. The study of field relationships is an exceptionally important aspect of structural geology because it provides limitations for formulating kinematic and mechanical models. In structural geology, we try to understand how small structures form and how they are related to larger structures and, ultimately, to crustal deformation and plate tectonics. A geologist undertaking a field-based structural study may: (1) make accurate geologic maps and cross sections of the structural geometry; (2) measure orientations of small structures to provide information about the shapes and relative positions of larger structures in the field; (3) study the overprinting sequence of structures to determine the variation in deformation conditions through time; (4) use these structures to understand the kinematic history; and (5) apply rock-mechanics principles and data to relate structures to forces that were present in the Earth during deformation. These different components will not be completed at the same time or in the sequence listed here. Today there are many tools available to structural geologists that improve our work in the field. The Global Positioning System (GPS) permits the precise geolocation of structural data and samples. Software on “smart” phones and tablet computers facilitates recording, viewing, and manipulating data in the field, and some feature compasses and clinometers that make accurate strike and dip measurements (Appendix 2). Rock mechanics is the application of physics to the study of rock materials. It deals with rock properties and the relationships between forces and resulting structures, as well as with the study of structures produced in the laboratory in an attempt to duplicate natural structures (Figure 1–6). In the laboratory, we can simulate the higher temperatures and pressures that exist at great depths. A lternatively, very weak materials such as salt, gelatin, clay, putty, and paraffin, which behave like rocks being deformed at higher temperatures, may be used to produce experimental structures at room temperature. A disadvantage of laboratory experiments is that they cannot be run | Introduction 7 0 1 centimeter FIGURE 1–6 Experimental structures made in a centrifuge from viscous materials of different densities and fluid properties. Compare the shapes of these structures at this scale with those in Figures 15–18, 15–28, 16–2, 16–9, 16–21, 16E–1, and 17–14a. (From Tectonophysics, v. 19, H. Ramberg and H. Sjöström, p. 105–132, Fig. 15, © 1973, with kind permission from Elsevier Science, Ltd., Kidlington, United Kingdom.) over geologic time—thousands to millions of years. They must be run on rocks and minerals at temperatures and pressures far above those normally occurring in nature so that deformation rates will occur rapidly enough that the person conducting the experiment will live to see the results! Artificial or natural materials deformed at reasonable rates that simulate the behavior of rocks must be scaled up to approximate natural processes. Tectonics and regional structural geology involve larger features. Studies of mountain ranges, parts of continents, trenches and island arcs, oceanic ridges, entire continents and ocean basins, and their relationships to stresses and tectonic plates are included in these subdisciplines. Plate tectonics deals specifically with plate generation, motion, and interactions. Separating tectonics from regional structural geology is difficult. Regional structural geology is more commonly concerned with continental structures or well-imaged parts of the ocean floor and uses data from detailed studies of small structures to reconstruct the deformational history and tectonics of a region. Moreover, geophysical data (Chapter 4) and information derived from other disciplines of geology must be integrated with structural data for use in regional structural geology and tectonics. Use of geophysical data in structural geology is more common now because technology has made available more data of higher quality, especially seismic reflection, magnetic, and gravity data. It is easy to see that the many subdivisions of structural geology are related to other disciplines in geology as well as to the other sciences. Direct applications are made from physics to study the origin of geologic structures. Isotopic data are frequently useful in working out the absolute timing of deformation, and geochemical data may help to determine mobility of fluids and elements during deformation. The chemical composition of highly deformed rocks may indicate the original material (protolith) and the environment before deformation. As mentioned earlier, the concept of scale is of great importance in structural geology. Structures—such as geologic contacts, foliations, faults, and folds—are commonly observed in the field in both hand specimen and at outcrop (or mesoscopic) scale. Microscopic structures require magnification to be observed, and include many foliations and linear structures. Mountainside to map-scale structures are called macroscopic structures. Scales and geometric perspectives of geologic cross sections must be maintained between the map from which the section is constructed and the section itself (Figure 1–7). Plate Tectonics Plate tectonics is the framework within which all tectonic structures form. This paradigm is as fundamental to the Earth sciences as atomic theory is to physics and chemistry and as evolution is to biology. Early formulation of the theory is attributed to Harry Hess, who during the 1930s conceived the tectogene concept of the subsiding crumpling crust driven by mantle convection. Isacks et al. (1968) first published a unified theory of plate tectonics. According to the principle of plate tectonics, new oceanic crust formed at the oceanic ridges ultimately is consumed by subduction in oceanic trenches (Figure 1–8). While this process can recycle all ocean crust in ~200 m.y., continental crust has a pivotal role in recording geologic events in the 4.5 Ga history of Earth. The present surface of the Earth is divisible into seven major plates and several smaller plates (Figure 1–2). The thickness of plates corresponds to that of the lithosphere, which is on average about 100 km thick and includes all of the crust and part of the upper mantle (Figure 1–8). The lithosphere is conveyed above a weaker, more plastic layer in the mantle known as the asthenosphere (Figure 1–9). Geophysical evidence demonstrates that the asthenosphere is a solid, but it is sufficiently weak so it flows over geologic time. Gravitational processes and convection in the mantle drive plate generation and consumption. There are three basic configurations of plate boundaries: (1) divergent (ocean ridges); (2) convergent (subduction zones); and (3) transform. 8 | Introduction FIGURE 1–7 Hypothetical geologic map (a) and cross section (b) illustrating macroscopic structures and relationships. Note that constructing an accurate cross section requires close attention to scale, strike, and dip of bedding (Appendix 1), and position of geologic contacts on the topographic surface. The symbols On, Oa, Ol, and so on identify each rock unit by its age (O—Ordovician, –C—Cambrian, p –C—Precambrian), and the name of each rock unit, e.g., On—Newala Formation. See inside front cover for explanation of dip-strike symbols. A Cp 46 51 39 37 Ol 48 41 41 45 Oc 34 62 49 36 Oa 43 40 38 58 42 42 46 Oc 68 47 71 Ol 52 73 63 Cp 69 On 43 67 76 Oa 57 74 67 74 Ol Cs Oc 66 59 64 62 63 57 58 77 55 61 Cn Cp 41 63 59 59 57 42 48 63 62 0 47 p Ci Ch 66 N 41 200 400 600 800 Cn 1000 meters 38 36 32 A' Cs contours contours in meters meters (a) A A' 1,100 1,100 900 800 Cp 700 600 500 (b) On Cs Oc Cn Ch Cs Cn Oa Ol Oc Cn Cp Cs No vertical exaggeration The kinematics of plate motion may be described using an Eulerian theorem that represents the motion of plates on a sphere, in which displacement on the surface increases away from a rotational axis (Euler pole). Angular displacement of a plate involves rotation about the Euler Cn Ch p Ci Cs 1,000 900 800 700 meters meters 1,000 600 500 pole, an imaginary line passing through the center of the Earth, and rotation of a plate about this axis is expressed by its angular velocity (ω) on the sphere (Figure 1–10a). Although the velocity increases away from the pole of the spreading axis, the angular velocity remains constant. Introduction LITHOSPHERE LITHOSPHERE A S T H E N O S P H E R E M E S O S P H E R E FIGURE 1–8 Generation of lithospheric plates at spreading centers (oceanic ridges) and destruction in subduction zones—a simple statement of plate tectonics theory. Differences in rate of motion or displacement between plates are taken up by transforms connecting segments of ridges, trenches, and other boundaries. Arrows indicate motion direction. Ocean crust is colored purple. (From Isacks et al., Seismology and the new global tectonics: Journal of Geophysical Research, v. 78, p. 5855–5899, © 1968 by the American Geophysical Union.) Each plate has an angular velocity on the sphere (determined by the absolute motion and its position relative to the pole) with respect to other plates. Differences in movement rate between plates are balanced by transform faults (Figure 1–10b). Plate boundaries where three plates meet are called triple junctions (Figure 1–10c) and they connect ridge, trench, transform segments, or various combinations of the three boundaries. Dewey and Bird (1970) outlined a model for the development of mountain chains as a result of either subduction | 9 (Cordilleran mountain chains—Andes, North American Cordillera) or continent-continent or continent-arc collision (collisional mountain chains—Alps, Appalachians, Himalayas). Generation of mountain chains is complex, and most collisional orogenic belts also had an earlier history of subduction. Wilson (1966) suggested that a proto-Atlantic Ocean had closed at the end of the Paleozoic, producing the Appalachian–Variscan mountain chain of North America and Europe, making up the supercontinent of Pangea, and then had reopened to form the present Atlantic. This cyclical closing and opening of ocean basins has become known as the Wilson cycle (supercontinent cycle). Another plate tectonic corollary is that of accretionary tectonics, whereby suspect and exotic terranes are moved by plate motion to collision with each other or with continents. A suspect terrane is a rock mass whose original position is questionable with respect to adjacent terranes or the continent to which it is presently attached. An exotic terrane bears no resemblance to the mass to which it is attached and may have originated on the opposite side of a major ocean. Hamilton’s (1979) compilation of the geology of the Indonesian region demonstrates that a complex of volcanic arcs, continental fragments, oceanic crust, and large continental blocks (such as Australia) are all in the initial stages of being accreted to Asia as Australia moves northward. The boundaries of suspect and exotic terranes with surrounding terranes are always faults. Overlap sequences, deformational and metamorphic overprints, and Volcanic hot spot 0–660 km Convection Upper man tle 1000 km Subducting slab 660–2890 km 2890–5150 km Lower mantle Outer core Inner core FIGURE 1–9 Plumes (red columns) that ascend through the mantle may originate in low-velocity zones near the outer core boundary in pools of material that could be partially melted or enriched in iron. They are strong and unbent by lower mantle convection—a sign that they are an important mechanism for releasing heat from the core (and driving convection in the upper mantle). Subducting slabs (black) plow downward into the mantle returning material to various depths. In addition, breakoff of descending slabs may produce rebound of the lithosphere and uplift of mountain chains above subduction zones. (From E. Hand, 2015, Science, Volume 349, Issue 6252.) 10 | Introduction Axis of rotation A' Angular velocity vector, ωAmAf B' A B 59° N 23° W N. America (fixed) Pole of rotation C D C' D' E' E (b) FIGURE 1–10 (a) Angular displacement of Africa with respect to North America predicted from the laws of spherical geometry. (From Hobbs, Means, and Williams, An Outline of Structural Geology, © 1976, John Wiley & Sons, Inc.) (b) Transforms at plate boundaries and within plates balance differences in displacement or relative motion. A–A’, B–B’, C–C’ . . . represent corresponding points on continents on opposite sides of the Atlantic. (From Wilson, reprinted by permission from Nature, v. 207, p. 343–347, © 1966, Macmillan Magazines, Ltd.) (c) Several kinds of triple junctions. (From McKenzie and Morgan, reprinted by permission from Nature, v. 224, p. 125–133, © 1969, Macmillan Magazines, Ltd.) 81 m.y. 155 m.y. (a) RRR A B TTF A C RRF B TTR A B TTR C C TTT A B TTT A B FFF A B TTF A B C C B A A B TTR A B C C (c) Trench (T) C Ridge (R) plutons that crosscut accretionary boundaries provide evidence of “docking” and frequently the timing of terrane accretion (Figure 1–11). Moreover, of interest to structural geologists is the deformation that occurs at and near plate boundaries. In addition to faults and folds, accretionary complexes ( deformed trench-fill sediments), block-in-matrix tectonic mélanges, and high-pressure mineral assemblages (e.g., blueschists) occur here. Plate boundary deformation can be very localized or extend for several kilometers into the plates on either side of the boundary. Plate kinematics from the Mesozoic to the present are well documented and largely based on sea-floor magnetic C C Transform fault (F) anomaly patterns, which are correlated to known geomagnetic reversal events. Further back in the geological record, paleomagnetism enables an estimate of the paleolatitude at which many igneous and sedimentary rocks formed, thereby providing critical data for paleogeographic reconstructions in the Paleozoic and Precambrian. At a more tangible human timescale, the motion of plates is being measured using satellite-based Global Positioning System (GPS) technology. GPS technology is in wide use for locating everything from ships and airplanes to hikers and automobiles. In order to make measurements precise enough to detect plate motion, GPS instruments must be capable of making measurements with an accuracy of a few mm. Introduction Terrane A Terrane B Overlap sequence (Terrane C) Continental crust A 0 1 kilometers Continental crust B | 11 FIGURE 1–11 Cross-sectional view of features provide critical information about when two terranes may have joined. Terrane A consists of continental crust with a sequence of flat-lying sedimentary rocks deposited on it. Terrane B consists of a different continental crust with a sequence of sedimentary rocks deposited on it that was folded before being joined to the other terrane. The green diabase dike later intruded both terranes before the overlap sequence of sedimentary rocks was deposited across both terranes. Knowing the ages of these rocks permits a structural geologist to decipher the tectonic history of two blocks of different continental crust with markedly different origins that are now joined along a terrane boundary. Terrane boundary (suture) Measuring plate motion requires sophisticated GPS receivers (Figure 1–12) that are carefully deployed at dedicated monuments over periods of several years, with the data transmitted by satellite to a central location. In addition, corrections must be made for seasonal variations in temperature, hydrologic conditions, and, in northern latitudes, glacial isostatic rebound. Once made and corrected, these measurements are very useful to help understand the present-day rates and kinematics of plate motion. Consider the GPS data from Auckland, New Zealand, illustrating the change in latitude, longitude, and elevation of the station over a 20-year period (Figure 1–13). These data demonstrate that Auckland had a northward movement component of over 800 mm during that time. When data from multiple stations are combined, a kinematic picture emerges of modern plate motion (Figure 1–14). Equilibrium FIGURE 1–12 EarthScope Project GPS station near Delta, Utah. This permanent battery-operated receiver station automatically records GPS measurements and communicates with the receiver facility. The GPS antenna is under the dome and the GPS receiver is located to the left. (EarthScope photo.) The Earth is a dynamic system. Energy from radioactive decay, the Earth’s gravity field, and residual primordial heat drive plate motion and other processes within the Earth. Heat converted to work moves plates, deforms rocks in the lithosphere, and produces melts and metamorphism. Any excess energy developed locally—say, at plate boundaries—must be dissipated to restore a state of rest, or equilibrium, to the part of the lithosphere where the excess develops. The balance may be restored by volcanic eruption, breaking the crust along a fault, plastic flow forming folds, or by other processes whereby heat is converted into mechanical energy. The second law of thermodynamics predicts that a certain amount of energy is never available to do work and will be lost in any energy- consuming p rocess, as long as the process is not 100 percent efficient. This amount of energy, called entropy, a measure Distance move Distance moved −300 −400 −400 −500 −500 −600 −600 −700 12 −800 −900 (a) | −700 Introduction −800 1998 2001 2004 2007 2010 2013 2016 Time (years) Latitude Longitude Distance Distancemoved moved(mm) (mm) −400 −40 −500 −60 −600 −80 −700 1998 1998 2001 2001 2004 2004 2007 2007 Time Time (years) (years) -1 Rate: Rate:39.632 39.632±± 0.091 0.091 mm mm yr yr–1 -1 Rate: Rate: 4.235 4.235 ±± 0.078 0.078 mm mm yr yr–1 2010 2013 2016 2010 2013 2016 20 −60 10 −80 0 −100 −10 70 2010 2013 2016 Time (years) Longitude 0 −20 −40 −60 −80 -1 Rate: Rate: 4.235 4.235 ±± 0.078 0.078 mm mm yr yr–1 −120 1998 (b) 2001 2004 2007 Time (years) 2010 2013 2016 Elevation FIGURE 1–13 GPS data from 1996 to mid-2016 for Auckland, 70 Longitude Elevation 50 −20 40 −40 30 (b) (c) 2007 −100 20 70 0 60 −20 −120 −30 2004 New60Zealand. (a) and (b) illustrate the lateral movement of the station; 50 (c) the vertical movement. Small blue dots represent the recorded position, with the black lines denoting recording error 40 bars.30Green lines indicate significant breaks. The graphs show a strong 20 northward and slight eastward movement over the 20-year period. 10 There is some variability in short-term (week to week) measurements, but the overall trends (red lines) are quite evident. 0 Data from Jet Propulsion Laboratory GPS Time Series website −10 (http://sideshow.jpl.nasa.gov/post/series.html). −20 –1 -1 Distance moved (mm) Distance Distance moved moved (mm) (mm) (a) (b) 2001 20 −300 −20 −800 −100 −900 −120 1998 (a) Distance moved (mm) 0 20 −100 0 −200 -1 Rate: Rate:39.632 39.632±± 0.091 0.091 mm mm yr yr–1 −900 -1 Rate: Rate:39.632 39.632±± 0.091 0.091 mm mm yr yr–1 1998 1998 2001 2001 2004 2007 2004 2007 Time (years) Time (years) Elevation -1 Rate: Rate: 4.235 4.235 ±± 0.078 0.078 mm mm yr yr–1 -1 Rate: Rate:−0.202 −0.202±± 0.298 0.298 mm mm yr yr–1 2010 2013 2016 2010 2013 2016 Rate: Rate:−0.202 −0.202±± 0.298 0.298 mm mm yr yr −30 1998 (c) 2001 2004 2007 Time (years) 2010 2013 2016 Distance moved (mm) 60 50 40 of disorder or energy not available to do work, increases 30 with20time as more energy is expended. All processes in nature move toward a state of equilib10 rium.0 If heat is added to a rock mass, the rock mass will re−10 adjust to once again establish a state of equilibrium at the −20 Rate: Rate: −0.202 ±± 0.298 0.298 mm mm yr yrof new temperature. The readjustment may be−0.202 in the form −30 1998 2001 2004 2007 chemical 2010 2013 2016 plastic deformation, recrystallization, reaction with (c) Time (years) fluids, change in deformation style from brittle to ductile –1 -1 Mont. M Albania Alb lb bania Serbia Macedonia (or vice versa), or some other process. Similar readjustments take place in response to changes in pressure (or stress). Striking a rock with a hammer produces an elastic rebound if it is not struck hard enough to exceed the elastic strength of the rock (Chapter 7). If we strike the rock hard enough to break it, permanent deformation in the form of a fracture is produced, and any excess remaining energy is dissipated as a tiny but measurable temperature increase around the fracture. Romania Russia Bulgaria Georgia Greece eece Azerbaijan Armenia FIGURE 1–14 Map of the eastern Mediterranean and Middle East plotting GPS–derived velocity vectors. Note that the tail of the arrow is the station location, and the length and orientation of the arrows represent the rate and direction of motion. The velocity vectors are plotted relative to a fixed Eurasia and thus are relative, not absolute, velocity vectors. The small size of the arrows along the northern part of the area indicates that Eurasia is a coherent block, whereas Africa, Arabia, Turkey, and the Hellenic region are moving relative to Eurasia. Note the relative western movement of Turkey. (Modified from Reilinger et al., 2006.) Az. Turkey Cyprus Iran Syria Lebanon Iraq Israel Libya 20 mm yr −1 Saudi Arabia Jordan GPS velocity vectors Egypt 0 500 kilometers Introduction | 13 remove 5 m of ice H = 10 m 0m 0m Ice ρ = 920 kg m‒3 D = 90 m 110 m (a) Water ρ = 1,000 kg m‒3 Z X Pressure = 1.078 × 106 Pa = 1.078 × 106 Pa 0m Ice ‒3 D = 85.5 m ρ = 920 kg m Ice ρ = 920 kg m‒3 95 m 110 m (b) Water ρ = 1,000 kg m‒3 Z H = 9.5 m X Pressure = 1.034 × 106 Pa ≠ 1.078 × 106 Pa 110 m (c) Water ρ= 1,000 kg m‒3 Z X Pressure = 1.078 × 106 Pa = 1.078 × 106 Pa FIGURE 1–15 (a) Simple model of isostasy with iceberg floating in water; (b) removal of 5 m of the iceberg; and (c) restoration of isostatic equilibrium. Consider an iceberg floating in a large body of water. We’ve all heard the phrase “it’s just the tip of the iceberg,” because ice is less dense than the water; the iceberg has a small part that extends above the waterline and a much deeper part below the waterline (Figure 1–15a). The height to depth ratio is controlled by the density contrast between the ice and the water, because ice is 92 percent as dense as water; 92 percent of the iceberg is below the waterline. The pressure at the base of the water may be calculated using the formula: Pressure = ρgh (1–1) where ρ is the density of the material, g the acceleration due to gravity, and h the height of the water column. For point X the pressure equals (1,000 kg m−3) (9.8 m s−2) (110 m) or 1,078,000 kg m−1 s−2 or Pascals (Chapter 5). The pressure at point Z is equal to that at X and as such the system is in equilibrium, but what happens if 5 m of ice are removed from the top of the iceberg (Figure 1–15b)? The pressure at point Z is now less than that at point X (out of equilibrium); therefore the water will flow toward the region of lower pressure, causing the iceberg to rise upward. Equilibrium is restored when the pressure at points X and Z are equal (Figure 1–15c): the iceberg is now 92 percent below the waterline, and for the 5 m of ice removed it has rebounded upward 4.5 m. What might control the rate at which the iceberg is restored to equilibrium? A large-scale attempt to restore equilibrium is still occurring in northern Europe and North America after melting of the last Pleistocene ice sheets. When the ice sheets formed and loaded the continents with additional mass, the more rigid lithosphere sank to a lower level in the less rigid asthenosphere to attain a new equilibrium state. As the ice melted, the lithosphere was again forced out of equilibrium and accordingly began rebounding to restore a new equilibrium state. As you might expect, the greatest rebound occurs where the ice was thickest. The condition of balance, involving a state of equilibrium between blocks that occurs within the continents and between continents and the adjacent oceans, is called isostatic equilibrium (Figure 1–16). We also can learn about parts of the Earth from areas that are out of isostatic equilibrium. It is possible to estimate the viscosity of the mantle from the rate of isostatic rebound of the continents where information on the uplift rate can be obtained. A good example of this is in the determination of uplift rate of raised beaches from 14C age determinations (Chapter 3) of wood fragments found in successive beach levels. The viscosity ( μ) of the mantle beneath the uplifted beaches may be estimated from μ = (tr ρgλ) / 4π (1–2) where tr is relaxation (rebound) time, ρ is density, g is the acceleration of gravity, and λ is the wavelength of the displacement of the Earth’s surface (derived in Turcotte and Schubert, 2014). The behavior of the mantle may be approximated as that of an ideal viscous material for our purposes. Consequently, calculations of this kind enable us to draw conclusions about the behavior of the mantle in areas that have undergone recent isostatic rebound. For example, we can calculate the viscosity of the mantle beneath the central Canadian Shield by determining the uplift rate of beach terraces along the shore of James Bay in northeastern Ontario, and by using estimated dimensions of the Keewatin ice sheet that covered this area during the Pleistocene. The oldest beaches in that area are now 180 m above sea level and it is assumed (from gravity data) that 20 m more uplift will occur from additional rebound. We can estimate the rate of uplift from the time of retreat of the glacier from this region about 8,000 years ago. 14 | Plateau Continental interior basin 2.7 2.8 Introduction Mountains 2.7 Ocean basin 2.6 2.8 Fluid substratum 3.0 3.3 (a) Continental interior Plateau basin Mountains Ocean basin 2.7 2.7 2.7 2.7 2.7 Fluid substratum 3.3 Moreover, sea level has already risen 125 m, and so 125 m must be added to the amount of uplift. The best estimate of the width of the Keewatin ice sheet was about 9,000 km, which is the wavelength of the surface displacement in equation 1–2. The density of the mantle is assumed to be 3,300 kg m−3. Relaxation time (tr ) must first be calculated to take into account the decreasing rate of uplift with respect to the amount of uplift that has already occurred and the amount still to occur calculated from 2.7 (b) w = wm e 2.8 2.7 2.75 2.8 Rigid mantle substratum Fluid substratum 3.0 3.2 (c) Lithosphere not loaded Lithosphere loaded Lithosphere unloaded and rebounding (d) FIGURE 1–16 Isostatic equilibrium between crustal blocks of different densities and thicknesses, as well as between the continents and oceans. (a) and (b) are the early models of Pratt and Airy based separately on different density (in units of g cm−3) and different sizes of blocks. We realize today that both density and size affect the isostatic equilibrium of the blocks (c), and are involved in isostatic compensation. (d) shows the effect of loading and unloading of a mass on the lithosphere. Arrows indicate directions of compensating flow in the asthenosphere during and after loading. (1–3) t ln wm − ln w . (1–3a) Substituting tr = 3.3 t tr , where w is uplift still to occur (~20 m), wm is total uplift to date (180 m from beach data plus 125 m rise in sea level = 305 m), and t is time since uplift began (8,000 y). Rewriting equation 1–3 in logarithmic form, then solving for tr,  t  ln w = ln wm −   ,  tr  tr = 3.0 − 8, 000 = 2, 936 y ln 305 − ln 20 Calculating μ from equation 1–2, μ = {[(2,936 y) (365 d y−1) (24 h d−1) (3,600 s h−1)] × 3,300 kg m−3 × 9.8 m s−2 × (9 × 106 m)} / 4π = 2.1 × 1021 kg m−1 s−1 or Pa s. (1–4) (The units of viscosity, here, Pa s, are pascal seconds. One pascal is 1 kg m−1 s−2.) The viscosity of water is approximately 1 × 10−3 Pa s; thus the Earth’s mantle is a very viscous material, but over time it flows and the consequences of this flow are profound. The calculation also demonstrates that the lithosphere responds to loads placed on it in relatively short periods of geologic time. The buoyancy of different crustal elements is fundamental and involves all parts of the lithosphere and asthenosphere. The phenomenon of isostasy was first discovered in surveys on the flanks of the Himalayas, where the great topographic relief led to an error in the calculations that could not be compensated by usual corrections. Early isostatic models based on either volume or density failed to satisfy the need for correction. Later, models incorporating both volume and density changes (Figure 1–16), along with flexural bending of the crust, best corrected the errors in the surveys and demonstrated the fundamental nature of the principle of isostatic adjustment. The emplacement of large thrust sheets (Chapter 12) with areas of hundreds of square kilometers and thicknesses Introduction 26° N T i b e t a n 27° N MFT 10 MBT MCT SL MCT 28° N South Tibetan detachment Gangdese batholith Metamorphosed Indian Plate rocks –30 MHT Indian crust –40 10 SL Tethyan sediments –20 North 30° N Zangpo suture zone –10 kilometers P l a t e a u 29° N T MC –10 Tethyan oceanic and forearc rocks –20 Asian crust (Lhasa terrane) –30 –40 –50 –50 –60 Indian mantle Moho –70 kilometers H i m a l a y a s South 15 | –60 –70 –80 –80 T ib Hi 30°N eta ma CHINA n Pla lay te a u as INDIA 20°N 80°E 90°E FIGURE 1–17 Cross section from northern India through the Himalayas into the Tibetan Plateau. Note that Indian crust is being subducted beneath the Himalayas, Tibetan Plateau, and Asia, creating the thickest crust and highest mountains in the world. The great elevation of the High Himalayas is considered to be at least partly related to this overthickened crust. MFT—Main frontal thrust. MBT—Main boundary thrust. MCT—Main central thrust. MHT—Main Himalayan thrust. No vertical exaggeration. (Modified from several published cross sections and geophysical data in Nelson et al., 1996, Science, v. 274, and Hauck et al., 1998, Tectonics, v. 17.) of 5 to 10 km would thicken the lithosphere in the immediate vicinity of the thrust sheet, and would require profound adjustments in the asthenosphere beneath to accommodate the increase in lithospheric thickness. The greatest thickness of crust on Earth (~70 km) is beneath the Himalayas and Tibetan Plateau (Figure 1–17). The isostatic buoyancy of Indian crust being subducted beneath Asia has driven the uplift of the Tibetan Plateau, and the High Himalayas are being gravitationally extruded from beneath the T ibetan Plateau. Similarly, crustal extension, like that affecting the Basin and Range Province in the western United States (Chapter 13), has unloaded and thinned the lithosphere, thus decreasing the amount of low density material above the asthenosphere. So, even though the mantle is a very viscous material (Equation 1–4), it flows to balance loading and unloading of crustal materials. Geologic Cycles Most geologic processes are driven by cyclic changes of energy fluxes, commonly over millions of years. The rock or geochemical cycle is probably the most familiar of these geologic cycles (Figure 1–18). Each stage in the cycle, from crystallization of magma to conversion of sedimentary or igneous rocks into metamorphic rocks, is in some way driven by thermal processes and, to a lesser degree, by changes in pressure. Inputs of heat or mechanical energy at particular places short-circuit the cycle. Chemical changes accompany deformation in several stages of the rock cycle. All stages attempt to restore equilibrium. The Wilson or supercontinent cycle (defined earlier in the plate tectonics section) involves plate motion, beginning with the opening of an ocean basin and producing a trailing plate margin like the present-day East Coast of the United States (Figure 1–19). The trailing margin phase is terminated by formation of a subduction zone along the margin that begins to subduct oceanic crust, generate heat and pressure, and form either a volcanic island arc offshore or a continental magmatic arc on the old continent. The Wilson cycle ends with continent-continent collision, closing the ocean. Stages in the cycle reflect response to changing physical conditions in an attempt to restore a state of equilibrium to all or part of the plate system. Mountain building is thus a direct consequence of a partial or completed Wilson cycle. The folds and faults we observe in modern mountain chains or the eroded roots of ancient chains formed in response to energy expenditure in plate collision zones. The exceptionally rapid uplift of the Himalayas indicates extreme isostatic imbalance in the crust because of the great thickness of continental crust there. Erosion is rapidly reducing the elevations in this chain to levels that will be closer to equilibrium, but rapid uplift has thus far outstripped the erosion rate. All processes operating upon or within the Earth act to achieve and maintain equilibrium. Energy is constantly being dissipated to keep the Earth in a dynamic state. Work is performed to melt rocks within the Earth to restore equilibrium, and energy is used to drive several cyclic processes. Structural geology is an exciting field and an important geologic discipline with both fundamental and real-world applicability in many other disciplines. In Chapter 2 we continue our review and turn to a discussion of nontectonic structures, including a consideration of primary structures, many of which are useful to the structural geologist to determine the facing direction (top) of a sequence and to help distinguish tectonic from nontectonic structures. 16 | Introduction FIGURE 1–18 The rock, or geochemical, cycle—a thermally and mechanically driven equilibrium cycle involving many intermediate states and shorter cycles. T—temperature. P—pressure. MAGMA T Cooli ng Gases nal T, T P Hydrosphere Atmosphere Weathering METAMORPHISM T Erosion Transportation Deposition Biosphere ct io Reg PLUTONS & IGNEOUS ROCKS Conta Water METAMORPHIC ROCKS P Burial SEDIMENTARY ROCKS SEDIMENTS Lithification Suture (from earlier cycle) Continent A Continent B Rifted Continent A New ocean Oceanic crust Oceanic crust Small ocean Continent A Continent B Crust A Continent A Mid-ocean ridge Continent B Fragment Volcanic arc Volcanic arc Continent B Continent A Subduct ion z on e Subduct ion z one Accreted volcanic arc block Continent A Continent B Continent A Continent B Continental collision zone (Wilson cycle complete) Continent A Continent B FIGURE 1–19 The Wilson cycle of the opening and closing of an ocean basin. The cycle may be complicated by formation and movement of suspect terranes, partial closing of small oceans, and lack of continent-continent collision to terminate the cycle. Introduction | 17 Chapter Highlights • Structural geology focuses on understanding the geometry, kinematics, dynamics, and mechanics of earth structures. • Structural geologists study the processes that cause deformation and produce the history of geologic structures and regions. • Structural geology has societal relevance, because it plays a key role in discovering mineral resources (hydrocarbon and ore deposits), understanding earthquakes, and recognizing geologic hazards. • Structural geologists commonly use field data to anchor their investigations, but also employ mechanical, experimental, and numerical techniques to answer research questions and test hypotheses. • Earth structures form primarily in response to plate tectonic processes, which provide a key framework for geological science. • Geologic cycles occur as earth systems work to restore or maintain equilibrium when mechanical or thermal conditions change. Questions 1. Why was plate tectonics theory not formulated in the nineteenth century, like the unifying theories of physics and biology? 2. Why do earthquake focal depths generally get deeper with distance inland from the Peru-Chile trench (Figure 1–1b)? 3. Plate tectonics is essentially a kinematic theory. What specific evidence demonstrates that lithospheric plates move over time? 4. Use the GPS data from Auckland, New Zealand (Figure 1–13), to determine the velocity vector (rate in mm yr−1 and direction in degrees, e.g., 14 mm yr−1 toward 145°). 5. The Wilson cycle predicts that old ocean basins eventually begin to close by subduction along their margins, causing passive continental margins to change into active margins. The Atlantic Ocean is an old ocean, and some have proposed that subduction and the closing of the Atlantic have already begun. Test that hypothesis using modern GPS time series data: a. A GPS station on the Island of Bermuda in the Atlantic Ocean is moving at a rate of 14.3 mm yr−1 toward 303°, and a station at Greenbelt, Maryland, in eastern North America is moving at a rate of 15.0 mm yr−1 toward 282°. Calculate the movement vector between these two stations. b. Is the value calculated in (a) a relative movement vector or absolute movement vector? Explain. c. Based on this information, is the western Atlantic Ocean closing? How can the velocity best be explained between the two stations? 6. Based on the GPS velocity vectors for the eastern Mediterranean region (Figure 1–14), estimate/locate the position of plate boundaries and their kinematics (divergent, convergent, or transform). 7. During the Cenozoic Era approximately 2.5 km of material was eroded from the central Appalachian Mountains. How much isostatic uplift should occur due to the removal of 2.5 km of material? Assume a crustal density of 2,700 kg m−3 and a mantle density of 3,300 kg m−3. 8. Derive an equation that relates the depth of the root (D) on a less dense layer, lying on top of a denser layer, to the height (H) it extends above the denser layer (analogous to the iceberg example in Figure 1–15). Use ρu and ρl to represent the densities of the upper and lower layers, respectively. 9. Using the mantle viscosity of 2.1 × 1021 Pa in equation 1–4, calculate the amount of up or down motion of the lithosphere (100 km thick, ρ = 2,900 kg m−3) that would result from loading of the crust (and lithosphere) with a thrust sheet 300 km long, 100 km wide, and 10 km thick and having a density of 2,700 kg m−3. Assume the thrust sheet was emplaced during an instantaneously short period of geologic time. 10. Why are the elevations of young mountain chains, like the Alps and Himalayas, so high, but those of older mountains, like the Appalachians, British Caledonides, and Urals relatively low? 18 | Introduction Further Reading Adams, F. D., 1954, Birth and development of the geological sciences: New York, Dover Publications, 506 p. Provides an interesting summary of the evolution of geological science from classical times through the beginnings of modern geology with Hutton, Lyell, Darwin, and others in the nineteenth century. Burchfiel, B. C., 2004, New technology, new geological challenges: GSA Today, v. 14, no. 2, p. 4–9. Cloud, P. E., 1970, Adventures in Earth history: San Francisco, W. H. Freeman and Company, 992 p. A compendium of classic papers on the foundations of ideas on the origin of the Earth, the atmosphere and life, the geologic record, and geologic processes. Cox, A., and Hart, R. B., 1986, Plate tectonics: How it works: Oxford, United Kingdom, Blackwell Scientific Publications, 392 p. Glen, W., 1982, The road to Jaramillo: Critical years of the revolution in Earth science: Stanford, California, Stanford University Press, 459 p. Outlines the history of the development of plate-tectonics theory, emphasizing use of paleomagnetic measurements. Hamilton, W. B., 1979, Tectonics of the Indonesian region: U.S. Geological Survey Professional Paper 1078, 345 p. A synthesis of the geology of the Indonesian region, containing numerous maps showing the elements of a dispersed group of terranes ranging from Precambrian basement to recent v olcanic-arc materials in the initial stages of being swept back into the Asian continent as Australia moves northward. Hoffman, P., 2013, The tooth of time: The North American Cordillera from Tanya Atwater to Karin Sigloch: Geoscience Canada, v. 40, p. 71-93. Provides insight into the development of plate tectonics principles based on connecting the seafloor with land geology. Howell, D. G., 1985, Terranes: Scientific American, v. 253, no. 5, p. 116–125. Summarizes the distribution of microplates, or terranes, in and around the Pacific basin, presenting the background of plate tectonics and accretion concepts. Kearey, P., Klepeis, K. A., and Vine, F. R., 2009, Global tectonics, 3rd edition: Chichester, United Kingdom, Wiley–Blackwell, 482 p. Prothero, D. R., and Dott, R. H., Jr., 2010, Evolution of the Earth, 8th edition: New York, McGraw-Hill, 576 p. Provides a comprehensive overview of Earth history, with additional background material. Reilinger, R., et al., 2006, GPS constraints on continental deformation in the Africa-Arabia-Eurasia continental collision zone and implications for the dynamics of plate interactions: Journal of Geophysical Research, v. 111, B05411, doi:10.1029/2005JB004051. Stanley, S. M. and Luczaj, J. A., 2014, Earth system history, 4th edition: New York, Freeman, 608 p. Wilson, J. T., 1966, Did the Atlantic close and then reopen?: Nature, v. 211, p. 676–681. This short paper sets the stage for the concept of the Wilson cycle. 2 Fundamental Concepts and Nontectonic Structures In Chapter 2 we review fundamental geologic concepts and laws, and discuss nontectonic structures. You may have become acquainted with the fundamental geologic laws in introductory geology courses, and also examined primary sedimentary structures in a stratigraphy-sedimentation course. All of these concepts and features provide a foundation with which to decipher and understand geologic structures. It is appropriate to review them here to lay the groundwork for our subsequent discussion of geologic structures and how they form. It has been said that stratigraphy is the basis of all geology . . . MARLAND P. BILLINGS, 1950, Geological Society of America Bulletin Fundamental Concepts The relationships to be discussed here provide us with powerful tools for understanding structural geology. Without these concepts, we would be so severely handicapped that no technologically advanced equipment, such as sophisticated computers, advanced microscopes, seismological equipment, or other analytical tools, could help solve structural problems. A fundamental doctrine in geology is uniformitarianism. James Hutton, an eighteenth-century Scottish farmer and scientist, was the first to articulate uniformitarianism as a geologic tenet. Hutton’s writing style was obscure, and his ideas did not become widely known until the early nineteenth century when John Playfair rewrote them. The Doctrine of Uniformitarianism states that processes occurring today upon and within the Earth have probably gone on similarly in the past and will continue in the future. Stated more simply, the present is the key to the past. Hutton’s conclusions were based on his observations along the coasts of Scotland (Figure 2–1). He observed that sand bars and beaches were constantly created and destroyed by storms, and were slowly rebuilt. Hutton also recognized that the sand in sandstone is the same as that being moved about on the beach. His observations mark the beginning of modern geology: for the first time, Hutton recognized that a huge amount of time is both available and necessary to carry out geologic processes. Before Hutton and long afterward, the prevailing notion was that unknown catastrophic events were responsible for geologic processes and features. Uniformitarianism 19 20 | Introduction FIGURE 2–1 Observations in the rocks at Siccar Point along the East Coast of Scotland by James Hutton provided key information that permitted him to formulate the doctrine of uniformitarianism. Devonian Old Red Sandstone beds are slightly tilted toward the North Sea and unconformably overlie nearly vertical Ordovician rocks. (Photo by Dave Souza, accessed through Wikipedia.) immediately led to conflict with religious dogma, resulting in debates between scientists and theologians during the nineteenth century that were further intensified with the rise of theories to explain organic evolution. Even so, the validity of the Doctrine of Uniformitarianism has been questioned (Gould, 1965; Shea, 1982; Rampino, 2017), bringing out several flaws in the doctrine. Ironically, catastrophism has again gained a place in modern geology. Meteorite impacts (near instantaneous events) are now recognized to have produced dramatic changes throughout Earth history (e.g., end-of-Mesozoic extinction; Alvarez et al., 1980). We also realize that, although movement along a large fault may total many kilometers, a large part of the motion may have occurred as meterscale displacements associated with near-instantaneous slip during individual earthquakes, not by continuous slip through time. Study of large active faults like the San Andreas indicates that some segments move by continuous creep, but other segments undergo instantaneous catastrophic movement–producing earthquakes. Hutton was correct when he recognized the immense amount of time involved in geologic processes, and so uniformitarianism is the best means of thinking about geologic processes through time. These long-term effects may, however, represent the sum of many instantaneous and even catastrophic events randomly distributed over the continuum of geologic time. The Law of Superposition is another cornerstone of geologic thought. It states that within a layered sequence, commonly sedimentary or volcanic rocks, the oldest rocks occur at the base of the sequence and successively younger rocks occur toward the top, unless the sequence has been inverted through tectonic activity. Nicolas Steno (Niels Stensen), a Danish physician with interests in geology, first stated the law of superposition during the seventeenth century. The law is of great importance in structural geology, because it is necessary to determine whether the stacking order in a sequence is upright or has been tectonically inverted. The sequence may have been tilted, completely overturned, or repeated by folding or faulting (Figure 2–2a). Superposition is therefore an inviolate second principle in the study of structural geology. A nother fundamental geologic law is the Law of Original Horizontality. It states that bedding planes within sediments or sedimentary rocks form in a horizontal to nearly horizontal orientation at the time of deposition. This law is fundamental in structural geology, because bedding is the common initial reference frame (Figure 2–2b). Another law that goes hand in hand with working out the structural history of an area is the Law of Crosscutting Relationships, applied as either the Law of Structural Relationships or the Law of Igneous Crosscutting Relationships (Figure 2–2c). Both state virtually the same thing: that an igneous body or a structure—that is, a dike, batholith, fold, or fault—must be younger than the rocks it cuts through or deforms. In other words, the rocks that form the host for an igneous body or that contain a structure must have been there before the igneous body was intruded or the structure formed. These laws provide a basis for placing structures in a relative time context. Truncation of an earlier structure or igneous body by a Youngest Normal (upright) sequence (a) Oldest Oldest Inverted (overturned) sequence (b) Youngest Horizontal to nearly horizontal bedding Former erosion surface Deformed layering no longer horizontal (c) Pluton must be younger than country rocks Fault younger than both pluton and intruded country rocks (d) of fossil organisms may have been restricted to a particular terrane. Examples are the fusulinid fauna of the late Paleozoic Tethys ocean, and the contrasting Cambrian trilobite faunas of North America and Europe. Structural geologists use the principle of multiple working hypotheses. It enables us to formulate more than one possible explanation of the same data, to evaluate each, and to select the most likely hypothesis. Say, for example, you get in your car to run some errands, but the car will not start. Several possibilities come to mind: (1) the battery may be dead; (2) the starter switch is broken; (3) the starter itself is broken; and (4) your car is out of fuel. Right away, you eliminate option (4), because you filled up the fuel tank the day before. The others are more difficult to sort out. The solution is to collect additional data to be able to eliminate all but one of the other possibilities. The same process applies to problems in structural geology. Suppose you are working in a field area that lacks a critical exposure needed to correctly interpret the contact between an igneous body and the overlying sedimentary sequence (Figure 2–3a). You hypothesize that the contact can be: (1) an intrusive contact; (2) a fault; or (3) an unconformity. Each hypothesis may initially be equally valid. You begin by sorting through your previous observations and ask: With regard to (1): have you observed metamorphism or other alteration of the sedimentary rocks near the contact? With regard to (2): have you observed crushed rocks or other evidence of faulting near the contact? With regard to (3): have you observed clasts of the igneous rocks incorporated into the base of the overlying sedimentary sequence? Exposures of thermally metamorphosed rocks along the contact eliminate the second and third possibilities (Figure 2–3b), but before discovery of the critical data, all working hypotheses were equally valid. FIGURE 2–2 Cross sections illustrating the laws of (a) superposition with an upright sequence, (b) superposition in the same sequence overturned, (c) original horizontality, and (d) crosscutting relationships. later structure, an unconformity (to be discussed later), or a younger pluton of known age provides a minimum age for the earlier features. Bracketing structures and igneous bodies in time is an essential part of understanding the geologic history of an area. Initially, the Law of Faunal Succession may seem far from useful to structural geologists. It states that fossil organisms should systematically change, with more advanced (evolved) organisms toward the top of a sequence. This provides the basis for determination of relative age of fossiliferous sequences and permits determination of whether a sequence is upright or tectonically overturned. It is therefore of major importance in unraveling the structural history of an area where the rocks are fossiliferous. Fossils have also played a key role in the identification of exotic terranes (see Chapter 1), because particular groups 21 | Fundamental Concepts and Nontectonic Structures The contact could be (1) an intrusive contact, (2) a fault, or (3) an unconformity Sand Contact covered by soil (a) Granite ? stone Lime stone Ah ha! Marble with wollastonite and garnet Sand stone Lime stone Granite Marb le (b) FIGURE 2–3 (a) Use of the principle of multiple working hypotheses to interpret the contact between a granite pluton and a host rock. (b) Without data collected at a critical exposure, the contact could be an intrusive contact, an unconformity, or a fault. 22 | Introduction There is also value in the outrageous hypothesis (Davis, 1926; Wise, 1963) as an alternative working hypothesis, because it provides a focus for critical pieces of data toward a solution to a problem. An outrageous hypothesis appears to be an impossible solution to the problem from the moment it is formulated. Considering the data, it may gain the position of a credible, alternative working hypothesis, or it may be quickly abandoned as other more likely working hypotheses are formulated. In the early twentieth century, Raphael Pumpelly first noted that small structures are a key to and mimic the styles and orientations of larger structures of the same generation in an area. Pumpelly’s rule holds if all structures referred to were formed at the same time by the same stresses in rocks of similar properties. They also must have been deformed similarly on all scales, so the structures would provide a basis for presuming that small and large structures of the same generation in an area are related. Because we are not always able to observe structures on all scales, Pumpelly’s rule allows us to assume similarity from hand specimen to map scale of structures formed at the same time (Figure 1–7a). Pumpelly’s rule may also be considered a statement of the principle of self-similarity or scale invariance. The scale invariance (fractal geometry) of many geological structures, such as fracture networks, folds, and mineral deposits, is important, because it enables us to visualize the configuration of large and small structures without ever directly observing the entire structure. structural geologist, primary structures, where present, are very useful for determining the facing (younging) direction (which way was up) in a sequence of rocks. Facing directions enable us to ascertain if a sequence is upright or overturned. Except for fossils, primary structures are probably the best tools for working out the structural geometry and history in deformed rocks. Shackleton (1958) used primary sedimentary structures to determine that a large part of the rocks in the southern Highlands of Scotland are upside down and make up the inverted limb of a large overturned fold (Figure 2–4). In studies of deformed rocks, we need to know whether the observed structures have a tectonic or nontectonic origin (Figure 2–5). Many structures that formed in primary depositional environments may mimic struc tures in rocks that formed in response to tectonic deformation. Thus, it is important to make the distinction. Moreover, many sedimentary structures that form at or near the surface provide useful models to compare with tectonic structures that form at elevated temperatures and pressures. For example, structures formed by ductile flow (Chapter 7) in water-saturated silt, glacial ice, and evaporite (halite, gypsum, anhydrite) deposits at surface pressure and temperature (P-T) conditions are almost identical to those formed at much higher P-T conditions in rocks deformed at depths of 20 km or more. Primary Sedimentary Structures The most common characteristic and most diagnostic feature of sedimentary rocks is bedding, and because it forms mostly in a horizontal orientation, it is the first-order reference surface for most structural measurements. Bedding planes form in primary sedimentary environments and become mechanical zones of weakness as the sediment is lithified—converted to rock (Figure 2–6). Bedding exists for several reasons, most commonly because of compositional or textural differences in sediment at the interfaces Primary sedimentary structures form along with the rock mass of which they are a part, and have a nontectonic origin. They include bedding and features such as mud cracks, ripples, sole marks, vesicles, and others. For the NW a Axi Upright limb anticline Aberfoyle SE Inverted limb of Tay nappe Subhorizontal overturned beds 5 kilometers 10 Upright limb H bou ighland nda r y fa ult 0 e of rfac u s l Bedding Facing direction of beds Fold axial surface FIGURE 2–4 Geologic cross section of the Tay nappe in the Scottish Highlands. The resolution of overturned and upright structures was accomplished by R. M. Shackleton using facing directions of sedimentary sequences determined from sedimentary structures. Heavy red arrows indicate facing direction. (Reproduced by permission of the Geological Society, from Downward-facing structures of the Highland Border, R. M. Shackleton, in Quarterly Journal of the Geology Society of London, v. 113, 1958.) Fundamental Concepts and Nontectonic Structures | 23 (a) (a) (b) FIGURE 2–5 (a) Folded beds in Quaternary lake sediment produced by an ancient earthquake and exposed today in a dry stream valley in Israel near Ein Boqeq near the Dead Sea. Even though these structures formed at surface conditions, they exhibit many of the characteristics of tectonic folds (b) that formed at high temperatures and pressures deep in the Earth. The folds in (a) are complex noncylindrical to sheath folds (Chapter 17), which are frequently observed in ductile sediments and rocks deformed at elevated temperatures and pressures. The example in (b) is sillimanite-grade gneiss-migmatite in the Thor-Odin dome in the Shuswap Complex, southern British Columbia. This highly folded layering is not bedding but the dominant foliation (Chapter 18). Hammer is 30 cm long. (RDH photos.) 24 | Introduction between adjacent beds. Differences in composition and texture reflect changes in sedimentary environment: sediment composed of particles of different size, shape, or (in many instances) composition may be deposited in various successions. For example, at a site where sand is being deposited, sand deposition may be interrupted for a short time, and smaller clay to silt-sized particles are deposited, and then deposition of sand continues. The layer of finegrained material forms a mechanical discontinuity in the mass of sand, and this discontinuity becomes a bedding plane. Repetition of this process produces a sequence of bedded sand and mud. Compaction of deposited sediment may also provide a mechanical discontinuity that leads to formation of a bedding plane. When the next influx of sediment occurs, it is initially compacted less than that deposited earlier. Consequently, a bedding plane may form between newly deposited sand and sand deposited previously without the need for different particle sizes to separate the two layers (Figure 2–6). Graded beds contain particle sizes ranging from large at the base to small at the top. In some graded beds, particle size ranges from pebble or boulder at the base to clay at the top, and the entire thickness of the bed may range up to 2 to 3 m; in others, particle size may range from 1 mm or smaller at the base to clay at the top, and the bed thickness may be less than 1 cm. They form where a mass of sediment of contrasting particle size, commonly a turbidity flow, encounters a change in flow regime—from rapid to slow—producing rapid deposition (Figure 2–7). The largest particles, because of their mass, settle to the bottom first, followed by successively smaller particles. After lithification, the bottom of the bed may be conglomerate, the middle part sandstone, and the top part shale, with gradual transitions within the bed between rock types. Graded beds form in both sedimentary FIGURE 2–6 Formation of bedding planes. and volcaniclastic deposits, and are important tools for determining the facing direction. Channels (Figure 2–7) and other primary features frequently occur at the base of graded beds. Reversed graded bedding is relatively rare but may form as a primary structure during deposition of pumice fragments in water, from grain and debris flows, or by a change in flow rate during the onset of flooding. Larger pumice fragments will occur at the tops of beds, and smaller particles of other compositions will occur beneath, because pumice fragments initially float and thus settle more slowly than denser particles. Cross bedding, or cross stratification, is the least ambiguous current-related structure with distinct dif ferences between the top and bottom of the bed. It is a common sedimentary structure that forms where sediment grains are transported by water or wind currents. The product is migrating dunes, or mounds, with inclined (foreset) planes within an individual bed, bounded by ordinary bedding. Common types of cross beds are tangential, planar, trough, and festoon (Figure 2–8). Tangential cross beds may be used for determining facing direction; planar cross beds, even though inclined, provide the same perspective whether overturned or upright and so cannot be used to determine facing direction. Cross beds may have a dip up to 30° and may have trough geometries. Both geometries require caution when measuring bedding attitudes, so you need to see either the top or the bottom of the bed in 3-D. Two other types—ripple cross laminations and hummocky laminations—are small-scale cross beds that form in finer sediment, and may be useful for determining facing directions. Those useful in determining tops (tangential) are generally concave upward, tangent to the bottom of the primary bedding plane, and truncated at the top (Figure 2–9). Deposition of sand layer Compaction through time, followed by deposition of more sand forms bedding plane Compositional difference forms bedding plane Compaction and deposition of thin mud or clay layer Mud or clay Water Compaction Bedding plane Compacted sand grains Uncompacted, watersaturated sand Compacted sand Bedding plane Compacted sand Fundamental Concepts and Nontectonic Structures | 25 Fine sediment Coarse sediment Fine sediment Bedding surface Bedding surface Small channels Coarse sediment Fine sediment Channels Coarse sediment Bedding surface (b) (b) (a) (a) FIGURE 2–7 (a) Graded beds in Middle Silurian Ekeberg graywacke exposed on a glacially striated surface near Jämtängen, Sweden. Note there are three cycles of graded beds (with load casts or current scours at the base of the upper two) and fining-upward sequences. Cross beds appear in the lowest bed. (Dark irregularly shaped areas are lichen.) (RDH photo.) (b) Sketch of photo in (a). (c) General relationships of graded beds and associated textures. Fine sediment Cross beds Coarse sediment Silt and clay layer Finer sand upward Conglomerate layer Channels (scours) (c) FIGURE 2–8 (a) Tangential, (b) planar Current direction Truncated at top of bed (abrupt, torrential), (c) trough, and (d) festoon cross beds. Facing direction can readily be determined in all but planar (torrential) cross beds (b). Concave up (a) Tangent to bottom of bed (c) Mud Cracks Fine sediment deposited in water and later exposed to the atmosphere forms extensional shrinkage cracks called mud or desiccation cracks (Figure 2–10). In plan view, they form polygonal (mostly hexagonal) blocks bounded by cracks that taper downward from the surface of the sediment and terminate. Because of its fine texture, the surface (b) (d) layer may separate from the one below and curl up, providing another indicator of facing direction. Mud cracks are common in the geologic record, but, because of the transient nature of the subaerial environment where they form, are not as common as cross beds or graded beds. Where preserved, they are quite useful in determining the facing direction and may also be used as indicators of natural strain (deformation) in rocks (Chapter 6). 26 | Introduction FIGURE 2–9 (a) Trough and festoon cross beds allow determination of facing direction; Pleistocene sand, Elmore County, Idaho. (H. E. Malde, U.S. Geological Survey.) (b) Folded cross beds in Moine Series metasandstone defined by cm-thick laminae that intersect bedding at a high angle, Cluanie Lake, Scotland. (RDH photo.) (a) (b) (a) (b) FIGURE 2–10 (a) Mud cracks in a dried-up shallow body of water near Salton Station, Riverside County, California. (G. K. Gilbert, U. S. Geological Survey.) (b) Middle Proterozoic mud cracks in siltstone, Isle Royale National Park, Michigan. (N. K. Huber, U. S. Geological Survey.) Fundamental Concepts and Nontectonic Structures 27 | Ripple Marks Rain Imprints Ripple marks form where a current moves sediment or where the bottom sediment surface is otherwise disturbed by water moving above a threshold velocity. This setting is very common along beaches and streams, as well as in deeper water, where bottom currents or surface waves interact with bottom sediment. Current (translational) ripple marks form where a prevailing transport direction and deposition of sediment occur; they are commonly asymmetric, and their steep sides face downstream in the direction of transport (Figure 2–11). Unless they contain tangential ripple cross laminae, current ripples have the same shape in cross section regardless of whether they are upright or overturned, and therefore are not useful for determining facing direction. Oscillatory ripple marks are symmetrical and generally consist of high and low crests. They form where a back-and-forth motion exists in a body of water (such as a lake), or where there is no prevailing current direction. The crests have sharp peaks separated by rounded troughs (Figure 2–12). Oscillatory ripples may therefore be used for determining facing directions in sediments. Unfortunately, oscillatory ripples are less common than current ripples. Rain imprints form where rain falls on fine sediment, and preservation in the sedimentary record depends on rapid, nondestructive covering of the imprints by another layer of sediment (Figure 2–13). Rain imprints can be used to determine facing direction but, because they are relatively delicate, are not as commonly preserved as many other primary structures. Motion of water FIGURE 2–12 Formation of oscillatory ripple marks on a shallow sea floor or the bottom of a lake. Current direction 0 (a) 4 centimeters (a) (b) FIGURE 2–11 (a) Current (translational) ripple marks. Lines below the surface indicate earlier surfaces that have been overrun by migrating ripples. (b) Deformed current ripples in silty carbonate and siltstone, Maddens Branch, Ocoee Gorge, Polk County, Tennessee. Bedding plane below (where the quarter is located) has minimal distortion, whereas the rippled top has been flattened into asymmetric fold-like structures. Flattening occurred parallel to slaty cleavage that dips approximately 50° to the right. (RDH photo.) (b) (b) FIGURE 2–13 (a) Lower Cambrian rain imprints in Rome Formation siltstone at Moores Gap Church in eastern Tennessee. (RDH photo.) (b) Rain imprints on desiccated recent mud cracks, Isle Royale National Park, Michigan. (Photo by N. K. Huber, U.S. Geological Survey.) 28 | Introduction Tracks and Trails Tracks and trails left by organisms may be preserved and, under certain conditions, may be used to determine facing direction of beds (Figure 2–14). The weight of an organism produces a track or trail, and if the impression is filled with sediment during deposition of the overlying bed, a cast is formed and the facing direction may be determined. In some instances, partly filled burrows may be useful for determining tops if the fillings can be properly recognized and interpreted. Sole Marks, Scour Marks, Flute Casts Marks formed as an object moves across a bottom surface or as currents scour a bedding surface are sole and scour marks (Figure 2–15a). Sediment that fills sole or scour marks by subsequent deposition may allow the marks to be preserved, provide a sense of asymmetry from the bed below to that above, and thus indicate the facing direction. Flute molds consist of scoop-shaped structures formed where currents scour and erode a surface. The molds are filled with sediment to form flute casts as the bed above is deposited, producing similar asymmetry and another useful tops criterion. Flute casts are commonly found at the base of turbidite beds (Figure 2–15b). (a) Dewatering Structures Load casts form after deposition and dewatering of sediment as a result of gravitational instability at the boundary between a layer of water-saturated sand and underlying mud. The weight of the newly deposited overlying sediment forces out the interstitial water. Compaction of the 0 30 centimeters (b) FIGURE 2–15 (a) Sole marks on siltstone beds, Borden Formation, Bullitt County, Kentucky. (R. C. Kepferle, U. S. Geological Survey.) (b) Flute casts on the bottom of a Devonian turbidite bed at Praia do Castelejo, Algarve, Portugal. (CMB photo.) FIGURE 2–14 Tracks left by an arthropod (probably a trilobite) as it crawled across the Cambrian sea floor; Pyramid Shale Member, Titanothere Canyon, Inyo County, California. Tracks are approximately 1 cm wide. (A. R. Palmer, Cambrian Institute, Boulder, Colorado.) underlying sediment (commonly mud) beneath a sand bed commonly results in depressions in the bed below (Figure 2–16), as water is expelled from the mud during compaction. Load casts may be used with relative ease to determine facing direction. The broadly convex sides of load casts face toward the bottom of the layer. Load casts are common in any accumulation of sediment where there is a contrast in grain size, significant dewatering, and opportunity for differential compaction. The most important factor in formation of load casts is the instability in sediment produced by rapid sedimentation that prevents some of the interstitial water from escaping. Fundamental Concepts and Nontectonic Structures NE Present-day land surface 2m 1m Reference line 3m 29 | 4m SW Land surface at time of earthquake FF F F 1m Organic matter (a) FIGURE 2–17 Dewatering structures in Holocene sediments near Charleston, South Carolina, attributed to a large prehistoric earthquake. F—faults. Vertical scale is exaggerated one and a half times the horizontal scale. (Modified from P. Talwani and J. Cox, Science, v. 229, p. 379–381, © 1985 by the AAAS.) the sequence where organisms of different ages are found. Sometimes, partly filled cavities also occur inside molds of organisms; other organisms, such as trees or bottomliving attached animals, may be preserved in the position in which they lived. If so, they may be used to determine the facing direction of a sequence. Reduction Spots (b) FIGURE 2–16 (a) Load casts on the bottom of a sandstone bed, that projects into underlying mudstone, Sunnyside No. 1 Coal, Carbon County, Utah. (J. O. Maberry, U.S. Geological Survey.) (b) Load casts on the bottom of a near-vertical sandstone bed, southwestern Montana. Bottom of bed faces into the road cut. (L. B. Gillett, SUNY College at Plattsburgh.) Reduction spots are sedimentary structures produced by a small grain or fragment of organic matter or other material that produces a chemically different environment from the surrounding sediment. The chemical difference may produce a nearly spherical area of reduction expressed as a color change in the immediate vicinity of the grain in the otherwise oxidized sediment (Figure 2–19). These features An interesting phenomenon in soft sediment is dewatering: water trapped between individual grains in sediment may remain under pressure as long as the sediment is in the stable confined mass. If an abrupt shaking occurs within a mass of soft sediment, the water may escape suddenly, disrupting bedding and other primary structures (Figure 2–17). Earthquakes have caused dewatering in unconsolidated sediments producing sand blows, mud volcanoes, and other liquefaction features (Obermeier, 2009). Fossils The fossilized remains of organisms preserved in the geologic record provide useful indicators of relative age (Figure 2–18). Fossils may also be used to determine facing direction in a sequence by studying the relative positions in FIGURE 2–18 Heads of several Middle Cambrian trilobites (Paradoxides) on a bedding surface in volcanic mudstone from near Batesburg, South Carolina. (Courtesy of Donald T. Secor, Jr., University of South Carolina.) 30 | Introduction FIGURE 2–19 Deformed reduction spots in a sawed block of Eocambrian Metawee Slate from near Rutland, Vermont. The broken surface on top of the specimen exposes light-colored elliptical reduction spots, whereas the sawed surface in front displays thin vertical sections through the reduction spots. The sawed front of the specimen is 15 cm high. (RDH photo.) cannot be used to determine the facing direction of a sequence, but they serve as an important indicator of strain if the rock mass was internally deformed (see Chapter 6). Sedimentary Facies By the early twentieth century, geologists recognized that sedimentary (and volcanic) rock units vary both laterally and vertically as paleoenvironments change. Such lateral and vertical differences of sediment (later rock) type are called sedimentary facies (Figure 2–20a), and each sediment (rock) type is called a facies or lithosome. One facies is separated from others by particular characteristics (composition, texture, sorting, physical and biogenic sedimentary structures, etc.) that set it apart from other facies within the same formation. Before this principle was recognized, numerous errors were made in interpreting the ages and nature of different rock types. It was assumed that each rock type was a separate formation (mappable unit), especially in non-fossiliferous sequences. The possibility of one rock type grading laterally into another within the same unit was not considered, nor was the possibility that both lateral and vertical changes in rock type were linked in transgressive and regressive sequences (Figure 2–20b). Careful studies of relations between interlayered and gradational sedimentary rocks and associated fossils showed that, although rock types may change laterally as well as vertically, different facies of the same rock unit may be deposited at the same time and should not be considered different rock units solely because of lateral differences in rock type. The interrelationship between horizontal and vertical variation of facies is called Walther’s principle, which states that only those facies (environments) that once existed side by side can be observed vertically juxtaposed in outcrop. Walther’s principle does not apply to sequences containing unconformities (see below). Unconformities A break in the sedimentary record, where part of a stratigraphic succession and thus history is not present, is called an unconformity. Unconformities are produced by erosion or nondeposition (or both), resulting in a lack of strata recording the history during a segment of geologic time. T2 Limestone facies Shale facies Sandstone facies T1 Gradational facies boundaries (a) East West Nonmarine facies ( regressive) Marine facies (transgressive (b) Clastic source area ) Nonmarine facies ( regressive) FIGURE 2–20 (a) Facies changes within the same rock unit in a sequence of sedimentary rocks. T1 and T2 refer to older and younger chronostratigraphic boundaries. (b) Lateral and vertical variations in facies related to transgression and regression of a shoreline with a clastic source to the west. T1, T2, and T3 are again reference time boundaries. T3 T2 T1 Fundamental Concepts and Nontectonic Structures The three fundamental types of unconformities are disconformities, angular unconformities, and nonconformities. A basal conglomerate composed of clasts of the underlying crystalline rocks may also occur at the base of the sedimentary sequence (Figure 2–21). A disconformity (Figure 2–21a) is produced by deposition of a sequence followed by erosion without tilting or deformation; then comes subsidence and renewed deposition. Bedding in the sediments above and below the unconformity remains parallel. Disconformities can be difficult to identify, but can be recognized where part of a sequence is missing either because it was eroded, or because it was never deposited. Topographic relief may occur along the unconformity. Paraconformities are disconformities with little relief and parallel bedding on both sides. An angular unconformity (Figure 2–21b) is produced where a sequence has been tilted as a result of slumping, or the tectonic processes of faulting or folding. Erosion commonly accompanies or follows tilting. When deposition is renewed, an angular relationship exists between the rocks below and those above the unconformity (Figure 2–22). Although this process can occur rapidly, millions of years typically elapse in the formation of angular unconformities. The angular unconformity at Siccar Point in Scotland (Fig. 2–1) is probably the best known in the world, because there James Hutton gathered some of the evidence that ultimately yielded the Doctrine of Uniformitarianism. A nonconformity (Figure 2–21c) occurs where igneous or metamorphic rocks (or both) occur below the erosion surface, and sedimentary (or metasedimentary) rocks occur above. Nonconformities indicate that a long time interval passed between formation of the igneous or metamorphic rocks at great depths in the Earth and deposition of sediment atop the exhumed and eroded crystalline rock mass. (a) | 31 (a) Disconformity (b) Angular unconformity (c) Nonconformity FIGURE 2–21 Types of unconformities. Note the topographic relief on the ancient erosion surfaces (red lines). Although conglomerate may occur on the erosion surface of any unconformity, it is shown on only (a) and (c). (a) Disconformity, where bedding both above and below the erosion surface are parallel (regardless of later tilting of the entire rock mass). (b) Angular unconformity, where an angular relationship exists between the rocks above and below the ancient erosion surface. (c) Nonconformity, where igneous and metamorphic rocks are truncated by the ancient erosion surface. Characteristics of the rocks above help to identify the boundary as an unconformity rather than an igneous contact, because there is no contact metamorphic aureole. A contact metamorphic zone in the sedimentary rocks would be expected if the contact is intrusive (Figure 2–23). (b) FIGURE 2–22 (a) Angular unconformity between near vertical layers of Jurassic sandstone and gently-dipping Paleocene to Eocene strata in Salina Canyon, Utah. (CMB photo.) (b) Tilted angular unconformity at Kingston, New York, between Ordovician Austin Glen (Normanskill) graywacke and Silurian Rondout Formation (sandy dolostone). This exposure provided some of the first evidence of the Taconic orogeny in the Appalachians. (RDH photo.) 32 | Introduction a period of prolonged weathering before accumulation of erosional debris. Ancient soils (paleosols) are recognized beneath many unconformities. Unconformities are important in structural geology because they mostly record some kind of tectonic event(s). The Early to Middle Ordovician disconformity in central and eastern North America records a tectonic event in the deep lithosphere that produced regional uplift. Angular unconformities provide insight into the timing of mountainbuilding events (with exceptions). Nonconformities record uplift following deformation, metamorphism, and intrusion deep in the crust. Primary Igneous Structures FIGURE 2–23 Nonconformity near Ouray, Colorado, of Devonian Elbert Formation resting on steeply dipping foliated Mesoproterozoic gneiss. Pebbles form a basal conglomerate on the unconformity. Because this unconformity truncates the foliation in the gneiss, it is also an angular unconformity. (Photo courtesy of Ed Hibbert, Delta Airlines, retired.) Disconformities, angular unconformities, and nonconformities may all be represented at an unconformable surface if the rocks below the unconformity are metamorphic, or if the surface changes character laterally. Layering or foliation in metamorphic rocks is commonly truncated at the unconformity, also producing an angular unconformity. The classic unconformity at the base of the Cambrian and Neoproterozoic sedimentary sequences in the Grand Canyon has all of those characteristics (Figure 2–24). Not all unconformities have residual debris, either because no material was deposited at the site of observation or because all debris was removed by erosion. Careful study of the rocks immediately beneath an unconformity may prove that the rocks along the old surface underwent Coconino Plateau Colorado River 2,500 Igneous plutons, pyroclastic flows, and lava flows commonly form in shapes ranging from approximately equidimensional to tabular (one dimension greatly exceeds the other two, as in a dike or sill). Less commonly, they contain features that result from flow within the magma that resemble sedimentary structures. Cross bedding, graded bedding, and other kinds of layering occur in some igneous bodies. The most common primary structures in igneous bodies include flow foliation, phenocrysts, compositional banding, inclusions or xenoliths (enclaves), and vesicles. A foliation consisting of aligned crystals that result from flow of crystallizing magma is difficult to distinguish from a tectonic foliation. Careful study of the structures in the enclosing rocks and texture of the igneous body may be necessary to document crosscutting relationships, or to show that the foliation is confined to the igneous body and is not a tectonic foliation in the country rock (Figure 2–25) Hopi Point 2,155 m Paleozoic Kaibab Limestone Toroweap Formation Coconino Sandstone Hermit Shale Supal Formation Dana Butte 1,478 m Redwall Limestone Muav Limestone Bright Angel Shale Tapeats Sandstone 1,067 m Granite Gorge 1,113 m Pipe fault meters 716 m 500 Mesoproterozoic schist and gneiss Intrusions Sea level FIGURE 2–24 Cross section through the Grand Canyon showing the unconformity at the Precambrian-Paleozoic boundary. Note that the boundary is both an angular unconformity and a nonconformity, where it is underlain by tilted sedimentary rocks or metamorphic rocks, and has considerable relief. (Modified from J. H. Maxson and F. Matthes, 1961, Geologic map of the Bright Angel quadrangle: Canyon Natural History Association, Grand Canyon, Arizona. Scale 1:48,000.) Fundamental Concepts and Nontectonic Structures the facing direction in a flow or sill, but special care must be taken to not mistake the amygdules for phenocrysts. Amygdules and vesicles may occur in layers, thus revealing the horizontal plane. Cracks and brecciated rocks at the tops of lava flows are also a useful indicator of facing direction. Pillow structures form where lava is extruded beneath or flows into water. Because of their shape, they can be used to determine facing direction (Figure 2–27). The vesicular, glassy curved tops and V-shaped nonvesicular bases are indicative of the top of a flow. In strongly deformed pillows this criterion is not useful, but where the pillows are slightly to moderately deformed, particularly in areas where other criteria are scarce or absent, it has been successfully employed as a facing indicator. Pyroclastic rocks, ignimbrites, and water-laid tuffs (volcaniclastic rocks) frequently contain graded beds, reversed graded beds (with large pumice fragments at the top), cross beds, and other primary structures that can provide facing directions. Pyroclastic flows frequently contain structures that are easily mistaken for ductile faults (mylonites; Chapter 10). Rapid facies changes may also occur within volcanic assemblages. Both rapid and gradual changes from volcanic to sedimentary assemblages and from one volcanic rock type to another characterize volcanic regions, making stratigraphic and structural studies more challenging. Resolution of the stratigraphy and younging directions of volcanic assemblages is frequently aided by geochronologic data (see Chapter 3). Contact metamorphic zones associated with sills and flows may be useful for determination of tops and in distinguishing sills from flows. Ideally, a sill (Figure 2–28a) could produce contact metamorphic zones on both the top and bottom contacts with the country rock. Therefore, the use of this phenomenon for tops determination is limited. Phantom Creek (see Chapter 20). Flow of magma also may produce folds in plutons that resemble tectonic structures in metamorphic rocks (Chapter 15). The tectonic aspects of pluton emplacement are discussed in Chapter 20. Compositional banding in an igneous body (Figure 2–26a) may result from crystal settling, differentiation, fractional crystallization, and multiple parallel intrusions or flow processes that flatten xenoliths. Careful study of a layered pluton may reveal a differentiation or fractional crystallization sequence that resulted in the bottom of a pluton being more mafic and the top more felsic. If layering formed by differentiation and gravitational settling, the upward change from mafic to felsic composition may be used to determine the top direction. Graded bedding or cross bedding may exist in rare instances and these features may be used in igneous bodies to determine facing directions in the same way as in a sedimentary sequence, except in a few places where they occur on the near-vertical walls of plutons. Granophyric quartz (intergrown quartz and alkali feldspar) toward the top of gabbroic sills has been used as a facing criterion in several places where differentiation has occurred. One example of where this texture occurs is in the upper part of the Palisades sill in New Jersey and New York. Vesicles are cavities left by gas bubbles that form in magma as the pressure decreases (Figure 2–26b). Vesicles form in pyroclastic and lava flows and, less commonly, in plutons where magma has moved rapidly from deep to shallow levels in the crust. The bubbles move upward, being less dense, and make their way toward the top of a shallow pluton or lava flow, producing a cavity-filled zone that may be preserved and used as a facing criterion. Vesicles may become filled with secondary minerals (e.g., calcite, epidote, zeolites), and as such are called amygdules (Figure 2–26c). Their presence obviously would not affect determination of 1,631 m Tiyo Point 2,366 m Kaibab Plateau 2,500 2,000 1,585 m 1,500 Pipe fault 1,000 meters Isis Temple 2,137 m 33 | Neoproterozoic Mesoproterozoic schist and gneiss Phantom fault 0 1 2 500 kilometers Sea level FIGURE 2–24 (continued) 34 | 121°30' W 40°00' N Introduction Oliver Lake Pluton 121°00' W Bar Bucks Lake Pluton fa ul t u f iver R es er l o n eath Me F h Grizzly Pluton au 5 10 15 kilometers fic ma ltra y bod DDo o oo d k f. ea 39°45' N aakk Pe Merrimac Merrimac Pluton 0 lt woo ggw Camel P 39°45' N 40°00' N Ric FIGURE 2–25 Geologic map of part of the Sierra Nevada Mountains in California showing crosscutting of layering in country rocks by plutons. Granitic plutons are light orange with a crosshatch pattern, gabbro by lavender fill and a + pattern. (After Anna Hietanen, 1981, U.S. Geological Survey Professional Paper 1226-B.) ltlt ffaauu ars Cree k f. Cascade Cascade Pluton Goodye Bald Bald Rock Rock Pluton 39°30' N 121°30' W 39°30' N 121°00' W 121°15' W FIGURE 2–26 (a) Compositional banding in a layered (cumulate) gabbro in the oceanic crustal section of the Semail ophiolite, Oman. The darker layers are composed predominantly of pyroxene and the lighter layers of plagioclase. (CMB photo.) (b) Vesicles and fractures, and (c) amygdules, in the tops of lava flows. (a) Top of flow Vesicles Fractures filled with minerals Fractures Top of flow Amygdules Massive lava (b) Mineral filling of calcite, quartz, epidote, zeolites, or other minerals Bottom of flow (c) Massive lava Bottom of flow Fundamental Concepts and Nontectonic Structures 35 | Chilled margin Vesicular tops Hyaloclasite and breccia Pointed base (b) (a) FIGURE 2–27 (a) Pillow structures in the Semail ophiolite, Oman. (CMB Photo.) (b) Cross section of idealized structure of pillows. A lava flow (Figure 2–28b), on the other hand, should metamorphose only the material below it, and there would be no metamorphism in a subsequently deposited overlying sequence. Thus, if a concordant tabular igneous body occurs in a sequence of sediments, and a contact metamorphic aureole occurs only below it, the body must be a lava flow and is useful for determination of facing direction. Contact metamorphic aureole Gravity-Related Features Sill (intrusive) Xenoliths Landslides and Submarine Flows Landslides occur both above and below sea level, and the results in either case may resemble tectonic structures. Earthquakes or other tectonic activity, either deep in the crust or on the surface many kilometers from the landslide, may trigger slides. The most obvious factor contributing to landslides is slope, but not all sloping surfaces produce landslides. In addition to slopes (some of less than 1°), parallelism of bedding, foliation, or fractures with the surface slope may provide conditions favoring landslides. Weak material at or near the surface may also produce favorable conditions for a landslide, but not actually cause one. Landslide-prone conditions exist in many places. Various phenomena trigger landslides: earthquakes, overloading of slopes, high precipitation, streams undercutting slopes, oversteepening slopes, and human activities. Poorly consolidated water-saturated material—commonly of fine silt or sand size—may spontaneously liquefy when loaded and produce a landslide; earthquakes can provide the necessary shock to liquefy the material. Contact metamorphic aureole (a) Overlying sediments not metamorphosed Weathered zone in top of flow Vesicular top Lava flow Massive base (b) Contact metamorphic aureole FIGURE 2–28 Distinguishing sills (a) from flows (b) by using contact metamorphic aureoles. 36 ESSAY | Introduction eciphering a Major Structure in the Southern D Highlands of Scotland The study by Robert M. Shackleton that was cited near the beginning of this chapter provided an important key to later work in the southern Highlands of Scotland (Figures 2–4 and 2E–1) and illustrates the power of using primary sedimentary features to work out the structure of complexly deformed rocks. To appreciate what Shackleton (1958) accomplished, it is important to know something about the deformed state of the rocks in this region. The sequence he studied consists of Neoproterozoic to lower Paleozoic clastic sedimentary rocks that contain few fossils. At least one early Paleozoic Caledonian regional metamorphic event recrystallized the sequence to greenschist- and amphibolite-facies assemblages. During the thermal event, the rocks were ductilely deformed and subjected to several phases of very tight folding, each of which overprinted the earlier episodes (see Chapter 17 for further discussion of complex folding). Ductile deformation also produced a strong foliation in most of the rocks. Reference Cited Shackleton, R. M., 1958, Downward-facing structures of the Highland Border: Quarterly Journal of the Geological Society of London, v. 113, p. 361–392. Ossia n steep LT EAT GR GLE AU NF oll Athppe na Glen Coe haig anticline Southwest Landsliding may occur along the toe of an advancing thrust sheet or any other escarpment consisting of poorly consolidated or fractured material, particularly in submarine environments. Blocks may fall from the escarpment and be deposited in finer sediment. Masses of matrix-supported blocks such as this are known as olistostromes (bedded) and diamictites (no obvious bedding). Olistostromes may consist of exotic blocks (olistoliths) of any size, ranging from a few centimeters in diameter up to several kilometers, contained within a fine-grained matrix (Figure 2–29). Olistostromes are commonly interlayered with nonchaotic sediments and have a lenticular overall geometry. Mélanges consist of mixtures of weak and strong rock materials—such as fragments of sandstone or basalt in P E N fo er Ab T Cowa antiform l Ben Ledi antiform yle T UL A HL HIG A YF AR ND OU B ND e lin tic an A ris Ard P A Y Loch Awe syncline Northeast km belt E Gr tive an ite Lorney lavas 100 Ra Gr nno an ch ite anticline Islay s thrust ol kerr hS Loc FIGURE 2E–1 Block diagram showing the major structures of the western Central Highlands of Scotland. Note the size of the Tay nappe relative to the other structures in this region, and compare with the geologic section in Figure 2–4. (Reproduced by permission of the Geological Society from The Caledonides in the British Isles—Reviewed, P. R. Thomas, 1979, in A. L. Harris, C. H. Holland, and B. E. Leake, eds., The Caledonides in the British Isles—Reviewed, Geological Society of London Special Publication 8.) Shackleton used the fairly abundant graded bedding and cross bedding that survived the rigors of Caledonian multiple deformation and metamorphism to determine that most of the rocks of the area (covering several hundred square kilometers) in the southern Highlands are downward-facing and therefore overturned. His conclusion must have been initially astounding, but it was reaffirmed by his many determinations of facing direction based on observation of primary sedimentary structures. This kind of observation should be made routinely in the course of the detailed structural study of any complexly deformed area. Other structural or stratigraphic criteria may help to determine if a sequence is upright or overturned, but primary structures may be the only criterion available to enable this important assessment of regional facing directions. NOT TO SCALE Major slides Axial surfaces Facing direction a clay matrix—of either tectonic or nontectonic origin (Figure 2–30). Greenly (1919) first used the term mélange for rocks in Anglesey (northwestern part of Wales) that are characterized by fragments of stronger rock embedded in a sheared matrix of weaker materials. Tectonic mélanges are probably the most common mélanges. They ordinarily form in accretionary prisms within subduction zones and consist of coherent rock masses of different sizes of variously deformed materials contained in a pervasively sheared matrix (Hsü, 1968). They are characterized by mixed assemblages of blocks and more homogeneous products of submarine landslides (olistostromes). Large amounts of strain in the finer-grained materials is also characteristic of mélanges. Other mixtures of coarse and Fundamental Concepts and Nontectonic Structures fine sediment form olistostromes from material broken off an escarpment of either a tectonic or nontectonic origin. Here, the matrix may not be sheared if the mass is preserved relatively undeformed, but the blocks in the mass will be both chaotic and of diverse lithology (Figure 2–31). The term wildflysch has been applied to a heterogeneous accumulation of angular blocks and smaller particles generally deposited in deep-water environments. Such an accumulation may result from either tectonic or nontectonic processes. The angular fragments in a nontectonic olistostrome or mélange may initially resemble those in a fault zone, and care should be taken to establish their origin. Turbidites are deposits produced by rapid flow of a sediment-laden turbidity current down a slope onto the sea floor or the floor of a large lake. They generally consist of an unsorted mass of sediment that cascades to lower levels, spreads out on the floor of the body of water, and settles as graded beds. Bouma (1962) recognized that these flows deposit graded, channeled, massive, and cross-bedded sequences that grade upward from the graded sequence at the base to the more massive and cross-bedded sequences near the top (Figure 2–32), which define a sequence that now bears his name. Because of the cyclic asymmetry of these sequences and the units that they comprise, an intact or partial Bouma sequence is another facing criterion. Complete Bouma sequences are not preserved as commonly as the lower (graded) parts, because of the scouring that accompanies the arrival of the next overlying turbidity flow. Salt Structures Evaporite deposits occur in sedimentary sequences at shallow crustal levels in many parts of the world. Layers of | 37 FIGURE 2–29 Olistostrome (wildflysch) near Albany, New York, composed of blocks of Ordovician Austin Glen Graywacke that were redeposited in Ordovician Normanskill Shale. They were derived from an approaching thrust sheet. (RDH photo.) anhydrite, halite, and gypsum undergo ductile deformation (Chapter 7) more readily than do the more common sedimentary rock types such as sandstone, dolostone, limestone, and shale. Rock salt, composed mostly of halite (NaCl), flows more readily than any other common rock type. Rock salt deposits, tens or hundreds of meters thick and formed by evaporation of seawater, occur in the United States in the Highly sheared matrix Deposition at base of submarine escarpment (fine-grained matrix not sheared) Blocks of diverse sizes and compositions Blocks of diverse sizes and compositions (a) (b) FIGURE 2–30 Formation of mélanges by tectonic (a) and nontectonic (b) mechanisms. 38 | Introduction FIGURE 2–31 Mélange terrane near Tarnilat in northern Morocco. The high hills in the distance are held up by mélange blocks of limestone, and the lower hills and lowlands are underlain by shale. Rocks in the foreground are part of an underlying unit. (RDH photo.) Sand Silt Mud Grain size (to granule at base) Texas-Louisiana Gulf Coast, West Texas, Kansas, Michigan, and New York, as well as in Germany, Poland, Spain, Jordan, Iran, and elsewhere. Salt flows at surface conditions under the force of gravity. The low density of salt (2.16 g/cm3) contrasts with the greater density and strength of the enclosing sediments (e.g., average U.S. Gulf Coast sediments 2.35 g/cm3), and at depth this may cause upward flow of salt masses. A great variety of structures are produced, ranging from salt glaciers at the surface to salt pillows, intrusive stocks, and domes. The internal structure of these salt features provides abundant evidence of plastic flow, with folds, foliations, and other structures resembling those formed in metamorphic rocks at high pressures and temperatures. Salt or other materials—commonly water-saturated “mud lumps”—that move upward and gravitationally intrude the overlying sediments are called diapirs. They are common in the Mississippi Delta and in subductionrelated accretionary complexes with high fluid pressures. They also serve as important hydrocarbon traps. Salt and mud diapirs provide useful analogs for deep crustal diapirs of lower-density rocks (such as granitic magma, Chapter 20) that move upward through denser rocks and form stocks (Figure 2–33). Salt deformation is well studied because of its importance for the formation of large hydrocarbon reservoirs in the U.S. Gulf Coast, the North Sea, Iran, and other regions. A more detailed discussion of salt structures can be found in Chapter 21. E Shale (pelite) D Silty pelite C Rippled or cross-bedded sand B Laminated sand (well sorted) Graded bedding A Sandstone (moderately well to poorly sorted) FIGURE 2–32 Bouma sequence. (Modified from Geologie en Mijnbouw, v. 21, A. H. Bouma, p. 223–227, Fig. 8, © 1962, with kind permission from Elsevier Science, Ltd., Kidlington, United Kingdom.) Fundamental Concepts and Nontectonic Structures 39 | 0 1 centimeters FIGURE 2–33 Sections through diapirs produced in centrifuge experiments showing the shapes of analog structures that resemble those in carefully mapped salt domes and some plutons. Orange-and-white layers are markers with the same mechanical properties. (From Journal of Structural Geology, v. 11, M. P. A. Jackson and C. J. Talbot, p. 211–230, © 1989, with kind permission from Elsevier Science Ltd., Kidlington, United Kingdom.) Impact Structures The surfaces of rocky moons and planets in the solar system reveal a history of impacts spanning billions of years. The Earth probably had a similar history, but evidence of this lengthy impact history is limited because of the dynamic surficial and tectonic processes that constantly change the surface of the Earth. Based on the rate of impact cratering on the other terrestrial planets throughout the history of the solar system, large objects should have impacted the Earth regularly over the past 4.5 billion years. A useful online resource for information on impact craters worldwide is the University of New Brunswick’s Earth Impact Database. It features maps displaying all verified major impact structures on Earth—and more will doubtlessly be discovered in the future. Impact structures generally have circular or elliptical outlines that are not obviously related to tectonic processes. Older (pre-Cenozoic) impact structures are typically deeply eroded, whereas others are buried by younger sedimentary rocks (e.g., Chesapeake Bay structure in Virginia, Chicxulub structure in the Yucatan). Some older craters are deformed by more recent tectonic deformation (e.g., Sudbury, Ontario) (Figure 2–34). Direct evidence of meteorite impact occurs at Meteor Crater in Arizona and includes rare meteorite fragments and the high-pressure (shock-related), low-temperature silica polymorphs coesite and stishovite. Some of the older structures, including the Wells Creek structure in Tennessee (Figure 2–35), Jephtha Knob in Kentucky, Serpent Mound in Ohio, Kentland in Indiana, and Manson in Iowa, were once considered cryptovolcanic structures, related to explosive volcanic activity at depth that disrupted the surface rocks, but did not produce surface evidence of volcanic activity—hence the prefix crypto- (hidden). Many impact craters contain shatter cones (Figure 2–36), which are produced by hypervelocity brittle deformation, similar to that produced by an explosive charge at the bottom of a drill hole, generating cone-shaped fractures propagating down and away from the explosion. Occasionally, shatter cones are obvious in highway cuts, radiating downward from the base of an exhumed drill hole. Where shatter cones can be seen in place, their apices mostly point upward (like those in an exploded drill hole), suggesting impact from above. Careful measurement of the orientation of many shatter cones at the Wells Creek structure indicates a common orientation (Figure 2–37), consistent with impact from above by a body with a trajectory inclined about 10° SU CB MC WC Chx 0 1,000 kilometers FIGURE 2–34 Meteorite impact structures in North America (National Aeronautics and Space Administration). CB—Chesapeake Bay; Chx—Chicxulub crater; MC—Meteor crater; SU—Sudbury; WC—Wells Creek impact structure. See Figures 2–35, 2–36, and 2–37. 40 | Introduction Mw Qal Msl Mw Mw Mw Mw Msl Mw Cu Msl Msl mb er Msl lan d Mfp Qal Msl Mw Qal Ri ve r OM Msl OM Mw Mfp Mw OM Mfp Mw Mw Qal Qal Msl Mw Msl OM Mfp OM Mpsl Msl Mpsl Mw O Ck Msl Mfp Msl Msl OM Mw Mpsl Mw Mpsl Mfp Msl Mw Mw Msl Msl Mw Mw Msl Msl Mw Mfp Mw Msl Mw Msl Msl Mfp Msl Msl Osr Msl Mw 0 1 Mw 2 3 kilometers FIGURE 2–35 Geologic map of the Wells Creek structure in west-central Tennessee. Note the circular character of the outcrop pattern produced by doming and radial and concentric faults that produced steep dips in the core of the structure. Oldest units are exposed in the central part of the structure. OЄk—Knox Group. Osr—Stones River Group. OM—Nashville Group through Chattanooga Shale. Mfp—Fort Payne Formation. Mw—Warsaw Limestone. Msl—St. Louis Limestone. Mpsl—Post-St. Louis Mississippian rocks. Qal—Alluvium. (From C. W. Wilson, Jr., and R. G. Stearns, 1968, Tennessee Division of Geology Bulletin 68.) Fundamental Concepts and Nontectonic Structures | 41 FIGURE 2–36 Shatter cones from the Wells Creek structure in Tennessee. (Specimen courtesy of Richard G. Stearns and John Hanchar, Vanderbilt University.) k loc lb a r t en fc o it im Cu mb erla nd R iv e r f megabrec it o c im ia L L Bolide trajectory Limi t of cen tral block 10° down 35° up 4 25° up 2 3 1 36° up 5 4° up 0 (a) Ring cracks N Rim Rim Ring cracks 1 kilometer Inner graben FIGURE 2–37 Reconstruction of the average orientations (numbered localities with arrows indicating directions and inclinations) of shatter cones at Wells Creek structure. Map (a) indicates an upward but not vertical orientation for the body at impact. Cross section (b) shows the sequential history of impact. (From C. W. Wilson, Jr., and R. G. Stearns, 1968, Tennessee Division of Geology Bulletin 68.) Horst Present Original apparent crater Inner erosion graben Central level uplift Horst Rim Rim Top of Knox Dolomite Top of "basement" 0 (b) 2 kilometers 4 42 | Introduction from the vertical. Estimates based on experiments and measurements of meteors traveling through the atmosphere suggest that the object that produced the Wells Creek structure was about 300 m in diameter, weighed 1.8 to 1.9 × 1010 kg, and was traveling at a velocity of about 40 to 50 km s−1 at the time of impact (Wilson and Stearns, 1968). The importance of large-body impacts on our Moon and other planets is widely known. Although the role of large-body impacts on Earth was vigorously debated a generation ago, impact cratering is now recognized as a significant process here on Earth. This concludes our review of basic principles and nontectonic structures. We now will discuss isotopic systems that have a bearing on structural geology. The next chapter focuses on isotopes and geochronology. Chapter Highlights • Structural geology builds upon many fundamental geological concepts; this chapter reviews those concepts, as well as many primary nontectonic structures that are frequently encountered during structural geology studies. • Fundamental geologic laws (uniformitarianism, superposition, crosscutting relationships, etc.) are commonsense statements that are applicable in most geological settings. • Primary sedimentary and igneous structures, including bedding and primary igneous layering, are distinct from tectonic structures but are useful for determining the relative age of rock bodies and as indicators of deformation. Questions 1. How do we commonly distinguish tectonic from nontectonic structures? Why is it important to do so? 2. How does bedding form in sedimentary rocks? 3. Based on the sedimentary structures in this interlayered sandstone/mudstone sequence, which way is stratigraphically up (younger)? Coin is ~3 cm in diameter. • Unconformities are important geologic contacts that represent gaps in the geologic record where erosion or non-deposition occurred. They may also separate tilted, metamorphosed, or intruded rocks from rocks that have been unaffected by these processes. • Evaporate deposits in sedimentary rocks can flow and form complex geologic structures that are not produced by tectonic processes. • Extraterrestrial objects that strike the Earth’s surface at very high velocities generate a distinct set of nontectonic features, such as impact craters and impact-related structures. 4. Why are current ripple marks (excluding ripple cross laminations) generally not useful for determining facing directions? 5. Why are mud cracks and rain imprints less useful for top determinations than are graded beds and cross beds? 6. How can you tell the difference between a sill and a lava flow that has been buried in a sequence of sedimentary rocks? 7. Why do some areas with conditions that favor landsliding never have slides? 8. What type of geologic contact is exposed in this outcrop (be specific)? The height of the exposure is ~20 m. Unmetamorphosed t ph d dolostone d Massive M i rhyolite rh rhy hy hy Fundamental Concepts and Nontectonic Structures 9. Why are the lower parts of Bouma sequences most commonly preserved? 10. How can you tell an igneous intrusive contact from a nonconformity? 11. How can a nonconformity also be an angular unconformity (see Figure 2–24)? 12. Use the photo and illustration of the famed double unconformity exposed on Beinn Garbh above Loch Assynt in the Scottish Highlands to (a) outline the geologic history and (b) offer an explanation for the geometry of the two unconformities. | SE 43 NW SE NW Cambrian strata ~800 Ma Torridonian strata ~3Ga Ga Lewisian Lewisian Gneiss ~3 Gneiss 250 0 Castle ruin Loch Assynt meters Further Reading Abbate, E., Bortolotti, V., and Passerini, P., 1970, Olistostromes and olistoliths: Sedimentary Geology, v. 4, p. 521–557. Development of the terminology and processes related to the formation of olistostromes and olistoliths. Examples primarily from the Alpine orogen are discussed clearly and summarized. Boggs, S., Jr., 1987, Principles of sedimentology and stratigraphy: New York, Macmillan, 784 p. Contains an excellent treatment of primary sedimentary structures (Chapter 6), in-depth discussion of sedimentary environments, and modern concepts of stratigraphy, including seismic and magnetostratigraphy. Collinson, J. D., and Thompson, D. B., 1989, Sedimentary structures, 2nd edition: London, Chapman & Hall, 224 p. Outlines the kinds and origins of various primary structures in sedimentary rocks. Grieve, R. A. F., 2006, Impact structures in Canada: Geological Association of Canada, GeoText 5, 210 p. Chronicles the geology, geochemistry, and geophysics of most of the known impact structures in Canada. Grieve, R. A. F., and Shoemaker, E. M., 1994, The record of past impacts on Earth, in Gehrels, G., ed., Hazards due to comets and asteroids: Tucson, University of Arizona Press, p. 417–462. Melosh, H. J., 1989, Impact cratering: A geologic process: New York, Oxford University Press, 245 p. Discusses the processes related to impacts and the physical processes that accompany this phenomenon. Rampino, M. R., 2017, Reexamining Lyell’s laws: American Scientist, v. 105, p. 224–231. Suggests that major catastrophic events are not random, but occur on a 30-million-year cycle based on the passage of our solar system through the mid plane of the Milky Way Galaxy. Reineck, H. E., and Singh, I. B., 1975, Depositional sedimentary environments: Berlin, Springer-Verlag, 439 p. Contains outstanding illustrations and photographs of sedimentary structures and textures, and discussions of modern depositional sedimentary environments. Shackleton, R. M., 1958, Downward-facing structures of the Highland Border: Quarterly Journal of the Geological Society of London, v. 113, p. 361–392. The author employed sedimentary structures to decipher a major tectonic structure in the southern Highlands of Scotland. Shea, J. H., 1982, Twelve fallacies of uniformitarianism: Geology, v. 10, p. 455–460. An interesting and very succinct paper that discusses some of the problems with the Doctrine of Uniformitarianism. 3 Geochronology in Structural Geology Time present and time past Are both perhaps present in time future And time future contained in time past. T. S. ELIOT, 1935, Four Quartets In this chapter we discuss how isotopic systems are harnessed to determine when magmatism, deformation, and even tectonic uplift occurred. Structural geologists have an array of tools and techniques that enable us to infer the temperature, pressure, and geochemical conditions to which rocks were subjected during deformation. A time and depth history of rocks, regions, and terranes is revealed when integrated with temporal information. This is an exciting time, as many of these techniques were not available a generation ago and modern geologists are learning about the dynamics and history of crustal deformation in ways that were never before possible. Geochronology Geology differs from most sciences in that historical events are important. In addition to understanding the geometry, kinematics, and mechanics of deformation, structural geologists strive to know when deformation occurred, and if and when only one, or more than one, deformation or metamorphic event affected the rocks of interest. Consider the hypothetical exposure in Figure 3–1: a folded sequence of quartzite and schist is exposed in the western part of the outcrop; these rocks are unconformably overlain by sedimentary rocks that are deformed into upright folds with an axial planar cleavage developed in the shale layers. Both the deformed metamorphic and sedimentary rocks are crosscut by a set of steeply dipping basalt dikes. The upper part of the outcrop exposes flat-lying sedimentary rocks that are cut by a high-angle fault flanked by a debris fan of boulder gravel on its downthrown side. How many deformation events affected these rocks? When, in both relative and absolute terms, did deformation occur? The folds in the metamorphic rocks are truncated against the unconformity (both an angular unconformity and a nonconformity), thus a deformational and metamorphic event occurred prior to deposition of the sedimentary rocks. The basalt dikes postdate folding of the sedimentary rocks and are truncated against the angular unconformity. A close look at the limestone reveals the presence of crinoids and the distinctive bryozoan Archimedes (Figure 3–1). Based on 44 Geochronology in Structural Geology West Maple leaf Debris fan with bouldery gravel 45 | East Weakly cemented sandstone with siltstone lenses Archimedes Axial planar cleavage Sandstone with basal conglomerate Quartzite and schist Crinoids Limestone Shale Thrust (reverse) fault Foliation Basalt dike FIGURE 3–1 Outcrop exposing multiple geologic units. The relative timing of deformation is evident from crosscutting relations, but when did folding, faulting, and metamorphism occur? What kind of unconformities are present and where are they? this fossil assemblage, these sedimentary rocks were deposited between the Mississippian and Permian periods (360 to 250 Ma). (See Geologic Time Scale, inside back cover.) In the uppermost sedimentary strata, impressions of maple leaves (genus Acer, an angiosperm) are present (Figure 3–1), indicating that the sequence is no older than the Paleogene (65 to 25 Ma). Thus the oldest deformation event, recorded in the metamorphic rocks, must be older than the late Paleozoic, while deformation of the sedimentary sequence and dike intrusion occurred after the Paleozoic (250 Ma), but before the Paleogene (65 Ma). The high-angle faulting cuts the Paleogene sedimentary rocks, but when did faulting occur and is this fault an active seismogenic structure today? Crosscutting relations and dating based on fossils provide broad constraints, but how best to determine when, numerically, the igneous, metamorphic, and deformation events occurred? This is where isotopic dating proves its merit. In this section we consider the theory, details, and assumptions associated with radioisotope dating and introduce a number of commonly employed isotopic systems. Throughout this section we will refer to the outcrop in Figure 3–1 to frame how isotopic dating helps structural geologists decipher the history of deformed rocks and regions. Radioactivity and Isotope Geochronology Chemical elements have stable and radioactive forms— all of which are isotopes of the given element. The most abundant isotopes of elements with atomic number (Z) 82 (Pb—lead) and below in the periodic table are stable. Above element 82 all isotopes of all elements are radioactive. Over time radioactive isotopes spontaneously decay to stable elements (frequently through a series of intermediate steps) by losing subatomic particles and giving off heat. The original radioactive atom is known as the parent and the new stable atom as the daughter. For instance, carbon-14 (14C) decays directly to nitrogen-14 (14N) by giving off a β particle (basically an electron generated in the nucleus). Uranium-235 (235U) through a series of intermediate daughter products that release α (basically a helium atom with the electrons removed) and β particles (plus γ radiation) decays to lead-207 (207Pb). The rate at which the parent atoms decay is given by dP = −λ P (3–1) dt where P represents the number of parent atoms present, t is time, and λ is the decay constant. Thus the rate of radioactive decay is directly related to the number of radioactive atoms; the more radioactive atoms that are present means that, for any time interval, more atoms will decay to the daughter. Equation 3–1 can be integrated between the initial number of atoms P0 at time t0 to yield an expression that relates the number of parent atoms to time as P dP ∫P0 P t = −λ ∫ dt (3–2) t0 and yields the general equation that describes the decay of a population of parent atoms P = e−λλt. (3–3) The curve tracking the percentage of parent atoms (relative to the original quantity) through time has a negative | Introduction exponential form (Figure 3–2a) decreasing as a function of e, the base of natural logarithms. Each isotopic system decays at its own rate (thus λ for 14 C differs from λ for 235U), the decay constant. The unit for the decay constant is reciprocal years or yr−1 (read per year). Although the decay constant appears to be an odd unit, it can be thought of as the percent chance that a given radioactive atom will decay in a given year. The rate at which radioactive isotopes decay has been accurately measured in the laboratory. A more specific solution of e quation 3–3 is 100 207 80 % of atoms 46 Pb 60 40 Pf = P0 e−λλt (3–4) where Pf equals the number of parent atoms remaining after a time t and P0 equals the original number of parent atoms in the sample at time t0. While the number of the parent atoms continuously decreases with time, the number of daughter atoms (D) grows over time (Figure 3–2a) following this relationship  1  D ln  + 1 (3–6)   λ P where D/P is the daughter/parent ratio and ln is the natural log function. In order to determine the age of a mineral or rock (containing a radioactive isotope), we need to measure the daughter/parent ratio and know the decay constant for that particular isotopic system. Half-life (t1/2) is another important concept related to radioactive isotopes and is simply the time required for a population of parent atoms to decrease by half. 235U has a half-life of 704 million years (Figure 3–2a), whereas 14C has a half-life of 5,573 years. The half-life and decay constant for a particular isotopic system are directly related: consider equation 3–4 and substitute 1/2P0 for Pf ; canceling terms and rearrangement yields  ln 2  t1/ 2 =   .  λλ  0 (3–7) Because half-life is expressed in years, it is an easier quantity to understand than the decay constant, but recall that in conjunction with a measured value for D/P, the decay constant is used to determine the age of geologic materials. 0 U 500 1000 1500 2000 2500 3000 3500 4000 Time (millions of years) (a) (3–5) For most minerals and rocks, we do not know the total number of parent atoms that made up the starting material, thus the age of the material cannot generally be determined from the abundance of parent atoms. There is, however, a relationship between the number of parent and daughter atoms with respect to time (Figure 3–2b). With time t, the number of daughter atoms increases at the expense of the parent atoms, so the daughter/parent ratio also increases; the relationship is given by t= 235 4000 3500 Time (millions of years) D = P0 (1 − eλλt ) . 20 3000 2500 2000 1500 1000 500 0 (b) 0 10 20 30 235 U/ 40 50 60 207 Pb FIGURE 3–2 (a) Parent and daughter curves over time. (b) Parent-to-daughter (P/D) ratio over time. Closure Temperature The closure or blocking temperature (Tc ) is the decreasing temperature at which diffusion of a particular daughter element out of a mineral effectively ceases. Diffusion is a chemical process whose rate strongly depends on temperature. Above the closure temperature the daughter element “leaks” out of the lattice (Figure 3–3a). Below the closure temperature the daughter product is essentially trapped within the crystal lattice of a mineral (Figures 3–3b and 3–3c). The closure temperature is different for each daughter element and for different minerals because of the differences in crystal structure, bond type, and bond Geochronology in Structural Geology T> > 500° 500° C C 40 Ar 40 muscovite 40 Ar 40 Ar 40 T= 400° C C = 400° 40 Ar K 40 40 Ar Ar Ar 40 40 40 40 40 K 40 40 Ar Ar 40 Ar hornblende (a) 40 Ar 40 K Hornblende closed; muscovite open Ar K Ar Ar Ar 40 Diffusion out of both minerals 40 47 40 Ar 40 40 Ar Ar Ar Ar 40 40 T= 300° C C = 300° 40 K | (b) 40 Ar K 40 Ar Hornblende closed; muscovite closed (c) FIGURE 3–3 Closure temperature in the K-Ar system. (a) T > 500° C, 40Ar diffuses out of both hornblende and muscovite. (b) T = 400° C, Ar is trapped in hornblende but still diffuses out of muscovite. (c) T = 300° C, 40Ar is trapped in hornblende and muscovite. 40 Closure temperature (° C) 100 200 300 400 500 600 700 800 900 FIGURE 3–4 Closure temperatures for various isotopic systems and minerals. U/Pb, zircon U/Pb, monazite U/Pb, titanite U/Pb, rutile 40 Ar/39Ar, hornblende 40 Ar/39Ar, muscovite 40 Ar/ Ar, biotite 40 Ar/39Ar, K-feldspar ? ? 39 fission track, zircon fission track, apatite (U-Th)/He, zircon (U-Th)/He, apatite strength within the lattice (Figure 3–4). Other factors that influence diffusion of elements out of mineral grains include cooling rate, grain size, and the microstructures within the lattice. Closure temperatures are determined both experimentally and from thermodynamic properties. Most isotopic ages are a measure of the time that has elapsed since a mineral cooled below its closure temperature for that mineral and for a given isotope. Consider a volcanic rock extruded at high temperature (~900° C) on the Earth’s surface and then cooled quickly to surface temperature (Figure 3–5a). An isotopic age effectively dates the time of extrusion because the lava cooled rapidly. Conversely, many metamorphic rocks cool slowly during exhumation such that ages determined from some isotopic systems are cooling ages and do not reflect the timing of peak metamorphism or necessarily deformation (Figure 3–5b). A picture of the time-temperature history can be constructed by determining isotopic ages from the same rock using different isotopes that have a range of closure temperatures. This process is known as t hermochronology. Some minerals form at temperatures below their closure temperature; for instance, a mineral may precipitate in a newly formed crack, such that the isotopic age is a growth age (Figure 3–5c). If a mineral formed below its closure temperature during deformation, the growth age effectively dates the deformation. Interpretation of isotopic ages must be tempered by the geologic history of each setting. Assumptions Radioisotope geochronology is based on a number of assumptions that must be correct for isotopic age data to have any geological meaning. A first-order assumption is that the rate of isotopic decay has been constant and has not varied over geologic time. Numerous studies have demonstrated that radioactive decay is not disturbed by heat, pressure, fluids, or chemical reaction. A common misconception is that radioactive decay starts after a mineral has crystallized; radioactive elements are decaying to 48 | Introduction lava flow erupted isotopic age = crystallization age Temp 900° C Volcanic Rock Tc (a) time isotopic age = cooling age peak metamorphism Temp Regional metamorphism/ deformation Tc (b) Deformed rock time isotopic age = growth age Temp crack opens mineral forms Tc 1 cm (c) crack opens mineral forms time FIGURE 3–5 (a) Crystallization age for fast cooling volcanic rock. (b) Cooling age for slow cooling of a regional metamorphic setting. (c) Growth age for mineral precipitated below the closure temperature (Tc). their daughter products in the magma chamber, but in the magma there is no mechanism to effectively “trap” either the parent or daughter atoms until minerals crystallize and incorporate those decaying elements in their lattices. Once a mineral has formed (crystallized, precipitated, etc.) it must remain a closed system for the parent/daughter ratio to be a function of time. Put another way, there can be no loss or gain of either parent or daughter isotopes since the mineral formed. Loss of an element may occur via dissolution due to hot fluids or chemical weathering at or near the surface. Similarly, elements may be added to the mineral by fluids percolating through the material (discussed in more detail later in the chapter). Fortunately, there are ways to evaluate whether an isotopic system has remained closed or has been opened. Even if the system has been open at some point during its history, some information may be gleaned from the isotopes. Radioisotopic Dating Techniques URANIUM-LEAD METHOD Uranium-lead geochronology is one of the most reliable and thus widely used isotopic systems for dating ancient rocks. Uranium has three naturally occurring isotopes, all of which are radioactive, with 238U and 235U accounting for over 99.99 percent of the total. We will focus on U-Pb dating using zircon (ZrSiO4) as an example of the method, Geochronology in Structural Geology although other minerals that contain uranium, such as monazite [(Ce, Y Th)PO4] and baddeleyite (ZrO2), are also useful. Zircon is a mineral that crystallizes at high temperatures (~900° C), forming an accessory mineral in many felsic to intermediate igneous rocks (Figure 3–6a). When a zircon forms it typically incorporates a small quantity of uranium (substituting for Zr), but also contains little to no lead. As the mineral ages, uranium isotopes decay through a series of intermediate radioactive elements to stable daughter products: 238 235 U → 206Pb U → 207Pb t1/2 = 4.47 × 109 yr t1/2 = 7.04 × 108 yr. Because the most abundant isotopes of uranium are unstable, an age for a particular zircon (or population) can be determined from both the 238U/206Pb and 235U/207Pb ratios. Ideally, the age determined from both systems is the same and the age is concordant. Graphically, for any given age, the ratios of 238U/ 206Pb versus 235U/ 207Pb form a line known as a concordia curve (Figure 3–6b). It is not uncommon for the isotopic ratios from a population of zircons to not plot on the concordia curve (e.g., the 238U/ 206Pb age differs from the 235U/ 207Pb age). These zircons are discordant and the mineral may have behaved as an open system at some point during its history. Discordant zircons generally plot below the concordia curve, indicating the zircons have less lead than would be expected for the quantity of uranium present (Figure 3–6c). In many cases, populations of discordant zircons (from the same sample or suite of samples) plot such that a trend line that intersects the concordia curve can be drawn through the points (Figure 3–6c). The upper and lower intercepts of this line may be geologically meaningful. For instance, the lower intercept (younger age) may 1 4000 Ma 4000 Ma 0 100 μm U 238 2000 Ma (b) 0.4 20 2000 Ma 0.2 500 Ma 0 Ma 10 Discordant zircons Lower intercept 1500 Ma 1000 Ma 0 3000 Ma 0.6 ve ia cur cord Upper intercept Pb/ 2500 Ma 0.4 Con 0.8 Concordant age 3000 Ma 0.2 (a) 1 ve ia cur cord Con 3500 Ma 0.6 49 result from episodic lead loss due to reheating, or the lower intercept age may represent the age of the rock if there was inheritance of older zircons (zircons that are partially absorbed into the magma from the host rock). The upper intercept may represent the age of the rock (in the case of episodic lead loss) or the age of inherited zircons. What we have just described is the conventional method for U-Pb dating of zircons. Today it is embodied in the TIMS (thermal ionization mass spectrometer) method. This method is especially accurate and precise if the zircons have a minimum of discordance, indicating the zircons crystallized in an igneous body without any complications. Inheritance of older zircons in a magma or the rock mass being subjected to metamorphism later may cause the zircon population to be discordant. The new geologic time scale (Walker et al., 2013) is based on a combination of very accurate age dates on volcanic ash beds (or other suitable material) and fossils from the same or nearby layers. If the zircons contain inherited earlier components, metamorphic rims, or other complexities, newer techniques permit analysis of minute amounts of vapor generated by a thin ion or laser beam submicroscopic spots on individual zircons. These are collectively referred to as SIMS (secondary ionization mass spectrometry), and include the use of an ion microprobe (e.g., a SHRIMP: sensitive high-resolution ion microprobe), or an LA–ICPMS (laser ablation inductively coupled plasma mass spectrometer). These techniques provide information about the timing of formation of different components of individual zircons and zircon populations that would otherwise be impossible to obtain. Traditionally, zircon geochronology involved the separation of zircon grains from the surrounding rock, partitioning the zircon populations based on size or morphology, followed by dissolution of the respective populations in 206 206 Pb/238U 0.8 | 30 40 207 235 Pb/ 50 U 60 70 0 80 (c) 1000 Ma 0 10 20 30 207 40 Pb/ 50 60 70 80 235 U FIGURE 3–6 (a) Photomicrograph of needle-like zircon grains from the Rabun pluton, northeast Georgia. (b) Concordia diagram illustrating c oncordant age at 3,400 Ma. (c) Concordia diagram with a discordant population of zircons. Trend line through discordant zircons intercepts concordia curve at two locations (upper and lower intercept). (Part [a] from B. V. Miller et al., 2006, Geological Society of America Bulletin.) 50 | Introduction acid to prepare the sample for the mass spectrometer, where the isotopic ratios are measured. A significant advance in zircon geochronology came with the advent of in situ analysis using an ion microprobe or an inductively coupled plasma mass spectrometer (ICP–MS). An ion beam bombards a narrow “spot,” typically 10 to 30 μm in diameter, and an age is calculated for the U, Th, and Pb that are vaporized at the spot. A number of analyses can be performed for a single grain such that the age of cores, rims, and overgrowths may be determined (Figure 3–7). Because zircon melts at very high temperatures (> 900° C), a central core of a zircon in an igneous rock may record an older (inherited) age than the time of crystallization for a felsic igneous rock. Zircons can also grow at temperatures below their closure temperature, and in many high-grade metamorphic rocks older zircons may have overgrowths formed during the m etamorphic event. Monazite, titanite (sphene), garnet, rutile, xenotime, and baddeleyite (ZrO2) all incorporate some uranium into their crystal lattices. The closure temperature for U-Pb in monazite is ~700° C, in titanite is 550° to 650° C and for rutile is ~400° C (Figure 3–4); collectively these minerals, FIGURE 3–7 Comparison of two different ages from the Rabun pluton and the zircons from which they were derived. (a) Hand specimen and zircons determined by TIMS (top right image); compared with zircons from the same rock body (lower left photo) determined by SHRIMP geochronology showing spot ages (bottom right image). (b) Concordia plot of the TIMS data. (From B. V. Miller et al., 2006, Geological Society of America Bulletin.) (c) (1) Tera-Wasserberg (an alternative way to plot these data) and (2) Concordia plots of the SHRIMP data, along with a probability plot (3) that shows the distribution of the zircon population through time. (From D. W. Stahr, III, 2008, M. S. thesis, University of Tennessee.) 100 μm 2 cm 346.1 ± 0.9 338.2 ± 1.2 341.7 ± 1.2 336.2 ± 1.4 965 ± 45 207 206 Pb/ Pb (discordant) 1131 ± 6 207 206 Pb/ Pb 349.8 ± 0.9 100 m GQ1450 (a) 0.09 zircon (shaded ellipses) 335.1 ± 2.8 Ma 340 and 64 ± 260 MSWD = 0.41 Z1 360 xenocrystic zircon 327 & 1115 Ma magmatic rims Z2 0.45 0.0515 0.376 0.380 0.384 0.388 0.392 0.396 0.400 0.404 235 U/ 207Pb 0.04 0 4 8 238 (c) (1) 0.060 and 29 ± 560 MSWD = 1.3 ity crystallization ~340 Ma 350 12 U/ 206Pb 16 20 24 Probability plot 370 340 ± 12 Ma 0.058 0.06 0.05 0.05 0.35 (b) 10 0 Z7 00 0.07 80 440 400 328 0 600 400 Pb/ 206Pb Z4 Z6 0.0525 336 207 U/ 206 Pb Z5 332 480 Tera-Wasserberg plot 120 Z8 Z3 238 0.0535 1400 0.08 520 monazite (open ellipses) 334.0 ± 0.9 Ma xenocrystic cores 344 Rabun pluton (RAB02-01) 0.0545 360 Geochronology in Structural Geology 0.45 235 U/ 207Pb 0.04 0 238 12 U/ 206Pb 16 20 | 51 24 Probability plot and 29 ± 560 MSWD = 1.3 FIGURE 3–7 (continued) Relative Probability crystallization ~340 Ma 350 U/ 206Pb 0.056 340 0.054 238 330 0.052 320 0.048 0.28 8 370 340 ± 12 Ma 0.050 4 (c) (1) 0.060 (c) (2) 80 0 Pb Z2 0.0515 0.376 0.380 0.384 0.388 0.392 0.396 0.400 0.404 0.058 magmatic rims 0.05 0.05 0.35 (b) 0.06 600 Z1 xenocrystic zircon 327 & 1115 Ma 400 328 Z7 400 Z6 0.0525 440 Z4 207 U 238 Z5 332 xenocrystic zircon cores ~450, ~950 Ma, ~1.0, 1.05, and 1.2 Ga 310 Concordia plot 0.32 0.36 235 0.40 0.44 300 U/ 207Pb FIGURE 3–8 (a) Thorium composition map of a monazite grain from the East Athabasca mylonite triangle, Saskatchewan. Interior of the grain yields an age of 2,450 Ma, whereas the overgrowths yield an age of 1,809 Ma inferred to be age of deformation. Red shades are higher concentrations of Th; yellow to white shades are lower Th concentrations. (b) Interpretation of dextral shearing (Chapter 10) and growth of monazite during deformation in the field of extension. (From Williams and Jercinovic, 2002.) 500 700 900 1100 1300 Age (Ma) (c) (3) M201 Th Ma 2450 Ma 1809 Ma (a) in addition to zircon, can be used to better understand the temperature-time path that a rock has followed. Monazite is an interesting mineral because, in rocks of sufficient age, an electron microprobe (in contrast to a mass spectrometer) can be employed to determine the U-Th-total Pb age (actually a “chemical” age, not an isotopic age) of domains within an individual grain and, in many cases, resolve the timing of deformation-related mineral growth (Figure 3–8). The key assumption in this method is there is no initial common lead, 204Pb, in the sample. Monazite is a useful mineral for determining the time of metamorphism and accompanying deformation. Zircon is a mechanically tough and chemically resistant mineral; consequently, it forms a common accessory (detrital) mineral in siliciclastic sedimentary (and metasedimentary) rocks. In the exposure illustrated in Figure 3–1, detrital zircons likely occur in the quartzite, the folded sandstone, and the flat-lying sandstone. These detrital zircons could be dated with the U-Pb method, but what information would that provide? Detrital sedimentary rocks incorporate minerals (and rocks) that formed 40 μm (b) prior to the deposition of the sedimentary rock; the age of the detrital zircons does not date the time of deposition, but rather provides information on the age of the source rocks (provenance). Detrital zircons can be used to establish the maximum age of a sedimentary rock, because a sedimentary rock can be no older than the youngest detritus (clasts) it contains. Figure 3–9 is a histogram and probability plot of detrital zircon ages from the quartzite in Figure 3–1; 125 individual zircon grains were dated and there are two distinct age populations (660–600 Ma and 1,000–900 Ma), with the youngest grain yielding an age of 580 Ma; thus the quartzite can be no older than 580 Ma. The source area that contributed sediment to the quartzite would have exposed rocks containing both 660–600 Ma and 1,000–900 Ma zircons. Combining fossil data from the overlying strata with the detrital zircon ages constrains the deposition of the metasedimentary sequence to the late Neoproterozoic and the Permian (580–250 Ma). The deformation and metamorphism of the metasedimentary sequence are also bracketed by the detrital zircon data. 52 | Introduction been useful to structural geologists attempting to work out the prehistoric earthquake activity in karst regions, provided they can relate the event to a seismic event in prehistoric times. Relative probability Number of detrital zircons 30 20 Youngest zircon 580 Ma 10 RUBIDIUM-STRONTIUM METHOD AND 87SR/86SR RATIOS Rubidium is a minor element that commonly substitutes for potassium and as such occurs in a number of rockforming minerals, especially the feldspars and micas. Strontium is an alkaline earth element that commonly occurs in Ca-bearing minerals. The decay scheme for Rb is 87 0 500 600 700 800 900 1000 Age (Ma) FIGURE 3–9 Histogram and probability plot of detrital zircon data from the quartzite in Figure 3–1. There are two age populations of detrital zircons (660–580 Ma and 980–880 Ma); thus the depositional age of the quartzite is younger than 580 Ma. Detrital zircon analysis has become common, as advances in mass spectrometry have enabled the rapid dating of individual grains. Detrital zircon age populations provide valuable information for both provenance and tectonic studies. In Paleozoic sandstones from the Appalachian foreland basin, Eriksson et al. (2004) demonstrated that the sequence is dominated by zircons formed during the 1.2 to 1.0 Ga Grenvillian orogen, but were recycled during Paleozoic orogenies. Dickinson and Gehrels (2003, 2009) dated detrital zircons in Jurassic eolian sandstones on the Colorado Plateau and concluded that these sediments were ultimately derived from rocks in the Appalachians and transported to western North America via a massive transcontinental river system (Figure 3–10), indicating a very different paleogeography for North America during the middle Mesozoic. URANIUM SERIES DATING While the common isotopes of U and Th have very long half-lives that permit us to date old rocks, they decay into relatively short-lived intermediate daughter products that have proved very useful for dating materials that formed during the past 600,000 years (Edwards et al., 2003). Decay of 234U to 230Th (t1/2 = 248,000 s) is commonly used for this technique. Dating of carbonate rocks, coral reefs, speleothems (cave deposits), and other young materials has provided information on recent Earth history. Dating of broken and recemented stalactites has Rb → 87Sr (t1/2 = 48.8 × 109 yr). The extremely long half-life for 87Rb makes this method best suited for rocks with ages that exceed 100 million years. Not all of the 87Sr in a mineral or rock is derived from the radioactive decay of 87Rb. Normalizing with 86Sr, a stable isotope (where 87Sr/ 86Sr is the initial ratio of the two isotopes), and combining with the decay equation yields 87 Sr/ 86Sr = (87Sr/ 86Sr)i + 87Rb/86Sr (eλt − 1) (3–8) that is employed for age determination. The values of 87 Sr/86Sr and 87Rb/86Sr for several minerals from the same rock (or the whole rock) are plotted on an isochron diagram and ideally the points will plot along a straight line producing an isochron. The age of the sample is calculated from the slope of the isochron (Figure 3–11). Consider an igneous rock at the time of crystallization. Analyses of individual minerals will plot along a straight line with a slope of zero, because they all have the same initial 87Sr/86Sr ratio (although different minerals such as K-feldspar and biotite will contain different amounts of Rb). With time, the decay of 87Rb reduces the 87Rb/86Sr ratio and increases the 87Sr/86Sr ratio by the same amount. These ratios change along a straight line with a slope of −1 such that the slope of the isochron increases over time (Figure 3–11a). Figure 3–11b is an isochron diagram of both whole-rock and plagioclase analyses from the basaltic dikes in Figure 3–1. These data fall along a line with a slope of 0.0033, which corresponds to an age of 230 Ma (Triassic). The basaltic dikes crosscut the Paleozoic sedimentary rocks; thus, the deformation event that folded the sedimentary rocks occurred prior to the Triassic. The y-intercept on an isochron diagram represents the initial 87Sr/86Sr ratio, or (87Sr/86Sr)i in equation 3–8. Studies of isotopic compositions reveal that middle to upper continental crustal rocks have an initial ratio of > 0.706, but oceanic crust, Rb-depleted lower continental crust, and mantle rocks have initial ratios < 0.706. The initial 87Sr/86Sr ratios for plutonic rocks in the western United States | Geochronology in Structural Geology 110° W 120° W Ear ly N 70° W James Bay Ju r a s s i c Grenville provinvce (1.0–1.3) Superior province (> 2.5) 50° N shor Canada U SA AppalachianOuachita Paleozoic lin e e elin re Cordilleran accreted and Mesozoic e sh o Penokean (~1.85) residual ARM (?) (1.4–1.8) Paleozoic platform 40° Ce ntra l pa leo (tru rive nk r stre am ) n d le oz 30° N o rog en Pa fo re la Jurassic eolian sandstones N n ddl sic si Mi N s Ju r a a 40° Hudson Bay 80° W 90° W b 50° 100° W Trans-Hudson (1.8–1.9) 53 USA Mexico Ou e lf Oaxaquia (1.0–1.25) 500 kilometers a c h ita 110° W 100° W e e dg 0 30° N Accreted Pan-African ? ? ? sh PA C I F I C OCEAN AT L A N T I C OCEAN o i c Yucatan-Campeche 90° W 80° W FIGURE 3–10 Mesozoic paleogeographic map of North America based, in part, on detrital zircon data. ARM—Ancestral Rocky M ountains. Numbers in parentheses are crustal ages in billions of years. (Modified from Dickinson and Gehrels, 2009, Geological Society of America Bulletin.) exhibit a clear-cut division that likely represents a boundary between Precambrian North America and the accreted terranes to the west (Figure 3–12). Although the Rb-Sr method has been utilized to date igneous, metamorphic, and sedimentary rocks (using authigenic clays), the Rb-Sr system is easily reopened by later metamorphism and hydrothermal fluids. Rb-Sr dating has generally been eclipsed by other dating methods in the past two decades, but the 87Sr/86Sr ratio is still a very useful tool for determination of crustal origin. POTASSIUM-ARGON AND 40ARGON/ ARGON METHODS 39 K is a radiogenic isotope that decays by a branching process into 40Ca and 40Ar. Although only a small percentage of the decay events yield 40Ar, it is still a viable method 40 because of the abundance of potassium in many rockforming minerals, such as the micas, hornblende, and the feldspars. 40 K 40Ca + β− 40 Ar (3–9) The 40K-40Ar method can be used to date igneous, metamorphic, and sedimentary minerals. The closure temperature for the 40K-40Ar system is relatively low (Figure 3–4) and age determinations for minerals such as K-feldspar, biotite, and muscovite are typically cooling ages in regionally metamorphosed terranes. The 40K-40Ar system is hampered by difficulties in measuring the absolute concentrations of the parent and daughter products as well as by argon loss at very low temperatures. 54 | Introduction 0.7057 0.7057 0.7056 0.7055 Sr/86Sr 0.7054 87 0.7053 87 Sr/86Sr 0.7056 T1 0.7055 Sr/86Sr = .0033(87Rb/86Sr) + 0.705 Age = 230 Ma 87 0.7052 0.7054 0.7053 0.7052 0.7051 Slope = 0.0033 0.7051 T0 0.7050 0 0.02 0.04 0.06 0.08 87 0.10 0.12 0.14 86 Rb/ Sr (a) 0.7050 0 (b) 0.02 0.04 0.06 87 0.08 0.10 0.12 0.14 86 Rb/ Sr FIGURE 3–11 (a) Rb/Sr isochron diagram, at T0 = all minerals (red diamonds) have the same 87Sr/86Sr ratio, but different 87Rb/86Sr ratios; with time the 87Sr/86Sr ratio increases and the 87Rb/86Sr ratio decreases, producing a sloping line at T1 (yellow diamonds). (b) Isochron plot for both whole-rock and plagioclase analyses from the basalt dikes in Figure 3–1; these data (orange diamonds) fall along a line with a slope of 0.0033, corresponding to an age of 230 Ma, and had an initial 87Sr/86Sr ratio of 0.705 (the y-intercept). Younger cover Displaced terranes 119° W 115° W WA OR Sonomia Precambrian North America 111° W > 0.706 < 0.706 ? 42° N ? ? ID UT ? North American Sonomia Sa > 0.706 NV A C Pacific Ocean lt au sf rea 38° N nd nA Continent 0 300 kilometers FIGURE 3–12 Map of western United States showing the 0.706 line (heavy dashed line) that separates North American terranes to the east from accreted terranes to the west. (Modified from Speed, 1982.) A refinement of the 40K-40Ar technique employs samples irradiated with neutrons in a nuclear reactor such that 39 K is converted to 39Ar. 39Ar effectively serves as a proxy for the parent isotope 40K, and calculated ages are based on 40Ar/39Ar ratios. An advantage of the 40Ar/39Ar method over the conventional method is that a sample can be incrementally heated (either in a furnace or by a laser) so that a spectrum of dates can be calculated. Ideally, the age obtained for each increment should be the same, thereby forming a plateau on a graph of age versus cumulative gas released during heating (Figure 3–13a). An irregular release spectrum permits the identification of samples containing excess argon or that experienced argon loss (Figure 3–13b). Multiple 40Ar/39Ar age populations on a spectrum may reveal both a detrital and a metamorphic component in the sample. Returning to the exposure in Figure 3–1, 40Ar/39Ar ages of muscovite in the schist yield ages of 440 Ma (Figure 3–13a), further bracketing the time of deformation. If the schist was subjected to peak metamorphic temperatures of > 350° C, these 40Ar/39Ar ages are cooling ages and provide a minimum age for the deformation event. Based on the geochronology, we know that the sedimentary protoliths for the quartzite and schist were deposited after 580 Ma (from detrital zircon ages), then metamorphosed and deformed by 440 Ma (from 40Ar/39Ar ages) and exhumed to the surface by the mid-Paleozoic (based on fossil ages in the overlying strata). Given the ubiquity of different K-bearing minerals (each with its own closure temperature), the 40Ar/39Ar technique is a powerful method to learn about deformation, cooling history, and uplift in upper and middle crustal terranes. In British Columbia, the Coast shear zone forms a major crustal boundary characterized by ductile deformation that is overprinted by brittle deformation (Figure 3–14a). 40Ar/39Ar cooling ages across the Coast shear zone indicate that the region cooled below | 55 80 100 Geochronology in Structural Geology 600 600 500 Plateau at ~440 Ma Apparent age (Ma) Apparent age (Ma) 500 400 300 200 100 0 400 300 200 100 20 0 40 60 80 Cumulative % 39Ar released (a) 0 100 20 0 40 60 Cumulative % 39Ar released (b) FIGURE 3–13 (a) Argon spectrum for the muscovite schist in Figure 3–1 illustrating the age versus the cumulative 39Ar released during heating. Note the ages are similar and define a “plateau” at ~440 Ma. (b) A U-shaped argon spectrum indicative of a disturbed system. Paleogene and Cretaceous plutons British Columbia Central gneiss complex (CGC) CSZ SE AK Work Channel amphibolite Quottoon Inlet Mid-Cretaceous plutons Western metamorphic belt (WMB) Q o u WMB tt oo Prince Rupert n P 54°15' N Ecsta N Sk Brittle fault occurrence lu to r ve Ri PT 40 n CGC P 29.8 ± 0.6 Ma (2σ) MSWD = 1.7 n = 23 of 25 steps 30 20 10 lu to Pacific Ocean ll a een 50 Trace of the Coast shear zone CGC Apparent age (Ma) Work Channel n 0 130° W (a) 25 0 kilometers (b) 0 20 40 60 80 100 Cumulative % 39Ar released FIGURE 3–14 (a) Geologic map of a portion of the Coast shear zone (CSZ) in British Columbia. PT—pseudotachylyte sample location. (Modified from Gareau [1997] and Hutchison [1982]). (b) Argon spectrum for glassy matrix in pseudotachylyte from Coast shear zone. MSWD—mean square of weighted deviation. (Modified from Davidson et al., 2003.) ~300° C between 70 and 50 Ma (Crawford et al., 1987; Hollister and Andronicos, 2000; Butler et al., 2001). Later brittle deformation along discrete faults generated cataclasite (brittle fault rock) and pseudotachylyte veins, a glassy fault rock produced by frictional heating from earthquakes (Chapter 10). Davidson et al. (2003) dated the pseudotachylyte at ~30 Ma by laser step-heating of the glassy matrix (Figure 3–14b). SAMARIUM-NEODYMIUM METHOD Samarium and neodymium are rare earth elements that occur in low abundance in numerous rock-forming minerals. 147Sm decays to 143Nd, has an extremely long halflife (t1/2 = 1.06 × 1011 yr), and is best employed on rocks with ages of several hundred million years. In practice the Sm-Nd method is similar to the Rb-Sr method, where 56 | Introduction an isochron is plotted and the slope determines the age of the rock. The Sm-Nd method is well suited for dating mafic and ultramafic rocks. Furthermore, Sm-Nd ages are less susceptible to alteration than Rb-Sr ages. The Sm-Nd technique commonly provides “model ages,” which, in essence, is the time since the separation of a magma from the parent mantle. The Nd isotope ratio called εNd is important in identifying the source of minerals comprising terranes in mountain belts. In conjunction with Sr isotopes, Sm-Nd ratios also provide data about seawater contamination and hydrothermal alteration. FISSION-TRACK METHOD As 238U undergoes fission (splitting of nuclei) it produces damage tracks in minerals and glasses. The number of tracks per unit area is a function of the U concentration in the material and the age. The U concentration in a specimen can be determined and the number of fission tracks counted by enlarging the tracks with an etching solution (Figure 3–15a). Fission-track ages can be obtained for minerals such as apatite, muscovite, titanite (sphene), and zircon, and even volcanic glasses. At elevated temperatures fission tracks fade with time by annealing (the slow rearrangement of elements within the solid), such that a fission-track age records the time since the mineral cooled through its specific blocking temperature (Figure 3–15b). Glasses anneal at low temperatures (< 100° C), while apatite (~120° C) and zircon (200–240° C) (Figure 3–4) anneal at higher temperatures. For young volcanic rocks, fissiontrack ages can provide information about when the sample crystallized, whereas for plutonic and metamorphic rocks fission-track ages delineate the thermal history associated with uplift and/or exhumation. The Norumbega fault zone in Maine has long been recognized as an important Paleozoic structure in the northern Appalachians. Apatite fission-track ages, however, range from 113–89 Ma west of the fault zone, with ages of 159–140 Ma to the east of the fault zone, indicating that ~2 km of east-side-down movement occurred along the Norumbega fault zone in the Late Cretaceous (West and Roden-Tice, 2003) (Figure 3–16). URANIUM-THORIUM/HELIUM METHOD The uranium-thorium/helium system has become widely used as a low temperature thermochronometer. As U and Th decay they emit α-particles—nuclei of 4He—a stable isotope. The closure temperature for apatite is ~70° C and for zircon is ~180° C at typical grain sizes and cooling rates on the order of ~10° C/m.y. For standard continental geothermal gradients (20 to 45° C/km), apatite (U-Th)/He ages record the time since the sample has been within 1.5 to 3.5 km of the surface, so this method is useful for understanding the uplift and erosional history of regions. Stockli (2005) provides a detailed overview of how the uraniumthorium/helium method, when combined with other low temperature thermochronometers, can be utilized to understand extensional tectonics and exhumation rates for footwall blocks in these terranes. In the central and southern Appalachians, the Blue Ridge escarpment forms a prominent topographic boundary separating the Blue Ridge upland (elevation > 800 km) from the Piedmont (elevation < 300 m) (Figure 3–17a). The origin of the Blue Ridge escarpment has remained t0,T = 150° C t1,T = 65° C Tracks absent Tracks accumulate t2,T = 115° C t3,T = 65° C Reheating 10 µm Tracks anneal out (a) Tracks accumulate t4,T = 50° C FIGURE 3–15 (a) Etched fission tracks in a zircon grain highlighted by red arrows. (From Gleadow et al., 1986.) (b) Accumulation of fission tracks and annealing related to reheating. (b) nt fa u kilometers Po i NFZ g ME-8 yi n ME FIGURE 3–16 Apatite fission-track ages from rock samples (black dots) gathered in the Norumbega fault zone in southern Maine illustrating later cooling to the west of the fault zone relative to the east. Black lines with teeth indicate Paleozoic thrust faults; red lines indicate younger faults. (Modified from West and Roden-Tice, 2003.) 5 lt 0 140 Ma Fl ME-3 113 Ma VT ME-2 89 Ma NH ME-6 MA ME-7 159 Ma ME-1 57 | Geochronology in Structural Geology 140 Ma 92 Ma CT fau lt RI th Paleozoic granitic rocks be ME-5 iza Central Maine sequence pe El 151 Ma Ca East Harpswell sequence Casco Bay group Falmouth–Brunswick sequence 70° W VA tol Bristol TN 36° N B l u NC u Mt. Rogers (1746 m) R i d e E s g c l a p 8 e a r p m e n t 19 4 (122 (122) 3 I n n e tz on ul fa t ul fa y ar nd 6 7 1733 (12 ) 944 (123) 1066 18 1466 P 13 68 d i e m e r AHe 21 922 (111) (111)) 1 o VA NC Upland sample Piedmont sample 8 sample number 146 (129) AFT 2 81° W G reensboro Greensboro 0 20 (127) 2 ) 127 (127) 40 kilometers 80° W 1400 FIGURE 3–17 (a) Blue Ridge escarpment in Virginia and North 1200 Elevation (m) Carolina. AFT—Apatite fisson track age (Ma). AHe—ApatiteHelium (U-Th/He) age (Ma). (b) AHe and AFT age dates from the Blue Ridge upland to the Piedmont. (Modified from Spotila et al., 2004.) d 109 91 98 Roan Mtn. (1916 m) 82° W 200 1822 1146 466 (129) (12 ) 204 17 t l l 10 n d 27 164 (152) n a e y 23 122 (133) Ri ve rb ou 100 V (a) a 500 n d Roanoke B lack Blacksburg ev ar 37° N 1000 g e Da n d R i 1500 Br Elevation (m) 1900 Upland AHe Piedmont AHe X AFT 1000 800 XX Pair 0.5 3 Pair X 400 0 60 R = 2 600 X 200 (b) 79° W 80 100 X X X 120 140 Age (Ma) 160 180 200 220 58 | Introduction enigmatic, with some researchers suggesting it represents a relict rift shoulder that developed during the opening of the Atlantic Ocean in the Triassic, while others suggest that the escarpment is the result of Cenozoic tectonic uplift. Spotila et al. (2004) studied the Blue Ridge escarpment in a region where the rock type on either side of the escarpment is the same, such that differential erosion due to rock type is not a factor. They determined apatite fission track and apatite (U-Th)/He ages along a transect across the Blue Ridge escarpment that revealed a younging trend toward the Piedmont. Ages on the Blue Ridge upland range from 200–120 Ma with ages in the Piedmont averaging to ~100 Ma (Figure 3–17b). The pattern of younging ages is similar to patterns observed across other great escarpments worldwide, which is inconsistent with Cenozoic tectonic rejuvenation and, as such, the Blue Ridge escarpment is a long-lived topographic feature. Fault (a) Cosmic rays Fault scarp Fault (b) Cosmic rays Cosmogenic Surface Exposure Dating The Earth is constantly bombarded by cosmic rays from outer space that interact with materials in the atmosphere and on the Earth’s surface. For instance, when cosmic rays strike quartz, small amounts of oxygen and silicon in the lattice are converted to 10Be and 26Al, respectively. If the production and decay rates of these cosmogenic isotopes are known, the quantity of these isotopes preserved in the quartz can be used to determine how long the material has been exposed at the Earth’s surface. If a surface is eroding, the concentration of cosmogenically derived isotopes can be used to estimate the steady-state erosion rate. This technique works well with sediments and surfaces < 1.5 Ma. Consider material exposed at the surface along the newly exposed fault scarp (Figure 3–18). While at depth the rocks would not have accumulated cosmogenic isotopes, because earth materials strongly attenuate cosmic rays and the penetration depths of these particles are typically a meter or so. Once exposed at the surface, cosmogenic isotopes will begin to accumulate in material exposed at the fault scarp (Figure 3–18). Currently, 3He, 10Be, 14C, 21Ne, 26Al, and 36Cl are being utilized to determine ages of exposed surfaces on landforms (fault scarps, landslide, moraines, etc.) and in sediment itself. The Denali fault system in central Alaska is a major zone of right-lateral slip that has produced large earthquakes. Matmon et al. (2006) used 10Be concentrations in boulders and sediment from moraines offset by the Denali fault and determined late Pleistocene-Holocene average slip rates of 8 to 12 mm yr−1 (Figure 3–19). This type of analysis is well suited for unraveling the temporal history of recent faulting and related neotectonic phenomena. Details of surface exposure dating are complex and consideration must be made for elevation, latitude, orientation, and original inheritance of isotopes in a sample. Radiogenic isotopes such as 10Be eventually reach a CRN accumulation Fault (c) Cosmic rays CRN accumulation Fault (d) FIGURE 3–18 Schematic cross section illustrating the accumulation of cosmogenic radionuclides (CRN) on a fault scarp. steady-state concentration (even on non-eroding surfaces) as radioactive decay balances accumulation; consequently, these isotopes cannot date extremely old surfaces, whereas stable isotopes such as 3He continuously accumulate. For these techniques to work, the target mineral must quantitatively retain the cosmogenic isotope; for instance, 3He diffuses out of quartz and volcanic glass but is retained in denser minerals such as olivine and pyroxene. OPTICALLY STIMULATED LUMINESCENCE Another technique gaining widespread use is optically stimulated luminescence (OSL), with quartz as the mineral of interest. This technique is very useful for dating materials that have been exposed to sunlight during the past 500,000 years (Watanuki et al., 2005), and the precision is Geochronology in Structural Geology | 59 11.2 ± 1.2 12.4 ± 1.3 12.1 ± 1.3 11.2 ± 1.2 11.9 ± 1.3 12.2 ± 1.3 12.1 ± 1.3 11.5 ± 1.2 12.8 ± 1.4 12.8 ± 1.4 11.9 ± 1.3 FIGURE 3–19 Denali fault scarp, Alaska, with cosmogenic radionuclide ages in (ka ± ka) of glacial moraine offset across the fault scarp. The red line indicates the fault trace; black lines indicate the crest of the offset moraine. The white arrow points at 2002 earthquake offset of ~5 m. Magenta ovals encircle sediment ages beside the moraine. (From Matmon et al., 2006. Photo courtesy of Peter J. Haeussler, U.S. Geological Survey.) improving so that dates obtained by 14C and OSL on young materials (< 50,000 y) are comparable and fall within analytical error. The technique has been used in neotectonic studies to date young materials involved in active faulting. Because of light sensitivity, samples must be collected to avoid exposure to light and opened for analysis in a dark room. The technique is implemented by irradiating a sample with visible (commonly green) and infrared light, and the luminescence is measured with an optical device. The intensity of luminescence is inversely proportional to the time elapsed since the quartz was exposed to sunlight. The Vital Role of Geochronology in Structural Geology Although the relative chronology of deformation in the outcrop depicted in Figure 3–1 is easy to work out, geochronology provides the means to determine when deformation occurred (Figure 3–20). These rocks underwent a number of distinct deformation episodes. The oldest deformation (D1) produced folds and foliation under regional metamorphic conditions that occurred between 580 Ma and 440 Ma (based on detrital zircons and 40Ar/39Ar ages). The middle to late Paleozoic sedimentary rocks were folded and cleaved prior to intrusion of the basaltic dikes at 230 Ma; 40 Ar/39Ar ages of micas that formed during cleavage formation place this deformation event (D2) at 300 Ma during the P ennsylvanian. Surface exposure ages on boulders in the debris fan yield ages of 500 ka to 700 ka, indicating that thrust faulting (D3) occurred during the Pleistocene. Additional information is gleaned from the low-temperature geochronometers—apatite fission track and apatite (U-Th)/ He ages in detrital grains from the P aleozoic sandstone yield ages of 240 Ma to 220 Ma, consistent with exhumation during the M esozoic. Similar ages from detrital apatite in the flat-lying Paleogene sandstone reveal that these rocks were never deeply buried. Modern structural geology studies are nearly always linked to geochronologic work, as the history of deformed rocks cannot be properly understood without temporal knowledge. 60 | Introduction Debris fan with bouldery gravel West East Maple leaf surface exposure ages 500–700 ka Weakly cemented sandstone with siltstone lenses Archimedes Ar/Ar muscovite growth ages in cleaved slate ~300 Ma Sandstone with basal conglomerate Quartzite... youngest detrital zircon 580 Ma ... and schist Crinoids Ar /Ar cooling age plateau ~440 Ma Limestone Shale Thrust fault Basalt dike Rb/Sr age of 230 Ma Foliation FIGURE 3–20 Summary illustration of the deformation history from the exposure in Figure 3–1 developed from relative and isotopic age determinations. Stable Isotopes Stable isotopes of several elements provide useful information about the sources of fluids and chemical environments in different parts of the crust. They are useful in estimating even the climatic conditions during deposition of sedimentary rocks and identifying the source of carbon in diamonds—organic or inorganic. Variations in C and O ratios (13C/12C, expressed as δ13C, and 18O/16O, expressed as δ18O or verbally stated as delta-O-18) occur because one of the isotopes becomes more or less concentrated (fractionated) in different environments or is affected by ESSAY different geologic processes. For example, metasomatism, crystallization of magma (variations in magma composition also produce different δ values), deposition of limestone in cold versus warm water, formation of mineral deposits from hydrothermal fluids, and organic versus inorganic carbon all affect isotopic compositions. Study of stable isotopes of sulfur, iron, chlorine, and other elements have also yielded useful information about the environments where rock masses form. Mulch et al. (2004) used isotopic compositions of deuterium (heavy hydrogen) from recrystallized quartz and muscovite in 49–48 Ma mylonites from the Shuswap metamorphic core complex in British Columbia ock Bodies That Appear to Be the Same in the Field R May Not Turn Out to Be When Their Ages Are Determined As field geologists we frequently develop working hypotheses to explain how structures form and how rock units and plutons are related to each other—or not. There are vast areas where the rocks are barren of fossils, such as the interiors of Phanerozoic mountain chains and the Precambrian shield areas that occur on all continents. As a result, we frequently are left with employing crosscutting relationships for determination of relative ages (Chapter 1) and determination of absolute ages by employing appropriate radiometric dating technologies. When only relative ages are available, we sometimes are led down a path to incorrect answers about rock units and their relationships to each other. The correct answer can frequently be found, however, if modern radiometric ages can be determined. Detailed geologic mapping of an area in northeastern Georgia revealed some spectacular structures related to the Tallulah Falls dome (Figure 3E–1), but questions remained about the ages of several granitic gneiss bodies that occur on the flanks of the dome. By comparison with similar granitic gneisses nearby in the Blue Ridge and Piedmont, RDH became convinced that a medium-grained granitic gneiss located on the northeastern side of the dome was intruded | Geochronology in Structural Geology 34˚45' N 83˚45' W Soque sheet thrust of of Opc Dahlonega Jd gold f. My My belt tfg tfu tfa tfu tfq gg City tfl tfl ms Ywc Tallulah ms tfq Jd ms ms tfu tfq Ysc gg dome ms tfu N Ysc tfa 0 1 2 3 Yw 5 Yw ms tfl tfa tfg tfa u ms tfg Ywc tfa GA WS tfg tfl tfg tfl SC u tfl tfl tfl tfg fault 4 tfg Ywc tfq q Brevard 83˚30' W Jd ms tfg tfg tfq ms tfa tfl Clayton tfl ms Yw Ywc Ywc Tiger tfq Falls ms tfa tfg Ywc Mountain Ywc tfl Yw fault Mr Olb of tfm chee ahoo Chatt of tfg My Opc Olb cg Chattahoochee 83˚30' W cg River 61 0 miles zone 5 10 34˚45' N kilometers FIGURE 3E–1 Geologic map of the Tallulah Falls dome and vicinity, northeastern Georgia. Chattahoochee thrust sheet: Ysc— Sutton Creek Gneiss (medium-grained gneiss). Yw—Wiley Gneiss (augen gneiss). Ywc—Wolf Creek Gneiss (medium-grained gneiss). Tallulah Falls Formation members: tfl—Graywacke-schist amphibolite member. tfa—Garnet-aluminous schist member (kyanite- or sillimanite-bearing). tfg—Graywacke-schist member. tfq—Tallulah Falls Quartzite. ms—metasandstone and muscovite-biotite schist beneath the Tallulah Falls Quartzite. tfu—undivided. tfm—migmatite derived from Tallulah Falls Formation metagraywacke. gg—granitoid gneiss, age unknown. q—quartzite and quartzose metasandstone. u—ultramafic rocks. Mr—Mississippian Rabun granodiorite. My—Mississippian Yonah granitoid. Dahlonega gold belt: of—Otto Formation, undivided. Olb—Ordovician Lake Burton mafic arc complex. Soque River thrust sheet: cg—Coleman River Formation metasandstone and schist. Opc—460 Ma Persimmon Creek tonalite. Cutting all thrust sheets and the Brevard fault zone: Jd—Jurassic diabase. WS—Woodall Shoals. (Modified from R. D. Hatcher, Jr., et al., 2004, Geological Society of America Memoir 197, p. 525–547.) during the early Paleozoic. A similar medium-grained granitic gneiss occurs on the southwest flank of the dome and contains xenoliths of a granitic augen (Ger., “eye”) gneiss (Wiley Gneiss), which occurs as mappable bodies along the southeastern flank of the dome. All of the granitic gneisses occur in the cores of isoclinal folds (Chapter 15). A graduate student working with RDH mapped the southern flank of the dome, collected fresh samples, and obtained Rb-Sr ages on both the medium-grained and augen granitic gneisses in her area, yielding an age of 1,103 ± 14 Ma on the medium-grained gneiss and an age of 1169 ± 19 Ma for the augen gneiss (Figure 3E–2) (Stieve and Sinha, 1989). Both also have 87Sr/86Sr initial ratios > 0.706, so they probably formed in continental crust. The surprise from the radiometric ages was that these granitic gneisses are Mesoproterozoic “basement” and not Paleozoic plutons, as RDH had predicted. SHRIMP zircon geochronologic data indicate all of these granitic gneisses, along with the one on the northeastern flank of the dome, have approximately the same age of 1150 Ma (Carrigan et al., 2003), further confirming 62 | Introduction ESSAY continued 0.800 Wiley Gneiss 0.900 1103 ± 14 Ma 1σ 0.780 0.860 0.760 0.820 87Sr / 86Sr 87 Sr / 86Sr 1169 ± 19 Ma 1σ 0.740 0.720 (a) + 0.780 0.740 0.7088 0.700 0.0 Sutton Creek Gneiss ++ ++ 0.7063 1.0 2.0 3.0 4.0 0.700 0.0 5.0 87Rb / 86Sr 2.0 (b) 4.0 6.0 8.0 10.0 87Rb / 86Sr FIGURE 3E–2 Rb-Sr isochrons for two basement gneisses of the Tallulah Falls dome: (a) whole-rock isochron for the Wiley Gneiss; (b) whole-rock isochron for the Sutton Creek Gneiss. (Modified from Stieve and Sinha, 1989, Georgia Geological Society Guidebook.) their antiquity. Therefore, the rocks that initially were thought to be intrusive into the enclosing metasedimentary rocks are actually separated from the enclosing rocks by a complexly deformed nonconformity. The basic structure of the flanks of the dome was not changed, and the answer to the question of the relative ages of these rocks was provided in part by the xenoliths of the augen gneiss in the medium-grained granitic gneiss, demonstrating that the augen gneiss is older than the medium-grained gneiss. Radiometric ages, however, were needed to confirm the antiquity of the m edium-grained granitic gneisses. Nevertheless, the radiometric age dates are not precise enough to resolve the absolute ages of the Wiley augen gneiss and the slightly younger grantic gneiss. Xenoliths of biotite gneiss were subsequently found in a new exposure of Wiley Gneiss and zircons from the xenoliths dated using the SHRIMP. They yielded ages of 1.3 (and 1.52) Ga, providing hints of a pre-Wiley Gneiss history of the host rocks into which the Wiley Gneiss and other basement units were intruded long before they were incorporated into the Appalachians (Merschat et al., 2010)—when they were part of the 1.0 to 1.15 Ga Grenville orogenic belt. to determine that deformation occurred at temperatures of 420 ± 40° C. Meteoric waters with low hydrogen isotopic compositions infiltrated the detachment fault system and indicate that, prior to Eocene extensional deformation, paleoelevations for the region were ~4,000 meters, more than a kilometer higher than the modern t opography (Figure 3–21). References Cited Carrigan, C. W., Miller, C. F., Fullagar, P. D., Hatcher, R. D., Jr., Bream, B. R., and Coath C. D., 2003, Ion microprobe age and geochemistry of southern Appalachian basement, with implications for Proterozoic and Paleozoic reconstructions: Precambrian Research, v. 120, p. 1–36. Merschat, A. J., Hatcher, R. D., Jr., Bream, B. R., Miller, C. F., Byars, H. E., Gatewood, M. P., and Wooden, J. L., 2010, Detrital zircon geochronology and provenance of southern Appalachian Blue Ridge and Inner Piedmont crystalline terranes, in Tollo, R. P., Bartholomew, M. J., Hibbard, J. P., and Karabinos, P. M., eds., From Rodinia to Pangea: The lithotectonic record of the Appalachian region: Boulder, Colorado, Geological Society of America Memoir 206, p. 661–699. Stieve, A. L., and Sinha, A. K., 1989, Grenville ages from Rb/Sr whole-rock analysis of two basement gneisses of the Tallulah Falls dome of northeast Georgia, in Fritz, W. J., Hatcher, R. D., Jr., and Hopson, J. L., eds., 1989, Geology of the eastern Blue Ridge of northeast Georgia and the adjacent Carolinas: Georgia Geological Society Guidebooks, v. 9, p. 57–74. We now move to a review of geophysical methods that provide data for structural geologic analysis. Geochronology in Structural Geology Infiltration of low δD meteoric water into the detachment Precipitation at high elevation: low δD δDms ≈ -160% | 63 FIGURE 3–21 (a) Shuswap metamorphic core complex, British Columbia prior to Eocene extension. (b) Modern topography and crustal structure. For details on faults and faulting processes, see Chapters 10 and 11. (Modified from Mulch et al., 2004.) { 0 0 Depth (km) Brittle 20 Ductile fault zone Detachment ≈ 400° C 20 δDms ≈ -80% Ductile 40 Moho 60 60 Mantle Footwall EOCENE (a) Metamorphic core complex Exhumed detachments: Reservoirs of meteoric fluid composition Eocene topography { { Eocene basin 0 Depth (km) 0 Migmatite dome 20 Moho ? ? 20 ? 40 ? 40 mantle PRESENT (b) Chapter Highlights • Geochronologic techniques are powerful tools that enable structural geologists to determine both when deformation occurred and also estimate rates of deformation, fault slip, and uplift. • The ages of minerals and rocks can be determined because radioactive parent elements incorporated in these minerals decay at known and constant rates into stable daughter products. • Isotopic ages record the time that has elapsed since an isotopic system (in a specific mineral) cooled through its closure temperature; these ages may be a crystallization, cooling, or growth age depending on the particular geologic situation. • The U-Pb system in zircons is widely used to date old igneous and metamorphic rocks. U-Pb detrital zircon ages can be utilized to understand the provenance of many sedimentary rocks. • The use of multiple geochronometers, each with different closure temperatures, from the same rock can yield valuable information related to burial, uplift, exhumation, and deformation. • New geochronologic techniques are being utilized to determine the age of relatively young sediments and to better understand neotectonics. 64 | Introduction Questions 1. A new isotopic system has been discovered and experimental analysis reveals the following relationship: TIME (DAYS) DAUGHTER/PARENT RATIO 0 0 100 0.35 200 0.74 3. Zircons from a foliated granite were imaged by catholuminescence and dated using a SHRIMP. The cores of the zircons yielded a peak in a frequency/probability time plot of 1,906 Ma, and the overgrowths on the cores yielded another peak at 477 Ma. How would you interpret these data? 4. A micaceous quartzite yielded the following age dates: Ar/39Ar muscovite 35 Ma 40 Ar/ Ar biotite 28 Ma 40 Ar/39Ar K-feldspar 20 Ma 40 39 300 1.35 zircon fission track 17 Ma 400 2.00 apatite fission track 8 Ma 500 3.00 apatite (U-Th)/He 4 Ma 600 4.26 Based on these data, determine the half-life (in days) and the decay constant, λ (in s−1) for this system. Would this system be useful for dating rocks? Explain. 2. Zircon fractions from five samples of massive granodiorite collected from a pluton have the following isotopic ratios: SAMPLE # 206 Pb/238U 207 Pb/235U 1 0.0491 0.3550 2 0.0490 0.3549 3 0.0492 0.3565 4 0.0492 0.3568 5 0.0493 0.3574 Based on these data, what is the age of the pluton (in Ma)? Are these age dates concordant? Recall the half-life of 238 U = 4.47 × 109 yr and half-life of 235U = 7.04 × 108 yr. Based on these data and the approximate closure temperature for each system (Figure 3–4), determine the longterm average cooling rate (in ° C/m.y.) for the quartzite. Construct a temperature vs. age plot for these data. Is the cooling rate linear over time? What are the implications? 5. 40Ar/39Ar studies on muscovite and biotite from a metasedimentary sequence in a thrust sheet yield plateau ages of 380 Ma and 320 Ma, respectively. Slate interlayers from a carbonate sequence in the footwall of the thrust sheet contain fine-grained metamorphic muscovite that yields 40 Ar/39Ar age of 460 Ma. Non-recrystallized detrital muscovite grains on bedding planes in the footwall slate yield a 40 Ar/39Ar age of 980 Ma. What do these numbers mean relative to deposition of the mud that formed the shale that was later metamorphosed into slate, the timing of metamorphism, and the emplacement of the thrust sheet? 6. A large gabbro pluton intruded a low-grade sequence of siliciclastic metasedimentary rocks. The gabbro is devoid of U-bearing phases. What isotopic system could be employed to determine the intrusive age of the pluton? Further Reading Albarède, F., 2011, Geochemistry, an introduction, 2nd edition: Cambridge, England, Cambridge University Press, 342 p. An introductory geochemistry text that approaches the subject from basic chemical principles, starting with the periodic table. It contains useful exercises and problems at the end of each chapter. Faure, G., and Messing, T. M., 2009, Isotopes: Principles and applications, 3rd edition: New York, John Wiley and Sons, 897 p. Very thorough but readable book on isotope geochemistry that includes detailed discussions of all techniques for dating geologic materials, and discussion of natural isotopic systems including applications. Misra, K. C., 2012, Introduction to geochemistry: Principles and applications: Chichester, Wiley-Blackwell, 438 p. This is a recent textbook that provides thorough coverage of most of the topics in geochemistry, along with useful problems. Stockli, D. F., 2005, Application of low-temperature thermochronometry to extensional tectonic settings, in Reiners, P., and Ehlers, T., eds., Thermochronometry. Reviews in Mineralogy and Geochemistry, vol. 58, p. 420–461. 4 Geophysical Techniques and Earth Structure Although the Earth’s lofty mountains and deep canyons expose many large outcrops that enable structural geologists to see the near-surface structure of the Earth, the vast majority of the Earth is hidden from view. The deepest drill holes extend only 12 kilometers, so even much of the crust, the Earth’s outer most layer, is beyond direct observation. This is where geophysical techniques prove their mettle as they provide a method to both image and understand structures at depth. Geophysical techniques are widely used to resolve indi vidual geologic structures ranging from a few kilometers in size to the crustalscale, and even the larger-scale deep structure of the Earth. Techniques useful in delineating geologic structure include seismic reflection, seismic refraction, earthquake seismology, magnetism, paleomagnetism, gravity, and electrical properties. The resolution and imaging capabilities of each technique are quite variable. These techniques will be discussed below with examples of applica tions relevant to structural geology. This chapter does not provide an in-depth background in geophysics, but rather is intended to demonstrate the importance of geophysical tech niques in modern structural geology and kindle interest in the subject. The techniques to be discussed here help most in interpreting large structures— faults and folds of map scale or larger, plutons, and crustal boundaries— and, as such, provide a useful springboard to tectonics. New technologies [that describe] the nature and evolution of the conti nental lithosphere from Earth’s sur face to deep within the mantle (the 3rd dimension), and through deep geological time (the 4th dimension) have transformed the way we think about the evolution of the Earth. . . . RAYMOND A. PRICE, 2012, Geological Association of Canada Special Paper 49 Seismic Reflection Seismic reflection is a technique developed largely in the oil and gas indus try as an exploration tool. It has developed rapidly during recent decades because computers and digital technologies have speeded data processing, and new processing techniques have also been invented. Structural geolo gists find seismic reflection profiles useful because they resemble geologic cross sections (Figure 4–1). While they do look like geologic cross sections, they contain artifacts from data acquisition and processing that can lead to misinterpretation of the geology represented in the seismic reflection profile. Seismic reflection was originally developed using an explosive source; a modification is the vibroseis technique. Vibroseis uses a truck (usually 65 300 400 500 600 700 Beaver Valley fault Copper Creek fault 800 Saltville fault Clinchport fault Wallen Valley fault Kingston fault Pine Mountain fault Powell Valley anticline 200 900 SE 1000 0.5 1 1.0 2 1.5 3 2.0 4 2.5 0 3.0 Top of basement 5 5 Master thrust fault Undeformed basement kilometers Depth (km) Two-way travel time (s) 100 Introduction 0 | Pine Mountain fault 66 NW 100 200 300 600 700 800 Saltville fault Beaver Valley fault Copper Creek fault Clinchport fault Wallen Valley fault 500 Kingston fault 400 900 SE 1000 0.5 1 1.0 2 1.5 3 2.0 2.5 3.0 0 5 kilometers Poor data quality 4 Top of basement Undeformed basement Master thrust fault Depth (km) Two-way travel time (s) 0 Pine Mountain fault NW Powell Valley anticline Pine Mountain fault (a) 5 (b) FIGURE 4–1 (a) Industry seismic reflection profile from the Cumberland Plateau across part of the Valley and Ridge of eastern Tennessee. Prominent reflectors along top of basement and beneath named faults are produced by interlayered shale and sandstone of strongly contrasting velocity, not the faults. (b) Partial interpretation of the seismic reflection profile in (a). Red lines highlight thrust faults. Chapters 10 through 14 provide detailed discussions of faulting. For conversion of two-way travel time to depth in kilometers, multiply travel time by 1.85 km sec−1. (From Hatcher et al., 2007, Geological Society of America Special Paper 433.) Geophysical Techniques and Earth Structure | 67 FIGURE 4–2 Vibroseis trucks working in tandem in the Nechako Basin in north-central British Columbia. Vibrating plates are raised and lowered by a hydraulic system located between the front and rear axles. Geophones are buried along the roadside at a predetermined interval. A recording truck (not shown) collects data received by the geophones. (Photo by A. J. Calvert, Simon Fraser University, Burnaby, British Columbia, Canada.) Vibroseis truck Recording truck Geophones FIGURE 4–3 Basis of seismic reflection data collection: the energy source (here vibroseis) moves along the geophone array emitting elastic waves into the ground at specific frequencies. The waves are reflected from layers of increasing or contrasting velocity and are recorded in the recording truck. The data are then processed by a computer to produce a seismic reflection image. Sound (elastic) waves more than one) that has a vibrating steel plate that is raised and lowered by a hydraulic system mounted to the frame (Figure 4–2); at regular intervals, the plate is lowered to the ground, where vibration energy in the form of sound (elastic) waves is passed into the ground over a specific frequency range. When more than one vibrator truck is used, the spacing and vibration frequencies are synchro nized. The elastic waves are transmitted into the crust; some are reflected from subsurface structures and are recorded at the surface (Figure 4–3). To record transmit ted and reflected waves, an array of geophones is laid out as in conventional seismic surveys (which use explosives as a seismic source). Multiple traces may be recorded and processed over the same structures, producing sharper records. An airgun may be used in much the same way, but it transmits less energy into the Earth from land than through water, so airguns are mainly used for marine sur veys. For maximum energy transmission, and therefore a maximum return of reflected energy, explosives are still the best energy source, but airguns are less destructive to the marine environment—even so, there is still concern about the effects of this source on marine life. Seismic reflection is best suited to recognize nearly horizontal structures, such as packages of layers that dip less than 30° or gently dipping faults. This is due to the way the technique was designed—to transmit elastic (sound) waves more or less vertically into the Earth and to receive almost vertical reflection of waves back to the surface from rock layers of contrasting elastic properties (Figure 4–4). Theoretically, it is possible to record or process reflections from steeply dipping surfaces, but in practice, few reflectors that dip more than 30° are observed in two-dimensional surveys, and they may be selectively removed during pro cessing. This probably introduces bias or even significant error. Steeply dipping structures, such as some faults, may be imaged only by displaced gently dipping layers on both sides of the structure, but modern processing technology and acquisition of three-dimensional data have enabled imaging of more steeply dipping surfaces than in the past. A processed seismic reflection profile consists of a 2D section or 3D block through part or all of the crust; 2D sec tions resemble a geologic cross section. The vertical axis of the profile is commonly two-way travel time of the elastic waves to a depth section. Knowledge of the velocity in dif ferent parts of the section permits conversion of a time section to a depth section, with a vertical scale in kilome ters or feet. The seismic section may be used (with care) to construct a well-constrained structural cross section 68 | Introduction Shot # 256 NW Shot # 255 Channel Shot # 254 Channel SE Channel 0 20 40 60 80 100 120 0 20 40 60 80 100 120 0 20 40 60 80 100 120 0 0 1 2 3 Depth (km) Two-way travel time (s) 5 4 NC GA SC 5 10 LINE 3 6 GA 0 7 SC N 20 kilometers 15 8 (a) FIGURE 4–4 (a) Field record for three vibrator shot points collected along part of a vibroseis line as part of the Appalachian Ultradeep Core Hole (ADCOH) site investigation in northeastern Georgia (arrow on inset map), showing major reflectors at 2.6-, 3.1-, and 8-second (s) two-way travel time. Field records for each shot point are correlated and stacked using the computer to construct the initial section— called a “brute stack.” along the line of the seismic profile. Many artifacts— unnatural flaws in the data introduced during data acqui sition and processing—are only partly removed during processing. Having seismic reflection profiles through an area of interest, however, is a tremendous asset over just having surface geologic maps and structural data to pro ject to depth. Construction of high-quality geologic cross sections augmented by seismic reflection profiles (Figure 4–1b; see also Figure 14–3) requires knowledge of seismic velocities, field and processing parameters, recognition of artifacts, and maximum use of surface geologic data and other geophysical data. High-quality seismic reflec tion profiles are probably the best tool available for imag ing the structural geometry of the crust and mantle, and for projecting surface structures to depth. The best seis mic reflection data available for structural interpretation today are acquired in foreland fold-thrust belts (Figure 4–1; see Chapter 12) and in marine surveys on continental margins (Figure 4–5). Seismic reflection profiling was originally designed as a tool for petroleum exploration. Since the mid-1970s it has been adapted for study of the deep crust of continents and interiors of mountain chains by numerous univer sity and government research groups. As a result, several thousand kilometers of new crustal data are available to help to confirm, delimit, or disprove hypotheses about the structure of the crust. For example, the hypothesis of large-scale, thin-skinned thrusting of crystalline rocks in the southern Appalachians had been suggested from surface geologic studies (Bryant and Reed, 1970; Hatcher, 1971, 1972), but COCORP (Consortium for Continental Reflection Profiling group at Cornell University) seismic reflection data provided the hypothesis greater credibility (Figure 4–4); it also raised new questions related to this and other regions in the crust. Some of these unsolved problems include determination of the nature of layered reflectors deep in the crust, the nature of curved reflectors, deep-seated “bright spots” (exceptionally strong reflectors Shot point number NW 850 0 800 750 700 650 600 550 500 450 SE 400 350 300 250 200 150 100 0 2 Data gap 3 5 Depth (km) Two-way travel time (s) 1 4 5 10 (c) NW Blue Ridge 850 0 800 Bfz 750 650 SE Inner Piedmont Chauga Belt 700 600 550 500 450 400 350 300 250 200 150 100 0 2 4 3 4 5 0 5 10 Depth (km) 1 8 kilometers FIGURE 4–4 (continued) | (b) Processed section constructed from field records collected in northwestern South Carolina as part of the ADCOH Project site investigation. Note where shot points 254, 255, and 256 in Figure 4–4(a) are located on the processed section (red vertical band in b and c). (Data processed at Virginia Tech by J. K. Costain and C. Çoruh.) (c) Reflectors in the right third of the seismic reflection profile in (b) image recumbent folds that are mappable on the surface. Reflectors are produced by strong acoustic (elastic) contrasts in folded granitic rocks and amphibolite. Geophysical Techniques and Earth Structure Two-way travel time (s) (b) 69 800 Bfz 750 Chauga Belt 700 650 Inner Piedmont 600 550 500 450 400 350 300 T A 250 200 150 70 Blue Ridge 850 0 100 0 | 2 T 4 4 6 Depth (km) Depth (km) A 6 0 5 kilometers 10 Basement 1.25× vertical exaggeration (d) FIGURE 4–4 (continued) (d) Geologic interpretation of the seismic reflection profile shown in (b). Pink area is the Blue Ridge-Piedmont crystalline thrust sheet. Strong reflectors around 8 to 9 km (3-second two-way travel time) are derived from flat-lying sedimentary rocks (blue unit) that were deposited on top of crystalline basement (purple unit). Inclined reflectors immediately beneath the blue unit are interpreted as small Cambrian rift basins (light orange units). Lavender color is interpreted as sedimentary rocks that have been overridden by the pink, green, and brown metamorphic rocks of the thrust sheet above. The Brevard fault zone is the distinct set of inclined reflectors that project to the surface near shot-point 700. Red lines mark interpreted faults. T—movement toward observer. A—movement away from observer. –600 –600 –1000 –1000 Depth (m) –1500 –2000 Salt Salt S –1500 Salt –2000 Depth (m) N Salt –2500 –2500 –3000 –3000 FIGURE 4–5 Marine seismic reflection profile from the Gulf of Mexico south of Louisiana containing numerous normal faults and small bodies of salt. Note that processing is uninterrupted beneath salt bodies. This is partly due to the modern computer processing technology, and also that this is a vertical section through a 3D seismic reflection profile. (From TGS data, AAPG Explorer, July 2010.) Introduction 2 Geophysical Techniques and Earth Structure originally identified in the shallow crust as hydrocarbons, but within the deeper crust they may be magma; de Voogd et al., 1988), and the zones of no reflectors, called “trans parent zones.” The Mohorovičić-discontinuity or Moho (named in honor of Andrija Mohorovičić, 1857–1936, a Croatian seis mologist) is visible on modern reflection profiles as a series of nearly horizontal layered reflectors (Figure 4–6). It was recognized in 1909 by Mohorovičić in seismograph records of refracted earthquake waves that yielded separate veloci ties for P and S waves (see discussion of earthquake waves later). The Moho was soon recognized as a deeper bound ary beneath the continents, some 35 to 50 or more kilome ters, but a shallower boundary beneath the oceans, some 10 kilometers or less. Seismic reflection imaging has enabled questions to be asked, such as: What does the Moho ac tually represent? Why are there, in some locations, several Moho reflections rather than a single reflector? Does the Moho represent a zone of laminar flow at a major material behavior (rheological) discontinuity? What is the depth to and the age of the Moho directly beneath you? Oliver (1988) formulated several alternative hypoth eses to explain the Moho—interpretations that were im possible without the abundant crustal geophysical data we now have. Reflection profiling has brought to light many previously unknown aspects of crustal structure. It has made possible the confirmation and description of several types of structures, and has permitted formulation of new models for the structure of the continental crust. Seismic Refraction Seismic waves are refracted as they pass from one layer to another, with their velocities and directions determined by the density of the material, and are used in seismic refraction studies. Behavior of refracted waves follows Snell’s Law: nλ = 2d sin θ (4–1) where λ is wavelength, θ is angle of refraction, d is layer thickness, and n is a constant representing the refractive index of the layer material, commonly assumed to be 1. Sound or other elastic waves are detected after they are produced by an explosion or an earthquake. The waves pass into the Earth and are refracted at boundaries be tween particular layers where elastic velocity changes downward; then the waves return to the surface, where they are detected by geophones (Figure 4–7). The technique generally involves angles from the source (called “offsets”) to the geophone that are much wider than with seismic reflection. Distances from the source to the detector are known, and so they may be calibrated with the travel times of acoustic waves of known frequency. Refraction is one of | 71 the best techniques for calculating seismic velocities and exploring the layered structure of the crust and mantle (Figure 4–7). It is particularly useful in conjunction with seismic reflection studies, which require detailed knowl edge of crustal velocities. Earthquakes and Seismic Waves Earthquakes are among the most devastating hazards on Earth. The largest and most destructive earthquakes occur along tectonic plate boundaries, where oceanic or continental crust is being subducted beneath another plate (Figure 1–1). Earthquakes that occur along plate boundaries are easy to explain, but they also occur within plates, and as a general rule are not as well understood. They are produced by buildup of elastic energy over time, then sudden release of this energy in the Earth, producing movement along a fault. The rocks on either side rebound, releasing energy, and produce variable motion on the fault depending on how much energy was stored along the fault. Earthquake Waves and Whole-Earth Structure Earthquakes produce several kinds of elastic waves as prod ucts of energy release. Compression or P waves are body waves that move through the Earth at the highest veloc ity. S waves are shear waves, and are also body waves that travel through the Earth at lower velocity than P waves. Since liquids have a shear modulus of zero, shear waves cannot travel through liquids. L (Love) and R (Raleigh) waves are surface waves that travel more slowly and have higher amplitude. Seismographs record the different waves, but require at least three instruments to properly record an earthquake: two in the horizontal plane perpendicular to each other and the third oriented vertically (Figure 4–8). Where seismic waves undergo an abrupt change in ve locity is called a discontinuity. The Moho, discussed ear lier, is probably the best-known discontinuity, but there are numerous others. These changes in wave velocity are a key to understanding the internal structure of the Earth (see Figure 1–9). In the mantle at a depth of ~3,000 km, P waves undergo an abrupt decrease in velocity, and S waves decrease veloc ity to zero—they cannot travel farther into the Earth. This property of shear waves provided key evidence that the Earth’s core is liquid. That both P and S waves travel unim peded to depths of 3,000 km indicates the mantle is solid, and probably composed of materials markedly different from the core or the crust, because both increase velocity with depth and cross several discontinuities in the mantle. 72 | Introduction West 0 Shot point number Fort Simpson 1,000 0 2,000 Fort Providence 3,000 4,000 5,000 6,000 7 Two-way travel time (s) 4 8 12 16 20 24 28 32 (a) Fort Simpson 0 Fort Simpson basin Fort Providence Fort Simpson terrane Great Bea Hottah terrane/Coronation margin Approximate depth (km) 14 28 42 56 70 84 98 112 (b) Approximate depth (km) 0 5.8 6.2 20 Moho 40 6.0 6.2 6.0 6.6 6.8 8.0 8.2 8.2 6.2 6.6 7.0 8.0 8.2 60 6.0 6.8 6.0 6.2 6.6 6.6 8.2 7.6 8.0 8.2 8.5 80 100 (c) FIGURE 4–6 (a) Lithoprobe SNORCLE (Slave-Northern Cordillera Lithosphere Evolution) line 1 east-west seismic reflection profile across part of western Canada east of the Canadian Rockies. (b) Interpreted section. Tan area to the east is Archean crust; yellow- and brown-colored areas are Proterozoic crust, with the brown being younger; light lavender and pale green areas to the west are Paleozoic rocks of the Fort Simpson terrane. The boundary between strong reflectivity in the upper crust and little reflectivity below is the Moho discontinuity separating the crust from the mantle. The group of reflectors in the west-cental part of the line that descends into the mantle is a possible “fossil” subduction zone. (c) Seismic refraction profile along Lithoprobe SNORCLE line 11. Numbers are P-wave velocities in km/second. Black (crust) and white (mantle) lines identify locations from which wide-angle reflections were recorded. Note the lower resolution of structure in the refraction line (c). (From F. A. Cook, 2012, Geological Association of Canada Special Paper 49, Chapter 5, his Figure 12.) The principal discontinuities in the mantle occur at depths of 410 km and 660 km (Figure 4–9), and are thought to be related to phase or polymorphic changes in one or more minerals, principally high temperature-pressure Mg sili cates, like olivine (Mg2SiO4) or enstatite (MgSiO3) that we see in the crust. A high temperature–high pressure mineral called bridgmanite first properly characterized and named by Tschauner et al. (2014) is thought to be the most abun dant mineral on Earth, making up a large volume of the lower mantle. Its composition is the same as enstatite, but has the crystal structure of perovskite; it is stable at ~24 GPa and 2030° C (2300° K). Bridgmanite has recently been 6.4 8.4 6. Geophysical Techniques and Earth Structure Shot point number Fort Providence 0 6,000 7,000 8,000 East Yellowknife 9,000 10,000 73 | 11,000 12,000 0 Two-way travel time (s) 4 8 12 16 20 24 28 32 Fort Providence Great Bear magnetic arc ronation margin Medial zone Yellowknife Rae Anton domain Yellowknife basin 0 Approximate depth (km) 14 28 42 56 70 84 50 100 kilometers 6.0 6.6 8.2 6.0 6.2 6.4 6.4 6.4 6.2 6.8 7.0 8.4 6.2 6.2 8.2 6.6 112 6.0 6.2 6.4 Moho 8.0 0 20 6.6 6.8 98 40 60 8.5 0 50 kilometers 100 80 Approximate depth (km) 0 100 FIGURE 4–6 (continued) found in a “shocked” meteorite in sufficient quantities that its physical and chemical properties could be described (Tschauner et al., 2014). The composition of the Earth’s core was estimated from calculated densities of the outer and inner core using P-wave velocity data, which yielded an average density of ~11 g cm−3. Various combinations of known materials can yield this density, but the population of iron-nickel mete orites (~90 percent iron and 10 percent nickel) approaches this density. Stony meteorites are commonly ultramafic rocks, and roughly match the compositions of mantle rocks we see on the surface to provide the other piece of the puzzle; they are by far the most abundant meteorites. For many years, it was thought that the Earth and other terrestrial planets could be modeled as analogues of ironnickel and chondritic meteorites—the “chondrite model” (e.g., Taylor, 1964). Campbell and O’Neill (2012), how ever, suggested that this model will not work based on 142 Nd/144Nd ratios in mantle rocks compared with those in chondritic meteorites. Locating Earthquakes There are hundreds of seismograph stations on Earth today, so the location of major earthquakes anywhere on Earth is made within minutes. Locating an earthquake | Introduction 10°E 12°E 14°E 16°E 18°E SWEDEN DENMARK E Copenhagen c ra 24°E 6.10 6.20 7.00 8.30 7.60 8.40 Mantle 7.50 10 6.50 20 6.60 6.70 6.80 0 6.10 6.30 6.50 6.60 6.70 NE 6.40 6.40 5.80 4240 6.30 4230 6.00 4220 6.10 4210 4190 4200 4180 4160 4140 9340 4120 4110 4090 4080 4070 9140 4050 n 4040 to ne zo 4030 n 4020 a 4010 40 e Depth (km) 42 20 p 50°N 200 6.30 7.40 50 100 kilometers 22°E 6.20 6.40 52°N East European craton 5.60 7.50 0 20°E 6.50 6.80 Moho 18°E 5.40 6.70 40 16°E 4.00 5.00 5.20 6.20 6.60 54°N UKRAINE Carpathian Mtns . Teisseyre–Tornquist zone 6.00 6.20 6.30 30 Wroclaw Kraków 14°E 5.90 20 Warsaw Te iss ey re– To rn qu ist POLAND CZECH REPUBLIC 6.00 6.10 80 41 40 95 5.90 10 o irge geb Erz 12°E Paleozoic platform 0 rm Sud ete sM t Nürnberg 10°E Vilnius BELARUS 80 c fo Prague (a) RUSSIA . ns 50°N SW u 90 l Pa oi p t la matio n 70 40 40 91 50 40 0 4 40 30 40 0 2 40 0 1 40 GERMANY defor 40 Berlin Hannover z eo Gdansk Koszalin 40 Limit of Alpine 52°N E atio n LITHUANIA t 60 41 0 5 41 0 4 41 40 93 0 2 41 0 1 41 Hamburg s r de for m a 56°N Sea 30 i t of Late Paleoz oic 26°E Baltic 42 54°N 24°E 10 42 00 42 90 41 Sea 22°E 42 Li m North 20°E 9540 8°E 56°N 4150 74 6.80 30 6.90 6.90 7.00 7.30 7.40 40 7.40 8.10 Moho 7.50 7.60 8.20 8.50 8.30 8.20 Mantle 50 Moho 60 60 0 (b) 100 200 300 400 500 Distance along profile (km) 600 700 800 FIGURE 4–7 Seismic refraction profile across parts of Lithuania and Poland acquired by setting off explosives in shallow drill holes, and collecting refracted energy with geophones. (a) Simplified tectonic map showing the location of the refraction profile line and shot points (purple line with numbers). Teisseyre-Tornquist zone in the suture between western and central European crust. (b) Seismic refraction profile along the line identified in (a). Colors separate parts of the crust and mantle with different velocities. Numbers represent seismic velocities in km/sec. The Moho in continental crust is commonly identified in seismic refraction surveys by the 8.0 km/second velocity boundary that contrasts with lower velocities above. (Modified from Grad et al., 2003, Journal of Geophysical Research, p. 108.) Geophysical Techniques and Earth Structure Support Support Weight Pen Hinge Rotating drum Horizontal-motion seismometer (a) (1) (2) Body waves (b) Time interval marks Rotating drum Arrival of P wave P–S time interval Arrival of S wave Vertical-motion seismometer Surface waves Arrival of first L waves Time North arrow Bullseye spirit level (c) (1) Pen Bedrock Bedrock Background noise Spring | 75 FIGURE 4–8 A seismograph utilizes a group of seismometers that detect movement in the x- (east-west), y- (north-south), and z- (up-down) directions. (a) (1) and (2) Classic horizontal- and vertical-motion seismometers record motion relative to the bedrock on which they are mounted. The motion is transferred to a rotating drum by a pen creating a seismogram (b), which depicts ground motion energy versus time. Traditional analog seismometers used for studying earthquakes are very sensitive and record ground movements as small as 10 −7 cm. (Modified from Nance and Murphy, 2016, Physical geology today.) (c) (1) A modern triaxial seismometer contains sensitive electronics that detect motion by confining a small “proof mass” by electrical force. When the earth moves, the device counteracts that motion holding the mass steady. The amount of force required to keep the mass still is recorded and provides an a ccurate measurement of the ground acceleration using the principle F = ma. Note the bullseye spirit level (light yellow circle in the center of the lid) and the north arrow on the handle used to set up the device on site for accurate operation. (Photo courtesy of Güralp Systems Ltd.) (2) Interior of a device similar to (1) showing the two mass-and-sensor modules (center) for recording x and y ground motion (the z-axis mass-andsensor is hidden beneath). Note that the modules are identical and installed perpendicular to one another. (Photo by Hannes Grobe, Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany.) (2) requires a minimum of three seismic stations, because there is little directional component to a seismic record. The time separation between the P and S waves in a seis mic record is proportional to distance to the earthquake, which enables the seismologist at one station to construct a circle on the Earth’s surface, with the radius of the circle equal to the distance to the earthquake (Figure 4–10). Another station does the same, but that provides two in tersections of two circles, so a third station is needed so that the three circles intersect at a point. The multitude of seismic stations worldwide today permits location of small and large earthquakes so that a large earthquake in an underdeveloped country like Nepal can be pinpointed, resulting in immediate mobilization of resources to pro vide assistance. Earthquake Magnitude and Intensity Whenever a major earthquake is reported in the news, a number called the earthquake magnitude is commonly also mentioned to provide information on the size of the earthquake. Before seismographs were invented and widely deployed, the only way that the size of an earth quake could be estimated was from an intensity scale that qualitatively determined the area of different amounts of damage and felt area (Table 4–1). The invention of seismo graphs permitted seismologists to study the amplitudes of the different seismic waves and the separation between P, S, and L waves in a seismic record. Charles Richter (1935) invented a quantitative scale that attempts to measure the 76 | Introduction FIGURE 4–9 The abrupt changes in velocity of P and S waves help identify the boundaries between Earth’s internal layers. (Modified from Nance and Murphy, 2016, Physical geology today.) 0 0 Seismic velocities (km sec–1) 2 4 6 8 10 12 14 km 100 410 660 Lithosphere (~100 km thick) Ast hen os ph ere 1,000 Depth (km) 2,000 Transition zone S wave Upper mantle 2,890 3,000 Lower mantle 4,000 P wave Solid inner core 6,000 energy released at the source or focus of the earthquake. Richter (or local) magnitude (ML) was reported for many years, and is based on  A   M L = log10 A − log10 A0 (δ ) = log10   A0 (δ )  (4–2) where A is the maximum amplitude of seismic waves recorded on a seismograph, and A0 is an experimentally determined value that varies with the distance in degrees (δ) from the earthquake to the seismic station. From one Richter scale unit to the next, the amplitude difference is 10 times, whereas the energy released is 101.5, or 32 times. FIGURE 4–10 Locating an earthquake accurately requires at least three seismic stations. Based on the time separating the P and S waves, seismologists at each station (dark pink dots) can construct circles with radii (dashed lines) equal to the distance from the station to the epicenter (red star), allowing them to pinpoint its location. NEIC—National Earthquake Information Center, Boulder, Colorado. LDEO—Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York. CCM— Cathedral Cave, Missouri seismic station, operated by Saint Louis University Earthquake Center, Saint Louis, Missouri. NM—New Madrid, Missouri. Liquid outer core 5,100 5,000 Problems with the Richter scale are that it only esti mates the energy released at the focus of the earthquake, and that it underestimates the magnitude of large earth quakes (Shearer, 2009). Because of this, other forms of de termining magnitude have been invented. One alternative is the body-wave magnitude (mb), which is expressed math ematically as mb = log10 A + Q(∆, h) T (4–3) where A is the amplitude of ground motion in nanometers of the P waves measured at period T in seconds, and Q(Δ,h) is a correction factor that is a function of angle, LDEO NEIC 1,410 km 1,434 km CCM 234 km NM 0 500 kilometers 1,000 Geophysical Techniques and Earth Structure TABLE 4–1 | 77 Comparison of Earthquake Magnitude and Intensity MAGNITUDE TYPICAL MAXIMUM MODIFIED MERCALLI INTENSITY 1.0–2.9 I 3.0–3.9 II–III 4.0–4.9 IV–V 5.0–5.9 VI–VII 6.0–6.9 VII–IX 7.0 and higher X or higher The Modified Mercalli Intensity Scale was developed in 1931 by American seismologists Harry Wood and Frank Neumann. Abbreviated descriptions of the scale: I. Not felt except by a very few under especially favorable conditions. II. Felt only by a few persons at rest, especially on upper floors of buildings. III. Felt quite noticeably by persons indoors, especially on upper floors of buildings. Many people do not recognize it as an earthquake. Standing motor cars may rock slightly. Vibrations similar to the passing of a truck. Duration estimated. IV. Felt indoors by many, outdoors by few during the day. At night, some awakened. Dishes, windows, doors disturbed; walls make cracking sound. Sensation like heavy truck striking building. Standing motor cars rocked noticeably. V. Felt by nearly everyone; many awakened. Some dishes, windows broken. Unstable objects overturned. Pendulum clocks may stop. VI. Felt by all, many frightened. Some heavy furniture moved; a few instances of fallen plaster. Damage slight. VII. Damage negligible in buildings of good design and construction; slight to moderate in well-built ordinary structures; considerable damage in poorly built or badly designed structures; some chimneys broken. VIII. Damage slight in specially designed structures; considerable damage in ordinary substantial buildings with partial collapse. Damage great in poorly built structures. Fall of chimneys, factory stacks, columns, monuments, walls. Heavy furniture overturned. IX. Damage considerable in specially designed structures; well-designed frame structures thrown out of plumb. Damage great in substantial buildings, with partial collapse. Buildings shifted off foundations. X. Some well-built wooden structures destroyed; most masonry and frame structures destroyed with foundations. Rails bent. XI. Few, if any (masonry) structures remain standing. Bridges destroyed. Rails bent greatly. XII. Damage total. Lines of sight and level are distorted. Objects thrown into the air. From “The severity of an earthquake,” U.S. Geological Survey, 2000. Δ, from the hypocenter to the seismograph station and the focal depth, h, in kilometers. But large earthquakes, which have larger rupture sur faces and systematically radiate more long-period energy, are also underestimated by body-wave magnitude mea surement as the time component confines its effective use to the first ~10 seconds of an event (Spence et al., 1989). With the disadvantages of previous magnitude measures identified, Keiiti Aki, a seismologist at MIT, introduced the concept of “seismic moment” in the mid-1960s result ing in the development of moment magnitude (Mw) in the 1970s. It is expressed as 2 M w = log10 M 0 − 10.7 3 (4–4) where M0 is the seismic moment calculated in dyne-cm (10−7 N-m) (Spence et al., 1989; Shearer, 2009). Seis mic moment measures the size of an earthquake based on three factors: the area of fault rupture, the average amount of slip, and the force that was required to over come the friction holding the faulted rocks together that releases stored elastic energy. The moment magnitude is an effective measure of the total energy released during an earthquake, especially large earthquakes. For example, the great Alaska Good Friday (March 28) 1964 earthquake had a Richter magnitude, ML , of 8.5, but had a moment magnitude, Mw , of 9.2. Moment magnitude remains the standard that is used worldwide for reporting the energy released at the focus of an earthquake, because Richter magnitude values are less accurate for large earthquakes than moment magnitude values. Seismic Tomography Seismic tomography is a technology developed over the past several decades that has provided greater insight into the structure of the crust and mantle than has ever been resolved before. The technique is based mostly on the study of P and S waves and their changes in velocity from place to place within the Earth. These velocity changes may be caused by variations in structure, composition, or thermal properties. Tomographic images can be 2D or 3D, depicting crust and mantle structure in cross sections or as maps depicting the variation in P- or S-wave velocities with depth at different levels in the Earth (Figure 4–11). 78 | Introduction Earthquake data collected by the recent EarthScope Proj ect from an array of seismographs placed at 100-km inter vals over large segments of the United States has provided larger amounts and more detailed data than has existed anywhere on Earth before. These data are currently yield ing dividends in the form of greater resolution of structure in the mantle and lower crust. While subduction zones and their significance have been known for many years (e.g., Isacks et al., 1968), the structure of subduction zones and plates descending into the mantle had not been resolved until tomographic data became available (Figure 4–12). Today tomographic data permit us to see cold slabs of ocean crust and litho sphere descending into the mantle—even to depths of the core-mantle boundary (French and Romanowicz, 2015) (Figure 4–13). has become employed universally to determine if earth quakes on an active fault are produced by strike-slip, thrust, or normal faults (Figure 4–14). We have learned that many times the mainshock of an earthquake will have a different movement sense than many of the smaller earthquakes that make up the foreshock and aftershock sequence. A useful way of portraying the motion sense of earth quakes is to plot the location of each earthquake along an active fault using a stereographic projection (Appendix 2) of all of the first-motion arrivals that make up the com ponents of the earthquake sequence. The points on the stereoplot that represent population of earthquakes com monly are concentrated into different parts of the diagram based on movement upward or downward that can be re solved from the seismograph record. The boundaries be tween these areas of different motion sense become fields in the stereoplot and the patterns formed by the boundar ies indicate the motion sense (Figure 4–14). These patterns resemble those on beach balls, hence this usage. Focal Mechanisms and “Beach Balls” Seismologists discovered several decades ago that the motion sense on an active fault can be determined from the first arrivals of earthquake waves at a seismograph. Sykes (1967) used focal mechanisms of earthquakes along the Mid-Atlantic Ridge to confirm the hypothesis of Wilson (1965) that there is a special class of faults—called transform faults—that compensates different movement rates of segments of a plate (see Chapters 10 and 13). Since the pioneering application of this technique by Sykes to understanding earthquake mechanisms, the technique A potential field is any force field that acts on an object within its domain. For geologists, the potential fields of gravity and magnetism provide useful insights into the structure of the crust and upper mantle. Each has its Canada Atlantic Ocean tes Sta ited n U Crust 0 Subducted Farallon Plate 0 70 pth De 00 ) 1,4 (km FIGURE 4–11 Tomographic image from Pwaves through the mantle based on earthquake data collected in North America. The red color in the section represents low velocity; the blue color is high velocity, with greens and yellows representing intermediate velocities. The Farallon Plate descent is interpreted from the geometry derived from the velocity contrast between the green (low) and the yellow (high) areas, suggesting this is a colder descending slab. (The tomographic image on the side of the diagram is from S van der Lee et al., 2008, Earth and Planetary Science Letters, v. 273; the 3D image is by S. van der Lee and D. Grand at https://www.iris.edu/hq/ inclass/fact-sheet/seismic_ tomography) Potential Field Methods 00 2,1 00 2,8 Mantle Geophysical Techniques and Earth Structure FIGURE 4–12 Tomographic P-wave v elocity image of the cooler Pacific Plate descending beneath Japan. White circles are earthquake epicenters, which are most abundant near the top of the descending plate. (From D. Zhao, 2004, Physics of the Earth and Planetary Interiors, v. 146, p. 3–34.) 134° E 38°N 0 Honshu volcanoes Sea of Japan | 79 Pacific 142° E Ocean 36°N Moho Depth (km) 100 Plate boundary 200 300 400 Mantle plume FIGURE 4–13 Composite S-wave tomography of a section (a) from the western Pacific into North America. The red color in (b) represents warmer, ascending material, for example, beneath Hawaii, and the blue represents cooler segments, for example, the subduction zone descending beneath North America. (From S. W. French and B. Romanowicz, 2015, Nature, v. 525, p. 95–99.) Hawaii 500 1,000 1,500 2,000 2,500 (a) (b) –2.0 δVs/Vs (%) +2.0 Depth (km) own limitations and degree of precision and resolution, but of the two, magnetism has the greater resolution in the crust. Terrestrial Magnetism Earth magnetism was known to the Chinese at least as early as the eleventh century, and in the late thirteenth century (ca 1295) Marco Polo brought magnetite (lode stone) from China to Europe. In the sixteenth century, William Gilbert (1540–1603), an English physicist, noted that a sliver of magnetite hung by a string would orient itself more or less north-south. The Earth’s magnetic field is believed to originate in the core (Figure 4–15a), yet temperatures in the core are well above the Curie temperatures for most materials, includ ing metallic iron, which probably is the dominant element (90 percent iron, 10 percent nickel). The Curie temperature (after Pierre Curie, 1859–1906, a French physicist) is the temperature above which strongly magnetic (ferromag netic) materials lose their ability to interact with a mag netic field (Table 4–2); a weaker (paramagnetic) property, like that of most materials, remains. Although it is not ex actly certain why the Earth has a magnetic field, the best model is the self-exciting (-sustaining) dynamo, which was first proposed by British mathematician Joseph Larmor in | Introduction Cross-section view Map view First-motion data from seismographs Earth surface Fault plane Depth T (a) (1) P Focal sphere P Conjugate shear plane Upward Extension axis ne la n t p io ul c t Fa roje p FIGURE 4–14 Origin of beach balls. (a) (1) Cross section through a hypothetical normal fault illustrating the compressional (P) and tensional (T) axes. All are projected onto a vertical plane that contains the different components labeled. These are projected onto a horizontal equal-area stereonet in (2). (2) Distribution of first-motion determinations from earthquakes on the normal fault surface in (1). Filled dots indicate upward motion; open dots indicate downward motion. Once plotted on a stereonet, the filled and open dots form areas between which lines may be drawn separating the upand down-motion fields. These areas are then colored by motion sense (red—up; light red—down) producing the “beach ball” pattern. The example here depicts a normal fault. (b) Beach balls for different possibilities for motion on different kinds of faults (Chapter 11). (Modified from U.S. Geological Survey, 1996.) s h Co ea nju r p ga la te ne 80 Cross section plane Downward (2) Compression axis Dip of T Fault plane Strike-slip T P P T Dextral (right-lateral) Sinistral (left-lateral) Normal T P Thrust T P Oblique Thrust T P (b) TABLE 4–2 Curie Temperatures for Common Magnetic Materials MATERIAL CURIE TEMPERATURE (K) Pyrrhotite (FeS) 590 MgOFe2O3 713 Magnetite [Iron(II,III) oxide (Fe3O4)] 858 Hematite [Iron(III) oxide (Fe2O3)] 948 Iron (Fe) 1043 Values from Buschow, K. H. J., et al., eds., 2001, Encyclopedia of Materials: Science and Technology, 10, 388 p. the late nineteenth century to explain the magnetic field of our sun. His idea was refined and applied by Walter M. Elsasser and Sir Edward Bullard to explain Earth magne tism (Rikitaki, 1966). The theory is based on the premise that convection currents exist in the liquid core, trans porting hotter material upward and returning cooler ma terial to the interior (Figure 1–9). The convection cells are assumed to be oriented by the Earth’s rotation. The con vective transfer of liquid iron-nickel through a thermal gradient generates an electrical potential difference with an associated magnetic field. After the magnetic field is generated, the convective motion enhances and perpetu ates it, producing a self-exciting dynamo. The magnetic field is comprised of three components: inclination, declination, and intensity (Figure 4–15b). The inclination is the angular deviation of the field from the horizontal—at the magnetic north pole the inclination is 90°, whereas at the magnetic equator the inclination is 0°. Geophysical Techniques and Earth Structure Ocean crust Continental crust 410 km discontinuity Mantle Lithosphere Continental crust Outer core ~3,000 Oceanic ridge– new ocean crust created Inner core km Lithosphere Ocean crust 660 km discontinuity Continental crust Subduction zone– ocean crust destroyed (a) True North x D Geomagnetic north H I | 81 FIGURE 4–15 (a) Generalized whole-Earth structure illustrating the different major components that make up the Earth’s interior. The largest volume of material in the Earth is the mantle, which is composed of peridotite, dunite, and related ultramafic rocks. Higher pressures in the deeper parts of the mantle contain high pressure-temperature polymorphs of the magnesium silicates that make up the mantle rocks. Thickness of continental crust, composed of quartz and feldspar-rich minerals, is exaggerated. The 410 and 660 km discontinuities represent rapid changes in velocities of earthquake (P and S) waves, and may represent transitions from one polymorph of one or more of the silicate minerals with increasing pressure and temperature. The magnetic field is derived from the core. (b) Components of Earth’s magnetic field and their trigonometric relationships. x, y, and z are the orthogonal strength components. D—declination. I—inclination. H—horizontal intensity of the magnetic field (geomagnetic north). F—total intensity of the magnetic field. D and I are measured in degrees. All other elements are measured in nanoteslas (nT). (Modified figure from “Further Understanding of Geomagnetism,” National Oceanic and Atmospheric Administration website, 2015.) y z F Field intensity F= x2+y2+z2 x = H cos(D) H= x2+y2 y = H sin(D) z = F sin(I) ( ) z I = tan ( H ) y D = tan–1 x –1 (b) Declination is the angle on the horizontal plane between magnetic north and true north. Remanent Magnetism Remanent magnetism develops in rocks when they crys tallize or are deposited. The magnetic axes of magnetically susceptible minerals, such as magnetite, are aligned in the magma chamber or the depositional environment parallel to the magnetic field that exists during crystallization or deposition. In a magma, alignment does not occur until the temperature falls below the Curie temperature for that mineral (Table 4–2). Some minerals may crystallize com pletely and cool below their Curie temperatures before the entire magma crystallizes. Thus, the orientation of the Earth’s magnetic field at the time of crystallization or deposition is locked in. The study of paleomagnetism in volves measurement of these remanent fields and attempts to reconstruct the positions of the ancient magnetic poles, continents, and oceans. Remanent magnetism in igneous rocks is termed thermo-remanent magnetism (TRM), while magne tism in sedimentary rocks is called depositional remanent magnetism (DRM). Red beds are the most useful sedimentary rocks for paleomagnetic study because of the concentration of magnetic minerals. Measuring re manent magnetism involves an oriented sample and shielding it from the present-day magnetic field so that the orientation of the ancient magnetic field can be mea sured (Figure 4–16). Ideally, the measurement provides 82 | Introduction both an azimuth and angle toward the magnetic pole— the ancient pole position. Sedimentary and volcanic rocks are more desirable for study than most plutonic rocks because bedding provides an originally horizontal reference surface to which rotations and translations may be related. Many rocks undergo changes after they form that can alter and even erase paleomagnetic signatures. Chemical changes in composition or oxidation state may alter remanent properties. Magnetic Reversals A major difficulty is that the self-exciting dynamo theory does not account for polarity reversals: at intervals since at least the Paleozoic, the Earth’s magnetic field has sponta neously reversed polarity many times (Figure 4–17). The intervals are not uniform, and the time it took to actually reverse polarity was probably on the order of a few thou sand years—perhaps only hundreds of years. The dipole magnetic field may be lost during the reversal, leaving a weaker nondipole field. During reversals, the strength of the magnetic field decreases to about 15 percent of its normal strength, remaining there until the reversal pro cess is complete (Watkins, 1969). The reversal phenom enon raises many questions about the effect on life forms (among other things) because the magnetic field acts as a radiation shield. Removal of the shield will allow more ra diation to reach the Earth’s surface, increasing the muta tion rate. The reversals have been used to effectively date the age of ocean crust and understand sea floor spreading rates, and so on. Induced Magnetism The Earth’s magnetic field affects materials, such that some minerals are induced to become magnetic. The same is true for many metals. This property has been used with suc cess in airports for many years worldwide to detect metal objects carried by travelers. The induced field is measured from an airplane carrying a magnetometer flying straightline traverses back and forth across an area; the closer the spacing of the traverses at low altitude (e.g., at 300 m), the more detailed the survey. Applications Using Magnetism Intensity of the magnetic field may be measured using a magnetometer on the ground, at sea, or from an airplane. Magnetic-intensity profiles may be plotted along the data contoured between successive traverse lines to produce a magnetic-anomaly map (Figure 4–18a). An anomaly is a deviation from an assumed average value for magneticfield intensity. Rocks that contain a high percentage of magnetically susceptible minerals (such as magnetite) commonly produce positive anomalies, and rocks that con tain a low percentage of magnetically susceptible miner als produce negative anomalies. The anomalies may also be enhanced, cancelled, or reversed if strong remanent magnetization is present. The total intensity of a magnetic field measured by a magnetometer is the vector sum of the Earth’s field and that produced by the induced magnetiza tion of the rock. These components consist of the primary field intensity, plus the induced magnetic susceptibilities of all crustal rocks (down to the Curie isotherm—the tem perature at which an otherwise magnetic material loses its magnetic properties), plus the remanent field component for the entire rock body. The amplitude of the magnetic anomaly produced by a rock body varies directly with the susceptibility of the body and with its shape, and inversely with the square 400° C FIGURE 4–16 When magnetite grains are heated above their Curie temperature, the grains demagnetize [(a)–(c)]. As the material cools back below the Curie temperature, the magnetic field of the grain will realign with the prevailing magnetic field (magnetic North) [(d) and (e)]. Remanent magnetism is measured relative to the conditions when the material was deposited or was last heated above its Curie temperature. Note that particles not heated above their Curie temperatures maintain their original magnetic orientation. (Modified from figure by Paul Linford, English Heritage/University of Bradford, UK.) 400° C (b) (a) 400° C 400° C (c) 400° C Demagnetization Prevailing magnetic field Induced magnetization (d) (e) Remagnetization Geophysical Techniques and Earth Structure CENOZOIC AGE MAGNETIC PERIOD (Ma) POLARITY EPOCH HOLOCENE QUATERPLEISTOCENE NARY MESOZOIC AGE MAGNETIC PERIOD EPOCH (Ma) POLARITY 70 90 100 110 120 OLIGOCENE 20 25 30 130 50 EOCENE 45 PALEOGENE 170 40 180 190 65 220 PALEOCENE 60 LATE MIDDLE EARLY 200 210 55 EARLY 150 160 35 LATE 140 JURASSIC MIOCENE 15 NEOGENE 10 80 230 240 250 TRIASSIC 5 CRETACEOUS PLIOCENE LATE MIDDLE EARLY FIGURE 4–17 Magnetic polarity reversals from the Mesozoic to the present. Black intervals are normal polarity—as at the present time—and white are reversed. The gray areas indicate times of rapid polarity change. (From Walker et al., 2013, Geological Society of America Geologic Time Scale, v. 4.0.) of the distance from the body to the magnetometer (Figure 4–19). The slope (or gradient) shown by the spacing of contours on the flank of the anomaly is actually used to determine depth to the anomaly. The technique should | 83 be used only for estimating depth; more accurate determi nations can be made by other techniques. Magnetic rock bodies, such as plutons, produce high-amplitude anomalies with steep gradients, wherein amplitudes (and gradients) decrease as the distance to the magnetometer increases. Dikes only a few meters thick, which generate sharp, high-amplitude anomalies when measured with a ground magnetometer or during a low-altitude (150 m) airborne survey, would not be resolved by high-altitude air borne surveys (500 to 800 m). Therefore, low-altitude airborne surveys are more useful in resolving near-surface geology and structure. Surveys flown at high altitude are more useful in resolving structure in the deep crust and upper mantle. The concepts of terrestrial magnetism are widely ap plied in solving structural problems. Faults may be rec ognized by associated linear trends and by truncation of magnetic trends in rock bodies (Figure 4–20). Folds may be identified by noting the curvature of contrasting mag netically susceptible units. Plutons may be recognized by the shape of the magnetic anomaly. The bulk mafic or felsic composition of plutons may be estimated by noting the kind of associated magnetic anomaly (positive or negative) in conjunction with the corresponding gravity anomaly (positive or negative). Magnetic-anomaly maps may be used to identify boundaries and assess the crustal charac ter of suspect terranes. Linear magnetic anomalies in the sea floor have been dated and correlated to provide a better understanding of the evolution of oceanic crust during the past 200 m.y. Data from paleomagnetic studies are useful in deter mining the paleolatitude of a rock body or a large crustal block, but cannot be used directly to determine longi tude. Local rotation of a rock body due to faulting may be measured. Apparent paleo-polar wandering (APW) curves derived from paleomagnetic studies are useful in repro ducing ancient positions of a continent (Figure 4–21). An important assumption made in paleomagnetic studies is that magnetic north, on average, corresponds with the Earth’s spin axis (geographic North or South). Such stud ies have been used to determine the original positions of cratonic blocks in Precambrian shields and also the posi tions of larger continents and suspect terranes during later geologic periods. Gravity Gravity is the force of mutual attraction among all bodies in the universe. It is exerted on and by all components of the Earth, including rock bodies. The more dense and volumi nous the body, the stronger the force of gravity, so denser rocks such as gabbro possess a stronger gravitational force. 84 | Introduction 100° W 95° W 90° W Manitoba Ontario North Dakota Minnesota 45° N 45° N Michigan Wisconsin South Dakota 400 300 200 150 125 100 90 80 70 60 50 40 30 25 20 15 10 5 0 –5 –10 –15 –20 –25 –30 –35 –40 –50 –60 –70 –80 –90 –100 –125 –150 –175 –200 –300 Iowa Nebraska Illinois Missouri Kansas 100° W 95° W 0 (a) 40° N 40° N (nT) 100 90° W 200 300 kilometers FIGURE 4–18 Magnetic-anomaly (a) and Bouguer gravity-anomaly maps (b) (next page) of the same area in the north-central United States depicting magnetic anomalies in the Precambrian basement. The structure that produced the prominent northeast-southwest linear gravity and magnetic high in the center of (a) and (b) is the Mid-Continent rift, formed during the Late Proterozoic. The high is interpreted in (c) as having been produced by mafic igneous rocks that have been traced to the surface as the Keweenawan basalts of northern Michigan. Note the greater detail in the aeromagnetic imagery in (a) due to its higher resolution. The flanking gravity low is interpreted to have been produced by rift-related sedimentary rocks. Magnetic field data in (a) are in nanoteslas (nT); gravity data in (b) are in milligals (mGal). (Magnetic data from Bankey et al., 2002, Digital data grids for the magnetic anomaly map of North America: U.S. Geological Survey Open-File Report 2002–414. Gravity data are from R. P. Kucks, 1999, Bouguer gravity-anomaly data grid for the conterminous United States: U.S. Geological Survey Digital Data Series DDS–9.) Geophysical Techniques and Earth Structure 100° W 95° W | 85 90° W Manitoba Ontario North Dakota Minnesota 45° N 45° N Michigan Wisconsin South Dakota (mGal) 10 0 –5 –10 –15 –20 –25 –30 –35 –40 Iowa –45 –50 –55 Nebraska –60 –65 Illinois –75 –80 40° N 40° N –90 –95 –105 –115 Missouri Kansas 100° W 95° W 0 (b) FIGURE 4–18 (continued) 100 90° W 200 kilometers 300 86 | Introduction Magnetic profile Depth WI MN SD Depth IA ks NB M afi c ro c Sedimentary rocks Sedimentary rocks MO Depth KS Axes of magnetic and gravity highs FIGURE 4–19 The width of magnetic anomalies is depth dependent. As the depth to the source of the anomaly increases, the amplitude decreases and the anomaly widens. (c) FIGURE 4–18 (continued) Newton’s law of gravitation states that the force of gravity (F ) is directly proportional to the masses (m) of the objects involved and inversely proportional to the square of the distance (r) between them. Written in vector form F12 = −G m1m2 r12 2 rˆ12 (4–5) where F12 is the force exerted by object 1 on object 2, G is the universal gravitational constant, 6.67408 × 10−11 N m2 kg−2 (or, 6.674 × 10−8 cm3 g−1 s−1; the negative sign before the G indicates that object 2 is attracted to object 1), |r12| is the absolute value of the distance (radius) between the objects, and r̂12 is the unit vector from m1 to m2 representing the direction of the force (Figure 4–22). Every object in our solar system exerts a force of attrac tion on every other body. The magnitude of gravity on the Earth is related to the fact that the Earth is large in compar ison with objects on it and to any rock body in it. Because we are relatively close to the source of gravity on the Earth, as compared with other objects in space, this force holds us on the Earth. Newton’s law and the force of gravity are used to calculate the amount of fuel needed to power spacecraft from the Earth to our moon and to other planets. A gravity meter (gravimeter) is used to measure varia tions in the force of gravity on the Earth. First, a value is assumed for average density of the crust where the meas urements are made. A density of 2.65 g cm−3 (the density of average granite) is commonly assumed for continental crust, and 3.0 g cm−3 (the density of average basalt) is as sumed for oceanic crust. These densities should lead to an acceleration of gravity of 1 Gal (1 cm s−2)—a unit named after Galileo (1564–1642). The average value of gravity is 980 Gals (9.8 m s−2). Measured values of gravity that de viate from average values define gravity anomalies. Meas urements of differences in the gravity field are made in units of mGal (10−3 Gal), and modern gravity meters (Figure 4–23) are capable of measurements within ± 0.04 mGal, provided the elevation of the station is accurately known. If the measured value of gravity at a station is greater than predicted by using the average density assumed, a positive gravity anomaly exists; if it is less, a negative gravity anomaly exists. Gravity profiles may be constructed or, Geophysical Techniques and Earth Structure 87 | VA 78°W Virginia NC Faults Mesozoic dike swarm 36°N 36°N Late fold axial surface Truncated fold Pluton Early fold axial surface Plutons (nT) Pluton 400 300 200 150 125 100 90 80 70 60 50 40 30 25 20 15 10 5 0 –5 –10 –15 –20 –25 –30 –35 –40 –50 –60 –70 –80 –90 –100 –125 –150 –175 –200 –300 North Carolina South Carolina 0 (a) 25 50 100 SC 78°W kilometers Pluton NC 0 (b) 25 50 100 kilometers FIGURE 4–20 Magnetic-anomaly map of part of the North Carolina Piedmont (a) and interpretation (b) [white dashed line in (a)] showing truncation of folds by faults. The fold is defined by highly magnetic amphibolite; a swarm of Jurassic diabase dikes is suggested by subparallel linear anomalies. nT—nanoteslas, a measure of magnetic field intensity. (c) (following page) Sea-floor magnetic anomalies in the Pacific off the Pacific Northwest coast. Magnetic field data in (a) and (c) are in nanoteslas (nT). (All magnetic data from Bankey et al., 2002, Digital data grids for the magnetic anomaly map of North America: U.S. Geological Survey Open-File Report 2002–414.) if the gravity measurements are distributed widely enough, the data may be contoured as a gravity anomaly map (Figures 4–18b and 4–24). If the map is corrected only for elevation above sea level, it is called a free-air gravity map; if data are corrected for differences in both elevation and density between sea level and the elevation where meas urements were made, a Bouguer gravity-anomaly map is produced (the name honors a French surveyor and hydrog rapher of the eighteenth century, Pierre Bouguer). Free-air measurements are most useful for determining how close a portion of the crust is to isostatic equilibrium. If a large free-air anomaly is present, the mass is out of isostatic equi librium. A terrain correction is frequently made for Bou guer data, and, if such corrections are made and plotted as a map, the result is a complete Bouguer anomaly map. The magnitude of the gravity field varies with latitude, elevation, and Earth tides. Gravity measurements are com monly made from ships, and may be made from aircraft, but with greater difficulty and much less reliability. Depth to a mass producing a gravity anomaly may be calculated after assuming a particular shape for the body causing the anomaly. The calculations remain simple if the shape is assumed to be a sphere or a cylinder. If the source of an anomaly of amplitude g 0 is assumed to be a spherical body, the depth to the body (center of the sphere) may be calculated from the half-width of a profile (at 1/2 the maxi mum amplitude) through the anomaly (Figure 4–25a) as 3 −  x 12  2   g ( x ) = g 0 1 + 22  ,  z    (4–6) | 134°W 132°W 130°W 128°W 126°W 54°N 136°W Introduction 124°W 120° E 120° W North Pole 48°N 400 300 200 150 125 100 90 80 70 60 50 40 30 25 20 15 10 5 0 –5 –10 –15 –20 –25 –30 –35 –40 –50 –60 –70 –80 –90 –100 –125 –150 –175 –200 –300 134°W 60 °N 60° W 60° E 40 °N 46°N PACIFIC OCEAN 20 42°N 44°N °N 0 3,000 kilometers 0° FIGURE 4–21 Plot of the apparent polar wandering (APW) paths of Europe and North America through the past 500 m.y. –C—Cambrian. S—Silurian. D—Devonian. C—Carboniferous. P—Permian. TR—Triassic. J—Jurassic. K—Cretaceous. PE—Paleogene. (Modified from H. L. Levin, 2013, The Earth through Time, 10th ed.) 40°N 48°N 46°N 44°N 42°N 40°N North American path 50°N 50°N 52°N 52°N British Columbia (nT) (c) European path 180° 54°N 88 132°W 130°W 0 200 128°W 126°W 124°W 400 z kilometers F12 FIGURE 4–20 (continued) m2 F21 where x is the width of the gravity anomaly and z is the depth to the anomaly. From the half-width of the anomaly, 3 −  x 12  2   x 1 = 1 + 22   z  , 2   −1  x 12    g ( x ) = g 0 1 + 22  .  z    r12 (4–7) where z = 1.305x1/2. Calculation of the depth of a cylindrical body (Figure 4–25b) is even simpler: (4–8) r x m1 y FIGURE 4–22 Components of the forces of gravity of two bjects acting upon one another. m1 and m2 —masses of the o objects. F12 and F21—force exerted by object 1 on object 2 and vice versa. r̂12 —unit vector representing the direction of the force. r—distance (radius) between the centers of the objects. Geophysical Techniques and Earth Structure 81°W Spartanburg Gabbros Rock Hill North Carolina 35°N 35°N 82°W 89 | Kershaw Granites (mGal) 5 0 Granites (plutons) –40 –60 –70 82°W 81°W 0 25 50 81°W (nT) North Carolina 400 100 35°N 82°W 35°N 100 kilometers (a) 50 10 0 –10 −1     x 1 = 1 + 22  .  z  2   x 12 34°N 34°N –50 FIGURE 4–23 Gravity measurement being made with a LaCoste Again, using the half-width of the anomaly, –20 –30 South Carolina and Romberg Model G gravity meter. This instrument combines the principles of the long-period seismograph and a “zerolength” spring—with tension proportional to the length of the spring. (RDH photo.) –10 –50 (4–9) –100 Plutons –300 If the body is assumed to be cylindrical, the half-width equals the depth to the anomaly. Gravity may be used to characterize large regions of the crust. Faults may be recognized by contrasting ampli tudes and patterns on adjacent blocks. The linearity of the actual fault is sometimes obvious, but more frequently the truncation, deflection, or offset of anomalies at faults is more readily observed, a result of fault displacement of the masses that produced the anomaly (Figures 4–18b and 4–26). Gravity data represent integrated values for the ac celeration due to gravity for the whole Earth at a single point. As a result, the data are less specific for near-surface features unless large density contrasts exist in surface rocks and the gravity survey is very detailed. Generally, with a station spacing of 2 to 5 km, the data yield only re gional patterns, gradients, crustal boundaries, very large faults, and plutons. Gravity data are useful for determin ing the shape and broad composition of plutons and sedi mentary basins. Granitic plutons produce gravity lows because of their lower density, and mafic plutons yield gravity highs because of their higher density. Granitic rocks commonly produce both gravity lows and magnetic 34°N 34°N Applications Using Gravity South Carolina 82°W 81°W 0 (b) 25 50 100 kilometers FIGURE 4–24 (a) Bouguer gravity-anomaly map of part of the South Carolina Piedmont. Circular anomalies indicate plutons. Gravity lows are granitic plutons; highs are mostly gabbros. (b) Magnetic-anomaly map of same area in (a) showing several plutons. [(a) After P. Talwani, L. T. Long, and S. R. Bridges, 1975, Simple Bouguer map of South Carolina, South Carolina Geological Survey. Gravity data in (a) are from R. P. Kucks, 1999, Bouguer gravity-anomaly data grid for the conterminous United States: U.S. Geological Survey Digital Data Series DDS–9. Magnetic data in (b) are from Bankey et al., 2002, Digital data grids for the magnetic anomaly map of North America: U.S. Geological Survey Open-File Report 2002–414.] lows, but if a granite contains enough magnetite, it will yield a gravity low and a magnetic high. Mafic plutons tend to produce both gravity highs and magnetic highs. Neither gravity nor magnetic data alone yield precise identification of individual features, although both used together are a 90 | Introduction A g0 20 40 40 z 20 0 z A' 1g 2 0 x1/2 x0 x1/2 x0 30 A' 1g 2 0 A A g0 0 A' 0 A A' Spherical body producing anomaly (a) (b) Cylindrical body producing anomaly FIGURE 4–25 Calculation from gravity data of the depth to spherical (a) and cylindrical (b) bodies. Surface Surface + + 0 mGal 0 mGal – (a) – (b) FIGURE 4–26 Geologic cross sections and gravity profiles showing kinds of anomalies that ideally develop along normal faults (a) and thrust faults (b). The striped layer has a higher density. powerful tool for delineating faults, plutons, and other structures (Figure 4–18). Gravity data can be used to cal culate a gravity model for a part of the crust (Figure 4–27). It is also possible using modern computer technology to remove the “long-wavelength” component of the gravity field to emphasize the near-surface crustal geology (Figure 4–28). Electrical Methods Measurements of electrical conductivity and resistivity are useful for determining certain crustal properties. Conduc tivity studies have been used for many years in the search for sulfide ore bodies, because metallic sulfides are better electrical conductors than most other rock minerals. Re sistivity and conductivity are usually measured by setting electrodes in the ground and recording for various lengths of time. Airborne techniques also exist. Rock layers of greater conductivity than neighboring layers are detectable, but depth to the conducting layer may only approximately be determined. Graphite-rich layers and water containing small quantities of dissolved solids are also conductive and detectable. Electrical-resistivity anomalies may be exhibited by bodies composed of silicate rocks in a terrane otherwise dominated by carbonate, or by evaporites in a sedimentary terrane dominated by clastic rocks (Figure 4–29). Borehole Geophysics Boreholes into the Earth provide valuable information about subsurface geology. Direct information about sub surface geology, fractures, mineral deposits, and hydro carbons is derived from core obtained from boreholes (Figure 4–30). Cuttings brought up in fluids, where it is not possible to core, provide much useful information about rock types and valuable minerals and hydrocarbons, but less information about the locations of geologic contacts and fractures. In many places, different factors make it Bouguer gravity anomaly Insubric line milligals 50 (a) –50 –150 Gravity model kilometers 0 2.5 3.4 3.4 gm cm–3 60 (b) 2.8 2.8 30 Seismic structure kilometers 0 6.1 5.5 6.2 30 6.8 5.3 6.1 6.0 5.8 6.3 6.7 5.4 6.15 6.1 6.9 8.1 8.2 (c) Rhine graben Geologic model Jura Molasse basin 6.0 5.4 6.3 7.2 8.2 5.9 6.2 8.1 60 6.1 6.2 5.4 6.4 6.6 8.1 km s–1 Aar massif Po basin 0 kilometers European crust African crust 30 0 60 (d) NNW 50 100 SSE kilometers Intensely deformed basement and Mesozoic sedimentary rocks of the Penninic zone. Crystalline basement of external massifs and underriding plate. Molasse sediments of foreland, and Mesozoic sedimentary rocks and Tertiary molasse of southern Alps and Po basin. Basement of obducted block. FIGURE 4–27 Gravity profiles observed (red line in part a) and calculated (dashed line in part a) for the Alps were employed to construct the gravity model in (b). Both gravity and seismic refraction data (c) were used to construct the geologic section in (d). (From G. D. Karner and A. B. Watts, Journal of Geophysical Research, v. 88, p. 10,449–10,477, 1983, © by the American Geophysical Union.) 91 86° W 84° W 82° W 80° W 78° W 76° W 92 88° W Introduction S CP 36° N A NY 34° N Peri-Gondwanan terranes 34° N NY A (nT) 300 220 180 140 100 60 40 20 0 –20 –60 –80 –100 –120 –140 –160 –200 –220 –240 –280 –320 –380 –460 CPS 32° N SS SS 32° N African crust 0 100 200 kilometers 300 30° N 30° N (a) 88° W 86° W 84° W 82° W | 36° N 80° W 78° W FIGURE 4–28 (a) Magnetic-anomaly map of several southeastern U.S. states in spectral pastel colors. Magnetic anomalies represent features in the crust at depths less than the Curie temperature (~30 km here) of magnetically susceptible minerals, most likely magnetite. Note the differences in the nature of magnetic anomalies. Large areas of a single color mark different crustal “terranes.” Near-circular anomalies are plutons. CPS—Central Piedmont suture. NYA—New York–Alabama magnetic lineament. SS—Suwannee suture. (Map generated by D. L. Daniels, U. S. Geological Survey.) 88° W 86° W 84° W 82° W 80° W 78° W 76° W 36° N S CP 36° N A NY 34° N Peri-Gondwanan terranes CPS 32° N 32° N SS SS African crust 0 100 200 kilometers 300 30° N 30° N (b) 88° W 86° W 84° W 82° W 80° W 78° W Geophysical Techniques and Earth Structure NY A 34° N FIGURE 4–28 (continued) | (b) Magnetic-anomaly map (in nanoteslas, nT) of the same area as in (a) using a different spectral color scheme. Note the difference in detail resolved along the Suwannee suture (SS) in southern Alabama, Georgia, and South Carolina. CPS—Central Piedmont suture. NYA—New York–Alabama lineament. Fuchsia and red colors represent magnetic highs; green and blue colors are magnetic lows. (Map generated by D. L. Daniels, U. S. Geological Survey.) 93 88° W 86° W 84° W 82° W 80° W 78° W 76° W 36° N 36° N 34° N 34° N 32° N 32° N 0 100 200 300 30° N kilometers 30° N 88° W 86° W 84° W 86° W 84° W 82° W 80° W 78° W (c) 88° W 82° W 80° W 78° W 76° W 36° N 36° N 34° N 34° N 32° N 32° N 0 100 200 kilometers 30° N (d) 88° W 86° W 84° W 82° W 80° W 300 30° N 78° W FIGURE 4–28 (continued) (c) Bouguer gravity map of the same area as (a) and (b). This map depicts the gravity field from the surface to some part of the mantle, so the near-surface geologic features are much less distinct than in the magnetic maps. Circular anomalies mostly represent plutons, however. Fuchsia and red colors represent gravity highs; green and blue colors are gravity lows. (Map generated by S. L. Snyder, U.S. Geological Survey.) (d) Fiftykilometer high-pass filtered spectral-colored gravity data from the same area. This process produces an image that filters out the long-wavelength component of the gravity field, leaving the near-surface features of greater or less density—much closer to representing geologic features. Fuchsia and red colors represent gravity highs; green and blue colors are gravity lows. (Map generated by D. L. Daniels, U. S. Geological Survey.) 94 Mt Jefferson W E 0 700 −60 500 90 0 800 60 B 300 A 0 00 10 11 12000 130 0 0 −40 140 0 70 0 −80 C 1300 00 14 0 120 0 1110000 1 0 130 0 110200 1 300 1 −180 0 140 10 0 140 0 −100 2 0 900 00 −160 −200 3 10 −140 −200 4 1100 1200 140 00 14 −120 95 1000 00 13 −100 400 500 600 700 800 900 400 500 600 700 0 80 0 90 00 0 11120 00 13 Depth (km) 400 80 10100 900 0 12 10 00 0 −20 | 0 100 Log10 (Resistivity Ohm-m) Geophysical Techniques and Earth Structure 200 300 0 Distance (km) FIGURE 4–29 Interpretation of magnetotelluric data from a transect across the Cascadia subduction zone from onshore California and Oregon into the Pacific Ocean to the west. Most of the data were collected on shore, but some were obtained from the ocean crust. Spectral colors represent the electrical resistivity (and conductivity) of the crust and mantle along the transect, so dark blue areas have very high electrical resistivity, whereas the red areas have high electrical conductivity. The areas labeled A, B, and C are thought to be regions above the subduction zone where conducting fluids (probably seawater) have been carried down the subduction zone. The lines with numbers are isotherms determined by other techniques, and the numbers are temperatures in °C. (From Evans et al., 2014, Earth and Planetary Science Letters, v. 402.) uneconomic or impractical to core every hole drilled into the Earth, so a technology—geophysical wireline logging— was developed over many decades to measure various physical and chemical properties of rocks, fluids, and the interactions between fluids and rocks in boreholes. Every year geophysical logs become more sophisticated as exist ing logs are improved and new logs are invented. The discussion in this section was derived from several sources. Online resources, along with several useful ref erences on geophysical logging, for example, Asquith and Gibson (1982), Schlumberger (1989), Lovell and Parkinson (2002), and Evenick (2008), served as principal sources of information. Common geophysical logs include: natural gamma ray, resistivity, spontaneous potential, neutron, density, temperature, and photoelectric logs (Figure 4–31). Geo physical logs measure the variations in a particular prop erty and are plotted versus depth in the borehole. Each log measures a different property of the rocks or the in teraction between the rocks and fluids in the borehole, so the graph recorded shifts to the right or left depending on rock type, porosity, nature of fluids in the rock, and in some areas (mostly unconsolidated sediments) pres sure boundaries (Figure 4–32). In addition, caliper (hole diameter), sonic, dip meter, conductivity, and nuclear magnetic resonance (NMR) logs may be recorded. Once a hole has been drilled, the drilling tools are removed and a logging truck (Figure 4–33a) and its associated logging tools replace the drilling equipment. Different tools are linked together into a single logging tool that may range from 12 m (~38 ft) to > 30 m (> 100 ft) long. The company drillling the borehole selects the logs to be acquired, and the wireline logging tool is assembled accordingly—the greater the variety of logs collected, the greater the cost of logging (Figure 4–34). Natural Gamma-Ray Log Different rock types produce different amounts of natural gamma rays, depending on the concentrations of uranium, thorium, and radioactive potassium in the rock. These ra dioactive isotopes produce gamma rays, and the concen tration of these elements is proportional to the number of gamma rays produced per second (counts/second). Rocks like limestone and dolostone contain almost none of these elements, whereas shale—and especially black shale— contains measurable quantities of these elements and pro duces a significant gamma-ray signature (Figure 4–35). 96 ESSAY | Introduction Geophysical Data and the Structure of Mountain Chains The proliferation of high-quality geophysical data that began in the 1970s has led to improved interpretations of geologic structure. Examples can be drawn from all of the continents. Structural trends in the Precambrian basement imaged by aeromagnetic data continue uninterrupted many kilometers westward beneath the foreland fold-thrust belt of the Ca nadian Rockies, helping to demonstrate the lack of basement involvement in the thrust belt. Continuity of the thin-skinned fold-thrust belt exists farther west beneath the crystalline core of the orogen and is more extensive than could be proved by surface geologic data alone (Price, 1981). Earlier, seismic reflection data (Bally, Gordy, and Stewart, 1966) from the outer parts of the foreland had revealed the thin-skinned 100 Precambrian milligals (mG) 100 style of deformation here. Earlier still, its existence had been only speculative (but correct), based on the work of Rich (1934; Chapter 12) in the Appalachians. An integral part of many mountain chains, from the Precambrian to the Tertiary (Figure 4E–1), is a gradient from gravity low toward the foreland to gravity high toward the closed ocean. There, the position of the gradient frequently coincides with the surface position of a suture, and on that basis, Thomas (1983) concluded that the gradient localized a former collision zone. Changes in the nature of aeromagnetic anomaly patterns also coincide in many places with gravity gradients and sutures, but in the same orogen the gravity gradient may follow a suture for some distance and then diverge from (b) kilometers (a) 0 0 ure Older province 40 120 0 0 Sut Younger province +0.07 −0.4 40 120 −0.33 Appalachian SE milligals (mG) NW (c) 20 120 0 80 milligals (mG) (d) M AA AM 0 0 0 0 kilometers (e) WA AP Sut Laurentian block ure −0.4 50 0 100 Accreted block +0.09 −0.31 s 50 kilometers FIGURE 4E–1 Gravity profiles (a) and a gravity-based crustal model (b) across several Precambrian orogens in the Canadian shield, and similar profiles (c) and (d), and a model (e) for the southern and central Appalachians. The gravity low is always found closer to the older province (older core of the continent) and the high closer to the internal parts of the mountain chain. AP—average Precambrian profile. AA—average Appalachians profile. AM—curve corresponding to the type Appalachian model. WA—West African craton curve. M—curve for the Musgrave block in Australia. (After M. D. Thomas, 1983, Geological Society of America Memoir 158.) Geophysical Techniques and Earth Structure it. The Appalachians is one example: the gravity gradient coincides with the suture between an exotic terrane and North America from Alabama to Virginia, then diverges from the suture to the north. Thus, Hutchinson et al. (1983) concluded that the Appalachian gravity gradient, and perhaps others, did not have a unique origin. Also, some geologists have speculated that the Appalachian gradient formed during Mesozoic extension and crustal thinning related to the opening of the Atlantic Ocean and not at all to contraction processes. Karner and Watts (1983) declared, however, that the gravity field over both ancient and modern mountain chains was consistent with the processes related to the construction of mountain chains by compression (also see Figure 4–27). The extent of the huge Appalachian Blue Ridge–Piedmont Type C thrust sheet (Chapter 12) has been better delineated by geophysical data (Figures 4–4b and 4–4c). Its existence throughout the Blue Ridge and part of the Piedmont had been deduced from surface geologic data (Bryant and Reed, 1970; Hatcher, 1972). Aeromagnetic data from the southern Appalachians reveal very little of the surface structure within the thrust sheet in both the Blue Ridge and much of the Piedmont, leading Hatcher and Zietz (1978, 1980) to suggest that the thin sheet extends across all the Blue Ridge and much of the Piedmont. The gravity data were incorporated into the interpretation and confirmed that the changes in magnetic and gravity patterns occur at the same place—the gravity gradient just discussed. In 1978, COCORP collected the data for a crustal seismic reflection line across the southern Appalachians. A strong set of subhorizontal reflectors was detected at depths of 2 km at the northwest end to 12 km or more at the southeast end. These reflectors were initially interpreted as the Appalachian–Blue Ridge thrust (Cook et al., 1979) but were later said to be derived from sedimentary rocks beneath the thrust sheet (Ando et al., 1983; Cook et al., 1983). Seismic reflection data acquired in 1984 in the Blue Ridge and western Piedmont (Çoruh et al., 1987) showed that the crystalline thrust sheet is much thinner in the Blue Ridge than suggested by the COCORP data and that the platform sedimentary sequence beneath is deformed into a series of duplexes that, in turn, have arched the crystalline sheet above the duplexes. Large recumbent folds have also been imaged within the crystalline sheet in the Piedmont (Figure 4–4b), but little of the near-surface structure is visible in the Blue Ridge, probably because the surface dip is moderate to steep. Geophysical data should provide more useful data on crustal structure in the future—and imaging of structures heretofore unknown will lead to new controversies. The greatest strides in our knowledge of crustal structure will continue to be made by structural geologists and geophysicists working together to interpret geologic and geophysical data. | 97 References Cited Ando, C. J., Cook, F. A., Oliver, J. E., Brown, L. D., and Kaufman, S., 1983, Crustal geometry of the Appalachian orogen from seismic reflection studies, in Hatcher, R. D., Jr., Williams, H., and Zietz, I., eds., Contributions to the tectonics and geophysics of mountain chains: Geological Society of America Memoir 158, p. 83–102. Bally, A. W., Gordy, P. L., and Stewart, G. A., 1966, Structure, seismic data, and orogenic evolution of the southern Canadian Rockies: Bulletin of Canadian Petroleum Geology, v. 14, p. 337–381. Bryant, B., and Reed, J. C., Jr., 1970, Geology of the Grandfather Mountain window and vicinity, North Carolina and Tennessee: U.S. Geological Survey Professional Paper 615, 190 p. Cook, F. A., Albaugh, D. S., Brown, L. D., Kaufman, S., Oliver, J. E., and Hatcher, R. D., Jr., 1979, Thin-skinned tectonics in the crystalline southern Appalachians; COCORP seismic reflection profiling of the Blue Ridge and Piedmont: Geology, v. 7, p. 563–567. Cook, F. A., Brown, L. D., Kaufman, S., and Oliver, J. E., 1983, The COCORP seismic reflection traverse across the southern Appalachians: American Association of Petroleum Geologists Studies in Geology, v. 14, 61 p. Çoruh, C., Costain, J. K., Hatcher, R. D., Jr., Pratt, T. L., Williams, R. T., and Phinney, R. A., 1987, Results from regional Vibroseis profiling: Appalachian ultradeep core hole site study: Geophysical Journal of the Royal Astronomical Society, v. 89, p. 473–474. Hatcher, R. D., Jr., 1972, Developmental model for the southern Appalachians: Geological Society of America Bulletin, v. 83, p. 2735–2760. Hatcher, R. D., Jr., and Zietz, I., 1978, Thin crystalline thrust sheets in the southern Appalachian Inner Piedmont and Blue Ridge: Interpretation based upon regional aeromagnetic data: Geological Society of America Abstracts with Programs, v. 10, p. 417. Hatcher, R. D., Jr., and Zietz, I., 1980, Tectonic implications of regional aeromagnetic and gravity data from the southern Appalachians, in Wones, D. R., ed., The Caledonides in the USA: Virginia Tech Geological Sciences Memoir 2, p. 235–244. Hutchinson, D. R., Grow, J. A., and Klitgord, K. D., 1983, Crustal structure beneath the southern Appalachians: Nonuniqueness of gravity modeling: Geology, v. 11, p. 611–615. Karner, G. D., and Watts, A. B., 1983, Gravity anomalies and flexure of the lithosphere at mountain ranges: Journal of Geophysical Research, v. 88, p. 10,449–10,477. Price, R. A., 1981, The Cordilleran foreland thrust and fold belt in the southern Canadian Rockies, in McClay, K. R., and Price, N. J., eds., Thrust and nappe tectonics: Geological Society of London Special Publication 9, p. 427–448. Rich, J. L., 1934, Mechanics of low-angle overthrust faulting as illustrated by Cumberland thrust block, Virginia, Kentucky and Tennessee: American Association of Petroleum Geologists Bulletin, v. 18, p. 1584–1596. Thomas, M. D., 1983, Tectonic significance of paired gravity anomalies in the southern and central Appalachians, in Hatcher, R. D., Jr., Williams, H., and Zietz, I., eds., Contributions to the tectonics and geophysics of mountain chains: Geological Society of America Memoir 158, p. 113–124. 98 | Introduction FIGURE 4–30 Core of several rock types (and formations) recovered from a borehole near Carthage, Tennessee. The core consists of partly weathered Mississippian crinoid reef that grades downward (left to right) into greenish Mississippian siltstone, then into black Devonian-Mississippian shale. Beneath the black shale is an unconformity separating the shale from Ordovician limestone. Some 90 m.y. are missing from the geologic record at this boundary. Each piece of core has a diameter of 3.4 cm (1.5 in) and a maximum length of 77.5 cm (30.5 in). (Core donated by F. Smith, Pasminco Mining Company; RDH photo.) Sandstone produces a gamma-ray signature that is related to the amount of clay impurities in the rock unit. Large amounts of clay would produce a larger gamma-ray anom aly, but small amounts of clay would produce very little deflection of the curve, like limestone. Electrical Logs RESISTIVITY Different rock types and fluids in rocks produce variations in the electrical resistivity from a current derived from the logging tool; this measurement must be made in a borehole filled with fluid. An electric current that passes into the rock mass is produced from an electrode at the top of the tool, and measurements of resistivity in ohm-meters (ohm-m) are made at 8, 16, 32, and 64 inches from the electric source. The longer electrode spacings measure the resistivity at greater depths into the formation, and permit measurement of resistivity with less influence of the borehole fluid. Sediment or saturated rock with a high porosity is gen erally conductive and will have a low resistivity. Salt water in the sediment produces high conductivity and low resistivity. Shales (and clays) are commonly conductive and thus have low resistivity (< 100 ohm-m), whereas sandstones have a moderate resistivity (100 to 1000 ohm-m), but limestone, dolostone, and crystalline rocks (igneous and metamorphic rocks) have very high resistivities (> 1,000 ohm-m). Rock type Symbol Fluids 0 Limestone Resistivity SP Ohm–m 200 1 1,000 mV –100 Gamma API Neutron Density CNL g/cm3 0 30 –10 2 PE bams/e– 3 0 5 Water (Fresh) Water (Salt) Bentonite (Volcanic ash) Shale Bentonite Shale Sandstone Gas Oil Water (Salt) Shale Sandstone Water (Salt) Siltstone Shale Coal Gypsum Anhydrite Salt Shale Limestone Gas Oil Water (Salt) Dolomite FIGURE 4–31 Hypothetical sequence of a variety of sedimentary rocks and the response of each rock type for several types of geophysical logs. (From J. C. Evenick, 2008, Introduction to well logs and subsurface maps, PennWell Corporation Publisher.) 99 100 | Introduction 0 Shallow Resistivity Density 1 50 Caliper Neutron Porosity 5 (in) 20 0 (pu) 100 1 (g/cm3) 3 0.2 Photoelectric Factor (barns\e–) (Ωm) 0 (Ωm) 20 0 (ppm) Thorium 20 Deep Resistivity 6 0.2 Uranium Natural Gamma Ray (gAPI) 0 100 0 (ppm) 15 C2 10 0 (in) 20 Potassium C1 Velocity (wt%) 1 0 (in) 20 1.5 (km/s) 5 100 150 Depth (mbsf) 200 250 300 350 400 450 500 FIGURE 4–32 Suite of geophysical logs from borehole 1196A drilled in Oligocene to Holocene carbonate and clastic sediments in the Marion Plateau off the northeastern coast of Australia. Note the similarities and differences in the peaks and lows in each log. (From Ocean Drilling Program, 2001, Texas A & M University.) SPONTANEOUS (SELF) POTENTIAL (SP) Rocks or sediments develop a natural electric current be tween the fluid in the formation and the fluid in the bore hole, so it is a way of understanding both porosity and rock type. The potential difference is measured between the electrode in the borehole and a grounded electrode on the surface. A charge difference develops between the fluid in the borehole and the fluids in the rocks immediately next to the fluid at a particular depth, depending on relative concentrations. The concentration of salt in the drilling fluid, relative to that in the rocks, determines which way the SP curve deflects. If the concentration of salts (= ionic charge) in the borehole fluid is less than that in the pore spaces in the rocks, a negative SP is developed and the SP curve is deflected to the left. If the concentration of ions in the borehole fluid is greater than that in the rocks, a posi tive SP develops and the measured curve deflects to the right. Spontaneous (self) potential is measured in millivolts, with values commonly in the range from –500 and 500 mV. Shales commonly produce a very small to no SP, because of their lack of permeability. Other non-permeable rocks, such as tightly cemented sandstone or metamorphic and igneous rocks, also produce little in the way of SP. Hydro carbons also suppress the SP curve because they do not contain ionic charge. Geophysical Techniques and Earth Structure | (a) FIGURE 4–33 (a) View of the interior of a geophysical logging truck cabin showing the data acquisition and computer equipment as well as the reels that can contain up to 10,000 m of logging cable. (b) Hypothetical drill site illustrating the location of the logging truck and a blown-up logging tool in the drillhole. (From Schlumberger, 1989, Log interpretation principles/applications.) Photoelectric Logs Gamma rays from a source like 137Cs can be used to excite atoms to scatter or re-emit the gamma rays. Scat tering of high-energy gamma rays (> 0.2 MeV—million electron volts) can be used to estimate the density of a rock mass, whereas absorption of low-energy gamma rays (< 0.2 MeV) can be useful for determining lithology and, to some extent, density and porosity of a rock unit. A measure of the absorptive capability of a material is Triple Combo FMS-Sonic Natural Gamma radiation γ Porosity Natural Gamma radiation Sonic velocity (b) Airgun Sonic wave n Sonic wave Up to 30m long Well Seismic Tool (WST) for vertical seismic profiling (outside drillhole) Geophone Litho-density γ FMS (resistivity images) Resistivity Electric current Electromagnetic induction FIGURE 4–34 Some possible combinations of logging tools. (From U.S. Geological Survey.) 101 102 | Introduction the photoelectric absorption index (Pe in barns/electron; 1 barn = 10 –24 cm 2), which is directly proportional to the photoelectric cross section σe in barns, and inversely proportional to the atomic number Z, which is equal to the number of electrons in an atom, expressed as an approximation Depth (ft) Limestone Gamma ray  Z 3.6 Pe ≈   .  10  Siltstone Density (4–10) The photoelectric index for calcite is 5.084, whereas for do lomite it is 3.142, so the photoelectric log is one of the few that will permit clear separation of limestone and dolo stone, as long as each lithology is dominated by calcite in limestone and dolomite in dolostone. Black shale Temperature Neutron Logs Bombardment of a rock with neutrons from a source, such as americium-beryllium, produces scattering of neutrons, which slows the neutrons down and creates a “static cloud” of neutrons the size of which is measured. The size of the cloud is proportional to the amount of hydrogen contained in the rock, primarily in pore spaces filled with water or hydrocarbons, so this log is also a measure of the porosity of the rock. Therefore, rocks with low porosity like shale will produce a negative response, whereas very porous water- or hydrocarbon-saturated sand will produce a posi tive response. Neutron logs also may be used to estimate density of rocks. Sandstone & shale Shale Sandstone & shale Sandstone Shale Sandstone Temperature, Caliper, and Sonic Logs Shaly limestone Neutron porosity Limestone Shaly limestone FIGURE 4–35 Gamma-ray (left) and density (right) logs with temperature, caliper, and neutron-porosity logs. This hole was drilled in southern Kentucky, with almost the same sequence of limestone, siltstone, black shale, and limestone as in Figure 4–29. (Kentucky Geological Survey.) It is useful to know the temperature in a well from the surface to the intended depth. Temperature commonly increases with depth, so the geothermal gradient can be determined by measuring the change in temperature with depth from the temperature log. Abrupt decrease in tem perature in a well may indicate an influx of water or gas into the well, so the temperature log is useful for locating ground water and also hydrocarbons. The caliper log measures the borehole diameter with depth. It is useful for determining the locations of zones of weak rock—either inherently weak rocks such as shale weakened (strain softened, see Chapter 7) by fractures pro duced by faults, or places in a borehole where rock spalls off of the sides of the hole because of high stress. The cali per log will record these zones as places where the borehole diameter increases. A sonic log uses sound (elastic) waves to determine porosity if the rock type is known (from other logs), and is useful for looking for potential hydrocarbon reservoirs. Geophysical Techniques and Earth Structure When the velocity of the rock matrix and borehole fluids are known, porosity (ϕ) can be calculated from 1 ϕ (1 − ϕ ) = + V Vf Vma (4–11) where V is seismic velocity, Vf is velocity in the fluid in the borehole, and Vma is seismic velocity in the matrix (rock plus fluid). Utility of Conventional Geophysical Logs—Geology from Wiggly Lines Geophysical logs have been utilized for many decades to determine various characteristics of rocks and sediments in boreholes, in addition to determining the physical characteristics of the rocks encountered in each borehole. Perhaps their greatest utility, however, has been in the correlation of stratigraphic units from place to place and recognition of geologic structures. Although SP and resis tivity logs were in common use during the mid-twentieth century, today the gamma-ray log, in concert with resis tivity (both deep and shallow penetration), are commonly used for correlation of geologic units. Seismic reflection data are also integrated into stratigraphic correlation with borehole data used for calibration of seismic reflection data where they are available. The correlation of geologic units using geophysical logs can provide great insight into the geologic history of a region that contains a reasonable number and den sity of logged boreholes. A geologist who is attempting to recognize stratigraphic units in geophysical logs will first attempt to understand what is known about the stratig raphy from other areas or from exposed sections of the same stratigraphic units that can be projected to depth into the area where there are no surface exposures. He/ she will then select logs that penetrate as much of the stratigraphic section as possible, or sections of interest, examine each log for characteristic patterns in the logs that will permit the geologist to separate the rock units present, and study available descriptions of cuttings and core. In areas where paleontologic data have been col lected from the cuttings, these data are also integrated into the analysis, along with any seismic reflection data that may be available. Figure 4–36 consists of a series of gamma-ray logs of wells from an oil-and-gas-producing area in southern Kentucky. The wells are distributed along a roughly westto-east trend across parts of two counties, and our goal is to identify the rock types in the wells and correlate the geology from well to well. The general geology in the area consists of a sedimentary sequence of Mississippian and | 103 Pennsylvanian rocks underlain by Ordovician and Si lurian rocks, but we are primarily interested in the geol ogy in the Ordovician sequence. The first thing to do is study the sections to see if there are prominent marker units that can be easily identified in the wells. The most obvious thing is a prominent segment of the log that has a very high gamma-ray intensity that caused the counter to go off scale. This segment serves as a good marker that is easily recognized in all of the logs, and is produced by a Devonian black shale that contains much higher amounts of uranium and thorium than any of the other rocks in the sequence. This marker can serve as a reference datum that makes it easier to correlate the logs. A second group of markers occurs farther down in the wells and consists of two or more sharp, narrow gamma-ray peaks that do not go off scale, but may register 50 API units. These mark volcanic ash beds (bentonites) in the sequence; they serve as very good time markers throughout the eastern United States in the Ordovician sequence. Once the prominent markers are identified in the logs in Figure 4–36, we can begin to subdivide the stratigraphic sequence by recognizing more subtle characteristics of in dividual rock units. Where we start varies with the nature of the geology, although many geologists would start at the top immediately beneath the black shale unit. Because there are several prominent bentonite beds in the se quence, and they tell us exactly where in the stratigraphic section we are located, it would be just as good to work our way upward and then downward from the bentonite beds. The lowest of the most prominent bentonites occurs at a contact between shaly (and sandy?—irregular, moder ate gamma-ray response) limestone above and pure lime stone (very little gamma-ray response) below. The shaly limestone continues upward and then gives way to a rock unit where there is very little to small, irregular gammaray response, indicating dominance by intervals of pure limestone interbedded with thin shale beds. The irregu lar pattern becomes more prominent above this sequence indicating a greater abundance of shale in the limestone sequence, and this is overlain by a dominantly shale unit up to the black shale. The section beneath the bentonites may similarly be subdivided using the same criteria, as has been done in Figure 4–36. Borehole Imaging Logs Another group of logs that are quite useful is called bore hole televiewer logs. One of several types of these logs is commonly run in a borehole. Some of these logs can be run in a hole that is empty or is filled with clear fluid or drilling mud, but some work better in holes containing opaque fluids. The optical televiewer requires clear fluid or no fluid in the hole, and produces images that record both fractures, bedding or foliation, and the color of the rocks in the borehole (Figure 4–37). The acoustic televiewer 1200 1300 Shaly limestone 1400 1500 1600 1700 Limestone with minor shale Massive limestone 1900 2000 2100 2200 2300 2400 Limestone with shale 2500 2600 2700 Shale with limestone Massive dolostone (a) 2800 2900 3000 3100 700 1900 800 2000 900 2100 1000 2200 1100 2300 1200 2400 1300 2500 1400 2600 1500 2700 1600 2800 1700 2900 1800 3000 1900 3100 2000 3200 2100 3300 2200 3400 2300 3500 2400 2500 2600 2700 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 1900 2000 2100 2200 2300 2400 2500 2600 2700 2700 2800 2800 2900 2900 3000 3000 3100 3100 3200 3200 3300 3300 3400 3400 3500 3500 3600 3600 3700 1600 1800 1700 1900 1800 2000 1900 2100 2000 2200 2100 2300 2200 2400 2300 2500 2400 2600 2500 2700 2600 2800 2700 2900 2800 3000 2900 3000 3100 3200 3300 3400 3500 3600 3700 1800 1500 1900 1600 2000 1700 2100 1800 2200 1900 2300 2000 2400 2100 2500 2200 2600 2300 2700 2400 2800 2500 2900 2600 3000 3100 3200 3300 3400 3500 3600 3700 3800 3800 3900 10 J. L. WHITE 7–B KY 102243 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 Depth (ft) Shale and sandy limestone Massive limestone Limestone with shale 1800 1800 1800 PHILLIP 9 PERKINS 1 KY 93030 Introduction 1100 3 BRYANT KY 37601 LOIS 8 REYNOLDS 1 KY 84495 | Shale with minor sandstone COFFEY 2 HEIRS 2 KY 87114 6 HARMON 1 KY 94533 PEIRER 7 TROXELL 1 KY 89228 104 Black shale BISHOP 1 HOFFMAN 2 KY 62035 LUM 4 CREEKMORE 1 KY 93179 ANNA MARY 5 CREEKMORE 1 KY 48667 2900 3000 3100 3200 3300 3400 3500 3600 3900 3700 4000 3800 3900 4000 FIGURE 4–36 (a) Gamma-ray logs for 10 wells from McCreary and Whitley Counties, Kentucky, illustrating the likely best correlation of rock units. The red lines represent two prominent volcanic ash beds that serve as conspicuous markers in each well because they produce an easily recognized gamma-ray peak and also are excellent time markers. (b) (following page) Map showing the locations of the well logs interpreted in (a). (Logs from Kentucky Geological Survey digital database.) Geophysical Techniques and Earth Structure 84°30'W 9 McC R EAR Y 36°45'N 36°45'N WHITLEY 2 10 8 7 6 5 3 0 5 10 KY TN 4 kilometers SC O T T 84°30'W (b) 105 records data using ultrasound pulses that are reflected from the wall of the borehole to a transducer that records clear images of fractures, breakouts, rock layering (bed ding or foliation), and contrasting properties of different rock types in the borehole (Figure 4–37). The acoustic tele viewer requires a fluid-filled borehole to be effective. These logs are recorded using a separate logging tool from the more conventional log tools. The resulting log is oriented so that the dip of fractures and faults can be measured di rectly, and a continuous dip-meter log can be obtained. A 2D image from a borehole appears to have a series of sine waves crossing it, but these represent the intersection of the borehole with an inclined planar feature such as a frac ture, fault, or bedding so that when “unrolled” the layers have a sinusoidal shape (Figure 4–38). 84°15'W 1 | CAMPBELL 84°15'W FIGURE 4–36 (continued) Depth Optical Image (m) 0° 90° 180° 270° 0° Accoustic image 0 Optical 3D Accoustic 3D 0° 0° Dipmeter Polar Diagram 1300 0° 90° 180° 270° 0° 0 Schmidt Plot — LH — Type 90 23.0 Schmidt Plot — LH — Type Depth: 20.00 m to 32.00 m 0° 24.0 60 25.0 30 270° 90° 26.0 27.0 180° 28.0 Mean Counts 47 Dip (°) 49.18 Azimuth (°) 220.66 36 11 44.40 60.09 219.37 50.08 29.0 (a) (b) (c) (d) (e) (f) FIGURE 4–37 Borehole televiewer logs. (a) Optical televiewer log. (b) Acoustic log of the same interval. (c) and (d) Three-dimensional images of the same interval. (e) Dipmeter log. (f) Equal-area plot of data recorded by the dipmeter. (From U.S. Geological Survey.) 106 | Introduction Suspension Logging Suspension logging is a technique to determine the veloci ties of the P and S waves in rock exposed in a borehole, and the log consists of a profile of P- and S- wave veloci ties with depth in the borehole. This technique employs a probe containing a source and one or two receivers spaced one or more meters apart. The hole must be filled with fluid for the technique to work. The probe is suspended from a cable and lowered into the hole to a desired depth where the source generates a pressure wave, which is con verted to P and S waves at the boundary between the fluid and the rock exposed in the borehole. The P and S waves are converted back to pressure waves and recorded by the geophone receivers. The data are recorded on the surface and the logging tool moved to another depth and the se quence is repeated. The resulting log consists of two sep arate curves connecting the data points, one for P-wave velocities and the other for S-wave velocities in the bore hole. Because S-wave velocities in rocks are almost always less than P-wave velocities, the two curves consist of sub parallel, mostly non-intersecting curves that reflect the variations in the two velocities with depth in the borehole (Figure 4–39). Different rock types can be recognized in these logs because we know from many measurements of seismic velocities the approximate values of P and S waves for many rock types. Contrasts in velocities in sedimentary East d South 0 North rock types like limestone and dolostone (high to very high), shale (low), and sandstone (moderate to high) are particularly evident. Metamorphic and igneous rocks may exhibit fewer contrasts. Suspension logs are used prima rily in shallow boreholes drilled for engineering studies of dams, roads, and other man-made features, and in hydro geologic studies. Vertical Seismic Profiles A seismic reflection profile can be made in a borehole com monly using a vibrator source located near the well outside the borehole, and data are recorded using geophones in the hole. The geophone array is moved systematically upward from the bottom to the top of the hole, moving at regular intervals up the borehole and locking in the receiver to the walls of the borehole before recording, until the geophone array reaches the surface. The data are processed like those from other seismic-reflection surveys described earlier in this chapter, and are used to recognize different rock units to help understand the geology in the borehole. Geophysical methods are powerful tools for visualizing Earth structures; with ever-increased computing power and the expansion of digital technology, these methods greatly aid the structural geologist in understanding Earth structures. We continue with a discussion of forces and stress in Earth’s crust. North East South West North 0° 90° 180° 270° 360° 588 0° 90° 180° 270° West A Depth (m) 590 592 594 596 (a) (b) (c) FIGURE 4–38 (a) Inclined layer or fracture (dashed line) intersected by a hypothetical borehole. (b) Sine wave produced by “unrolling” (projecting) the 3D borehole image in (a) onto a 2D (flat) surface. (c) Example of two inclined surfaces with opposing dips in an acoustic televiewer log. (From U.S. Geological Survey.) 360° Geophysical Techniques and Earth Structure Near-Far Receivers, VS Source-Near Receiver, VS Near-Far Receivers, VP Source-Near Receiver, VP Shaly limestone 107 FIGURE 4–39 Suspension log measuring VS and VP from a borehole that penetrated several rock types. The curve on the left plots the variation in S-wave velocity with depth, whereas the right-hand curve plots the change in P-wave velocity with depth Geologic interpretation by RDH. (Courtesy of Jeffery W. Munsey, Tennessee Valley Authority.) 0 10 | Impure limestone Shale or cave 30 Limestone & dolostone Depth (m) 20 Shale 40 Limestone & dolostone 50 60 0 1500 3000 4500 Velocity (ms−1) 6000 7500 Chapter Highlights • Geophysical techniques provide valuable information regarding the structure of the Earth’s interior, most of which is inaccessible to direct observation and sampling. • Seismic reflection, a technique widely used in the oil and gas industry, is a powerful method for imaging upper crustal structures. • Seismic refraction techniques illustrate deeper crustal and mantle structures. • Earthquake magnitudes today are determined by measuring the moment magnitude from seismograph records, producing an open-ended scale. This replaced the Richter scale, because moment magnitudes provide a closer estimate of the magnitudes of large earthquakes. • Earthquake records and seismometers spaced 100 km or closer over large parts of the continents have produced a tremendous data set that is being used to resolve the structure of the mantle. • Earthquake focal mechanisms (from seismic first motions) reveal important information on the movement sense of active faults. 108 | Introduction • Potential fields, including gravity and magnetism, can be utilized to constrain the geometry of crustal structures, although potential field data do not provide unique geometric solutions. • Instruments that log boreholes—for example, gamma ray, resistivity, neutron porosity, and acoustic televiewer logs—are useful for discerning rock type and structure where core is not available. Questions 1. Why does seismic reflection not detect steeply dipping features? 2. What is the basis of the self-exciting dynamo theory? 3. We assume that the Earth’s core consists of 90 percent iron and 10 percent nickel and that the mantle is peridotite. On what do we base our assumption? 4. Why did we abandon the use of the Richter scale for moment magnitude to estimate earthquake magnitude? 5. What kinds of faults are represented by the beach balls in an area near Charleston, South Carolina, plotted in the following diagram? (From M. C. Chapman et al., 2016, Bulletin of the Seismological Society of America.) 80° W 33°7'30" N 0 10 kilometers er op Co BERKEL EY CO. 33°7'30" N 80°15' W gravity anomaly R i ve l ey DORCHESTER C O. 80°15' W Riv er CHARL ESTON CO. 80° W 6. Why is gravity less precise than seismic reflection as an imaging technique? + + – – 0 kilometers 32°52'30" N 33° N 33° N r sh A 32°52'30" N 7. Calculate the depth at which most common magnetically susceptible minerals will no longer interact with the Earth’s magnetic field. 8. Why are magnetic anomalies over a single source separated into high and low pairs at low latitudes, but at high latitudes consist of a single anomaly? 9. How can paleomagnetic measurements that do not meet a fold test be rendered usable? 10. What are the differences between free-air and Bouguer gravity maps? 11. What does a gravity model for part of the crust or a body represent? 12. Why are paleomagnetic measurements unable to determine longitude? 13. Calculate the depth to a 7 km wide gravity anomaly thought to be produced by a nearly spherical pluton. 14. Sketch a gravity-anomaly profile for the following subsurface geometry. basalt (ρ = 3.0 g/cm3) −1 −2 3 3 sandstone sandstone (ρ (ρ==2.5 2.5g/cm g/cm ) ) 0 2 sandstone sandstone(ρ (ρ = = 2.5 2.5 g/cm g/cm3)3) basalt (ρ = 3.0 g/cm3) kilometers kilometers 15. A number of Russian geologists and geophysicists have suggested that a 55 to 60 km deep root of thickened continental crust exists beneath the Ural Mountains, yet the maximum elevations anywhere in the Urals range only slightly above 2,000 m. From your knowledge of gravity and isostasy, do you think this is a reasonable hypothesis? Why? Further Reading Bally, A. W., 1983, Seismic expression of structural styles: American Association of Petroleum Geologists, Studies in Geology 15, 3 volumes. A compendium of seismic reflection profiles showing various kinds of structures and providing examples of artifacts. Barazangi, M., and Brown, L. D., eds., 1986a, Reflection seismology: A global perspective: American Geophysical Union Geodynamics Series, v. 13, 311 p. Barazangi, M., and Brown, L. D., eds., 1986b, Reflection seismology: The continental crust: American Geophysical Union Geodynamics Series, v. 14, 339 p. Geophysical Techniques and Earth Structure Each volume applies reflection seismology to solving structural and tectonics problems and recognizes new unsolved problems. Some papers present new data not previously published; others interpret existing data. Breiner, S., 1973, Applications manual for portable magnetometers: Sunnyvale, California, E. G. & G. Geometrics, 58 p. Primarily for use of Geometrics’ magnetometers, but summarizes interpretation of magnetic data and adds some elementary theory. May not be widely available. Dobrin, M. B., 1976, Introduction to geophysical prospecting: New York, McGraw-Hill, 630 p. Compiles seismic reflection theory and applications; less emphasis on other techniques. Evenick, J. C., 2008, Introduction to well logs and subsurface maps: Tulsa, PennWell Books, 236 p. A summary with examples and problems of most geophysical logging techniques. Hoffman, K. A., 1988, Ancient magnetic reversals: Clues to the geodynamo: Scientific American, v. 256, no. 5, p. 76–83. | 109 Discusses the Earth’s magnetic field, polarity reversals, and evidence that decrease in magnetic-field intensity during the past century may presage a reversal of polarity in the next 1,500 years or so. Percival, J. A., Cook, F. A., and Clowes, R. M., eds., 2012, Tectonic styles in Canada: The LITHOPROBE perspective: Geological Association of Canada Special Paper 49, 498 p. This book contains numerous examples of various kinds of geophysical data as maps and cross sections, as well as geologic interpretations of these data. Sharma, P. V., 1976, Geophysical methods in geology: Amsterdam, Elsevier, 428 p. Surveys the various geophysical methods, probably treating gravity and magnetism best. Telford, W. M., Geldart, L. P., Sheriff, R. E., and Keys, D. A., 1990, Applied geophysics, 2nd edition: Cambridge, England, Cambridge University Press, 770 p. A balanced treatment of geophysical methods, giving the limitations of each. PART 2 Mechanics: How Rocks Deform OUTLINE 112 5 Stress 6 Strain and Strain Measurement 7 Mechanical Behavior of Rock Materials 165 8 Microstructures and Deformation Mechanisms 181 131 5 Stress In all quantitative studies on the relationship between original forces and the resulting deformations, an intermediate field of investigation enters, the condition of stress in the earth’s crust. W. HAFNER, 1951, Geological Society of America Bulletin 112 We are all familiar with daily effects of forces and stresses. The most pervasive force affecting us is gravity: it holds the atmosphere, the oceans, and us to the Earth, and keeps the Earth and other planets from fragmenting. The Earth is a large enough body to be deformed into a nearly spherical shape because of gravity, whereas small objects in space, like asteroids and smaller bodies, are affected by gravity, but their mass and the influence of gravity are not great enough to transform them into spherical shapes. Forces change the velocity or direction of bodies in motion. We use forces to open and close doors, ride bicycles and exercise machines, turn on lamps, push a gas or brake pedal on a car, and perform other everyday activities. In the Earth, forces act on rock bodies and drive certain kinds of deformation, but force is not as meaningful as stress in the study of rock deformation, because we must consider the area affected by the force. Stress (σ) is a force applied to an area—force per unit area. Hafner’s chapter opening statement above about the direct connection between stresses and deformation can be demonstrated only for elastic deformation. There, a direct proportion exists between the amount of stress and the amount of deformation that results; elastic deformation (Chapter 6) is, by definition, recoverable. Other forms of deformation, or strain, are not as easily related to forces, or stresses, in the Earth (Figure 5–1). We commonly think of tectonic structures as products of stress (Figure 5–1), but ironically, we observe most of the effects of stress in tectonic structures without being able to measure the stress that produced the structure. A tectonic structure is a manifestation of deformation that is assumed to result from stress on a rock mass. Stress originates in processes that generate, move, and consume lithospheric plates, with the aid of gravity. Gravity alone induces the stresses primarily responsible for deformation in salt and impact structures (Chapter 2). Thus, understanding the nature of stress is important to understanding tectonic structures. One of the goals of structural geology is to reconstruct the orientations and magnitudes of stresses that produced the structures we encounter in the field. Unfortunately, these stresses are usually no longer present, and thus cannot be measured directly. Experiments that duplicate natural structures in rocks also help us to estimate the orientations and magnitudes of stresses needed to produce deformation in rocks. Stress | 113 FIGURE 5–1 The strongly folded Mesoproterozoic Moine metasandstone, pegmatite, and schist exposed at Cluanie Lake in the Scottish Highlands, like most other structures, are assumed to be a product of stress in the crust. (RDH photo.) Definitions either be stationary or already in motion. Newton’s second law of motion states that Several terms are useful in describing forces and stresses mathematically. A scalar possesses only magnitude; a vector possesses both magnitude and direction (Figure 5–2). A scalar is a number (for example, the price of oil, the score in a baseball game, temperature, or the thickness of a rock unit). A vector is a number with an indication of d irection. For example, if we say a car is traveling northwest at 100 km per hour, we have defined a vector; if we say only that it is traveling 100 km per hour—with no indication of direction—we have defined a scalar. In this book, vectors in equations are indicated by bold-italic type. A force (Figure 5–3) is a vector that produces a change in the velocity or direction of motion of a body that may Volume Scalars Speed Time Length Mass Temperature gradient FIGURE 5–2 Examples of scalars and vectors. Acceleration Vectors Earth's gravity field Earth’s magnetic field Velocity (5–1) where F is force (a vector), m is mass (a scalar), and a is acceleration (also a vector). Body forces act equally on all parts of a body. Examples are the effect of gravity or electromagnetic forces on a mass. Body forces must be considered if the behavior of fluid or ductile material is involved, but do not depend on the rheology (state of “flow”) of the material under consideration. Surface forces act on external or internal surfaces within rock masses and include forces acting along a fault or a major plate boundary. The magnitude of a gravitational body force is proportional to the amount of mass present, but the magnitude of Force and stress (on a surface) Viscosity Temperature F = ma, Ocean currents Mantle convection flow 114 | Mechanics: How Rocks Deform 70 kg 70 kg Mariana Trench Force 1m 10 km 1m Sea level Force (a) Stress Surface 1m 1m 10 km Stress FIGURE 5–3 Difference between forces and stresses. Two persons weighing 70 kg each stand on one foot on the edge of a box so that all of the weight is concentrated on the heel of the shoe. The person to the left is wearing a shoe with a narrow heel, but the shoe on the person on the right has a wide heel. Note that the same force is applied to the box by both people, but the applied stress is much greater with the person to the left because it is concentrated in a smaller area. a surface force is independent of the surface area affected. For example, the same force is exerted by the heel of a shoe regardless of whether the person is wearing street shoes, field boots, or cowboy boots, or is a woman in spike heels, but the force on the heels is distributed over a smaller area beneath the lady in spike heels than beneath the same lady wearing field boots. Moreover, a surface force can be resolved into mutually perpendicular components: one normal to the surface, and one or two parallel to the surface. This relationship will reappear when we discuss normal and shear stress. Force may be converted to stress by dividing by the area (A) affected by the force (Figure 5–4). For example, the force on a body submerged at a depth of 10 km near the bottom of the Mariana Trench would equal the weight of the mass of water on it, expressed as F = weight of water = density of sea water (ρ) × acceleration of gravity (g) × height (h) × area (A in m2) = ρghA = 1,030 kg m−3 × 9.8 m s−2 × 104 m × 1 m2 = 1.009 × 108 kg m s−2 (5–2) or 104 m × 1,030 kg m−3 × 9.8 m s−2 = 100.9 × 106 kg m−1 s−2 = 101 MPa. (5–3) (1 Pa = 1 pascal = 1 kg m−1 s−2; 1 MPa = 106 pascals. 1 megapascal is the standard unit of stress in the Earth; it also is equal to 10 bars or 9.8 atmospheres of pressure.) (b) Crust Mantle FIGURE 5–4 Stress on a body 10 km under water (a) or 10 km deep in the crust (b), assuming the stresses are distributed isotropically. The differences would arise principally from the weight of the column of water (a) or rock (b) above the 1-m2 area at depth. If the same body were buried 10 km deep in the continental crust, the lithostatic stress could be calculated by substituting the average density of the column of rock above the body, assumed to be 2,750 kg m−3. Substituting for seawater density in equation 5–3, we obtain the lithostatic value of stress 104 m × 2,750 kg m−3 × 9.8 m s−2 = 269.5 × 106 kg m−1 s−2 = 269.5 MPa. (5–4) Stresses may be tensional (pulling apart) or compressional (pushing together). Stress acting on a surface may be resolved into two vector components: normal stress, σn, acts perpendicular to a reference surface; shear stress, τ, acts parallel to a surface. Stress vectors acting across planes of zero shear stress are principal stresses, commonly distinguished as three principal normal stress components, σ1, σ2, and σ3, of σn. The three principal normal stress components are oriented perpendicular to each other, and σ1 ≥ σ2 ≥ σ3. Their directions are principal directions of stress. The planes that contain the principal stresses are principal planes of stress. Differential stress is the difference between the maximum (σ1) and minimum (σ3) principal normal stresses (σ1 − σ3); see equations 5–15 through 5–18 later in the chapter, and related text. Mean stress is (σ1 + σ2 + σ3)/3. Deviatoric stress is the nonhydrostatic component of stress, Stress Earth’s surface Depth constant σ (a) Horizontal plane P Earth’s surface Depth variable σ (b) Horizontal plane P FIGURE 5–5 Stress vectors acting on a horizontal plane beneath the surface below smooth topography (a) and irregular topography (b). The vertical arrows represent a randomly oriented stress, σ. Magnitude of stress on the horizontal plane also depends on the product of density (ρ), force of gravity (g), and the height (h), ρgh, of the column of rock above any point along the horizontal plane (P). expressed as total stress with mean stress subtracted from the normal stress components. Permanent deformation results if the differential stress exceeds the strength of the rock. The strength of a material is the stress required to cause permanent deformation. A lithostatic state of stress occurs where normal stress is the same in all directions in the Earth; a hydrostatic pres‑ sure is the confining stress acting on a body submerged in water at a known depth. In the case of a body buried in the Earth, the weight of the column of rock (instead of water) per unit area above it is called the lithostatic pres‑ sure (Figure 5–4). Under both lithostatic and hydrostatic conditions, one-third of the sum of all three principal stress components equals the mean stress. Shear components will still exist under any deviation from lithostatic conditions (Figure 5–5). | 115 vertical stress σ (Figure 5–6), the stress across a small part of the plane can be written as ∆F , (5–5) σ= ∆A where A is area. If we assume this segment of the plane is infinitesimally small (equivalent to the statement of stress at a point, discussed in the next section), ∆F (5–6) σi = lim ∆A→ 0 ∆A or dF (5–7) σ= dA Equation 5–6 indicates that stress on a plane σ is a vector quantity—from the product of a vector (force) and a scalar (1/area)—and that the stress on each plane can be expressed as a unique set of normal and shear stress vectors (the latter also known as tractions). Stress on any plane we choose in a mass of rock, particularly near the surface, is likely to vary from place to place on the plane, either because the amount of overburden varies or because the plane is inclined to the surface (Figure 5–7). At depths greater than a few kilometers in the Earth, stress on a horizontal plane is related to the density and height of the column of rock above it (ρgh = density × gravity × height), although at depths of a few kilometers, variations in the amount of stress can occur, even within the plane. Determining the stress on an inclined plane is more difficult and is best accomplished using tensors (see Nye, 1957). The area of the plane, the density of the column of rock, and the height of the column are all involved, but the angles between the plane and the principal stress directions must also be known. Because the plane is inclined, the height of Earth’s surface α σn σ τ Stress on a Plane Now that we have defined the terms used in describing and measuring stress, we should consider ways of using them. If we define a plane P in a mass of rock subjected to a FIGURE 5–6 Stress vectors acting on an inclined plane, such as a fault surface, several kilometers deep in the crust. σ is the vertical component of stress resolved into normal (σn) and shear (τ) components. 116 | Mechanics: How Rocks Deform the column of rock varies along the plane. On the plane, the stress (σ) may be resolved into components of normal stress (σn) and shear stress (τ). If we assume that our 1-m2 area in Figure 5–7 is a different plane now inclined 45° to the horizontal (for convenience here), we should be able to calculate the vertical stress on the plane (Figure 5–7a). Because the plane is now inclined above the 1-m2 area, the area of the plane is greater—1.41 m2 (= √2 m2). The vertical force, using F = ma = volume × density × acceleration of gravity, is F = 104 m3 × 2,750 kg m−3 × 9.8 m s−2 = 2.7 × 108 kg m s−2. (5–8) Conversion of force to stress involves dividing force by the area of 1.41 m2, which yields a stress on the inclined plane of 191 MPa. Note that the area has increased, and so the normal stress on the inclined surface has decreased, because the same force is distributed over a larger area. (Shear stress on the plane, however, must increase from zero to a nonzero value.) Because any plane will have a unique stress vector resolvable into normal and shear components, the normal and shear components of stress (Figure 5–7b) can also be calculated from σn = σ cos 45° = 191 MPa × 0.707 = 135 MPa (5–9) τ = σ sin 45° = 191 MPa × 0.707 = 135 MPa, (5–10) and where σ is the traction on the plane. Note that we are considering only a uniaxial vertical stress here; much greater complexity would be introduced if we considered a triaxial case including horizontal stresses that result from the horizontal resistance to expansion due to vertical loading. Mohr Circle Derivation The Mohr circle forms a simple and useful means of both visualizing and calculating normal and shear stresses acting on planes of any orientation. Here we derive the Mohr circle from the mathematical relationship between the principal stresses in a rock mass, and between the normal and shear stresses on a plane or surface within the mass. If we define an inclined plane P having unit area, and a randomly oriented stress σ acts on it (Figure 5–8), we can derive several expressions for the normal (σn) and shear stress (τ) on the plane. If a triangular segment ABC represents a small prismatic element with two sides, AC and BC, perpendicular to each other, and AC makes the angle θ with AB (which lies in the larger element P), AC and BC are also assumed to be perpendicular to the greatest and least principal (normal) stress components— σ1 and σ3. If A represents the area of the hypotenuse face P (one unit wide) of the prismatic element, and σn and τ are normal and shear stresses acting on this surface, we can derive several useful relationships from the prismatic element ABC. Assume that the prism ABC is infinitesimally small, so that the weight is negligible compared to the forces acting on it. We can also assume that the prism is in a state of static equilibrium: all forces acting to move the prism in any direction are countered by equal and opposite forces. The same is true for forces acting to move the prism in either direction horizontally. (These statements embody Newton’s third law of motion.) We have already defined the area of the hypotenuse of the prism (plane P) as unity, so the area of the left (vertical) face of the prism is 1 × sin θ, and the area of the base (horizontal face) is 1 × cos θ. The forces acting on the three faces are the stresses multiplied times the area of each face (force = force/area × area). If we sum the forces acting in both the horizontal (FH) and vertical (FV) directions (they must sum to zero in both directions), ΣFH = 0 = Fx − N cos θ − S sin θ, (5–11) ΣFV = 0 = Fy + S cos θ − N sin θ. (5–12) and 45° A 1. rea 41 = m2 1m n = Pa M = (b) (c) τ 1m 191 MPa = σ Pa M (a) τ 45° 5 13 1m 13 5 σn σ σ FIGURE 5–7 (a) Vertical stress acting on an inclined plane with an area of 1.41 m2. (b) Resolution of normal and shear stress components of the vertical stress in (a). (c) Calculation of the magnitude of stresses. N and S are normal and shear forces, respectively. The force on the left side of the prism (directed parallel to the x-axis in an xy coordinate system) is Fx = σ1 cos θ; that on the base (directed parallel to the y-axis) is Fy = σ3 sin θ. If the force terms are rewritten using stress components, we can write expressions for normal and shear stresses acting on a plane at an angle θ to σ1 in terms of the principal stresses. When ΣFH = 0, σ1 cos θ − σn cos θ − τ sin θ = 0. (5–13) Stress Solving for σn and then τ τ sin θ = σ1 cos θ – σn cos θ σn = σ1 cos θ − τ sin θ (5–13a) cos θ and ττ = σ1 cos θ − σn cos θ sin θ When ΣFV = 0, (5–14) σ3 sin θ – σn sin θ + τ cos θ = 0. sin 2 θ = 1 − cos 2θ 1 + cos 2θ . and cos 2 θ = 2 2 Substituting in equations 5–15 and 5–16 to replace the single-angle with double-angle trigonometric terms, we obtain σn = Solving for σn and then τ σn = σ3 sin θ − ττ cos θ (5–14a) sin θ σ1 + σ3 ττ = σn sin θ − σ3 sin θ cos θ , (5–14b) combining equations 5–13b and 5–14b, σ1 cos θ − σn cos θ sin θ = σn sin θ − σ3 sin θ cos θ , cross multiplying σ1 cos2 θ – σn cos2 θ = σ3 sin2 θ – σn sin2 θ, collecting terms σ1 cos2 θ + σ3 sin2 θ = σn sin2 θ + σn cos2 θ = σn (sin2 θ + cos2 θ), and, because sin2 θ + cos2 θ = 1, (5–15) σn = σ1 cos2 θ + σ3 sin2 θ. Combining equations 5–13a and 5–14a, σ1 cos θ − ττ sin θ cos θ = σ3 sin θ − ττ cos θ sin θ solving for τ, including substituting sin2 θ + cos2 θ = 1, τ = (σ1 – σ3) cos θ sin θ. (5–16) Otto Mohr, a German engineer who in 1882 developed the construction that bears his name, exhibited considerable insight when he realized that if equations 5–15 and 5–16 were rewritten to incorporate double angles, determinations of σn and τ could be made for all cases graphically from a limited number of experimental measurements. He found a graphical solution to the problem much easier than one 2 + σ1 − σ3 2 cos θ (5–17) and τ τ= and 117 based on calculations—computers were not available then. Consequently, it was advantageous to introduce an imaginary double angle to replace the real angle. Recall the trigonometric relationships sin 2θ = 2 sin θ cos θ, cos 2θ = 1 – 2 sin2 θ, and cos 2θ = 2 cos2 θ – 1, and the identities (5–13b) . | σ1 − σ3 2 sin 2θ. (5–18) Note that in these equations, θ is the angle between σ and the plane P (Figures 5–8 and 5–9). Equations 5–17 and 5–18 define the x and y coordinates of a circle—the Mohr circle—centered on the x-axis in a Cartesian coordinate system where the axes are the normal σn (x) and the shear τ (y) stresses. Here the general (x, y) = (σn, τ) coordinates for the circle are (x-axis value of the center + radius × cos 2θ, radius × sin 2θ). Therefore, the radius of the circle for this graphical construction is (σ1 − σ3)/2, and the x-axis value of the center is (σ1 + σ3)/2 (Figure 5–9). Given θ, σ1, and σ3, values of σn and τ may be calculated for any plane P that is normal to the σ1 σ3 plane. A Mohr circle allows us to determine the normal and shear stresses across any plane that is normal to two of the principal stresses. Although we have done this here in two dimensions, some very important relationships will be produced from this type of analysis. In three dimensions, the three Mohr circles that define the normal and shear stresses on planes normal to two principal stresses bound all of the possible normal and shear stresses. DePaor (1986a) represented normal and shear stress with a graphic method employing an “orthonet.” His technique provides a way to obtain values for σn and τ without trigonometry. The angle θ is measured between σ3 and the plane in the Mohr construction. The relationship may also be stated in terms of the angle α, which is the complement of θ, or the angle between σ3 and plane P in Figure 5–8. These angles reappear in Mohr circles as 2θ and 2α. Consider the face of a cube of rock in Figure 5–10a in which σ1 and σ3 are 27 and 5 MPa, respectively, and plane A is oriented 20° clockwise from σ3. What are σn and τ acting on plane A? We could solve equations 5–17 and 5–18 or construct a solution using the Mohr circle (Figure 5–10b). The state of stress is represented by the circle that 118 | Mechanics: How Rocks Deform FIGURE 5–8 (a) Relationships between a randomly oriented force are resolved into normal stress σn, and shear stress τ, components within a plane P having an area dA (or ∆A) on which the force is applied, and resolved principal normal stress components σ1 and σ3, and the angles α and θ within the prism. (b) 2D representation of the relationships expressed in 3D in (a). α A θ Area of end = 1 sin θ or ∆A sin θ N = σn S=τ Plane P Area = 1 Fx = σ1 cos θ α it un B 1 C (a) Area of base = 1 cos θ or ∆A cos θ Fy = σ3 sin θ y Randomly oriented stress σ σn θ Resolved normal and shear stress components τ ∆A cos θ Fx = σ1 cos θ ∆A α x τ∆A sin θ Fy = σ3 sin θ (b) intersects the τ = 0 axis at 27 and 5 MPa; the point on the Mohr circle that represents the σn and τ acting on plane A is found by plotting the point made by a 2θ (40°) rotated counterclockwise from the σ1 side of the τ = 0 axis (Figure 5–10b). The normal stress (σn) is 24.5 MPa, and the FIGURE 5–9 Mohr circles plotted on σ and τ axes, the envelopes, and the relationships between 2α and 2θ. shear stress (τ) is 8 MPa. Planes oriented at a high angle to σ1 have high normal stresses and low shear stresses acting on them. Based on the geometry of the Mohr circle, it is easy to see that the plane of maximum shear stress is oriented 45° to σ1 and will equal the radius of the circle (σ1 − σ3)/2. (σn, τ) = τ σ= ( σ +2 σ cos 2θ , σ 2– σ sin 2θ ) 1 3 1 3 σ1 + σ3 σ1 – σ3 + cos 2θ 2 2 State of stress on plane P σ1 – σ3 2 2α τ= 2θ 0 σ3 σ1 – σ3 ( 2 σ1 (σn, τ) = ( σ +2 σ , 0 ) 1 3 2 × angle between σ3 and plane sin 2θ σn ) Stress τ σ1 = 27 MPa Plane A 10 σn = 24.5 MPa τ = 8 MPa θ = 20° Pla ne A σ3 = 5 MPa 0 σ3 2θ = 40° 10 20 σ1 30 | 119 FIGURE 5–10 Physical space (a) and Mohr space (b) illustrating the state of stress acting on plane A. σn –10 (a) (b) Mohr Construction Now we can use experimental results to calculate values of material properties. A cylindrical sample of rock is placed in the test cylinder of a triaxial test apparatus (Figure 5–11a). The specimen is jacketed in a thin sleeve of a soft metal such as copper or thermal plastic, to protect it from a fluid (such as a low-viscosity oil) that is used to vary the confining pressure externally. In an axial compression test, the confining pressure is equal to both σ2 and σ3 because pressure is being applied equally around the cylinder. The load on the ends of the cylinder is usually increased until the material ruptures (Figure 5–11b). This load is a measure of the axial stress σ1. Plotting each value of σ1 and σ3 on the σn (horizontal) axis permits construction of a Mohr diagram for the limestone at failure (Figures 5–12a, b), and determines the diameter of the Mohr circle. If the rock is loaded to the rupture point, a new cylinder of the same material is required for each run at increasing confining pressure σ3. When the sample ruptures, a shear fracture develops in one of two orientations [with both shear fractures developing at the same angle with respect to σ1 and σ3 (Figure 5–12b)]. Table 5–1 contains values for successive runs to failure on cylindrical specimens of limestone using an axial load apparatus. Each successive run was conducted at a higher confining pressure (σ3), and runs 1 to 4 each required a greater differential stress, σd, for fracturing to occur. The Mohr failure envelope can be constructed with 90 − ϕ = 2α. TABLE 5–1 TEST RUN ease, by constructing tangents to the circles both above and below the σn axis (Figure 5–12c). The Mohr envelope separates unfailed (no permanent deformation) from failed (permanently deformed) regions in the diagram; the unfailed region lies within the envelope (Figure 5–12d). A Mohr circle that does not intersect the envelope indicates that the sample did not rupture with the values of σ1 and σ3 employed in that run. Put another way, if the Mohr circles do not intersect the Mohr envelope, the sample undergoes no permanent deformation (Figure 5–12d). Curvature of the Mohr envelope is frequently related to inherent properties of the material (Figure 5–13). Brittle materials tend to produce relatively straight Mohr envelopes with steep slopes. With increasing confining stress (σ3), even a brittle material behaves ductilely on the megascopic scale. If the materials are ductile, they undergo some permanent, nonrecoverable strain before rupture (Chapter 7). With an increase in ductility, the Mohr envelopes become flattened, resulting in an overall curvature. In general, the greater the curvature, the greater the amount of ductile strain before rupture, but Griffith materials (Chapter 9), which are actually brittle, also produce curved envelopes. Their properties are related to the amounts of dilation of the preexisting microcrack population. The angle 2α, the conjugate shear angle, is related to the coefficient of internal friction μi (or tan ϕ, defined below in equation 5–22), and α is the angle between σ1 and the fracture that forms during rupture. The relationship is σ3 (kg cm−2) σ1 (kg cm−2) 1 0 750 2 250 1,750 3 500 2,400 4 1,050 3,550 (5–19) (Here α is defined in degrees, as in Figures 5–9 and 5–12b.) As the radii of the Mohr circles increase and approach a limit (with increasing stress difference and confining pressure), the slope of the envelope flattens as a function of increased ductility, and 2α approaches a maximum value of 90°. Therefore, the maximum shear angle α is 45°. This angle is most commonly attained (and sometimes exceeded) in ductile materials. 120 | Mechanics: How Rocks Deform τ Fixed platten Dial gauge Baldwin load cell State of stress at failure 10 Output to recording potentiometer t1 0 Output to recording potentiometer To packing pressure intensifier t4 20 σn increasing σdd –10 (a) Insulation τ σ1 = 17 MPa Thermo couple Calrod tubular heating elements t3 10 To interstitial fluids pump Newhall packing sleeve t2 10 θ = 60° σn = 4 MPa τ = 7 MPa σ3 = 0 MPa Rock specimen 2α 0 Movable platen 2θ = = –120° -120° 2θ –10 σn σn = 4 MPa τ = –7 MPa τ Mohr envelope Test run 4 Hydraulic jack (σ1) Test run 4 σ33 0 20 θ = -60° –60° σ3 = 0 MPa (b) (a) 2θ = 120° 10 σ1 = 17 MPa To confining pressure intensifier and 500 MPa pump State of stress at failure 1,000 σ1 2,000 3,000 4,000 σn (c) τ Failed Unfailed 0 σn Failed (d) (b) (1) (2) FIGURE 5–11 (a) Triaxial test apparatus. Axial stress (σ1) is applied with a hydraulic jack. The axial load is measured directly by the load cell. The dial gauge provides a direct measure of strain as a percentage of shortening of the rock cylinder. (From D. T. Griggs, F. J. Turner, and H. C. Heard, 1960, Geological Society of America Memoir 79.) (b) Limestone cylinder before (1) and after (2) being tested. [Photos from Vertek Material Properties Laboratory (www.rocktestinglab.com).] FIGURE 5–12 (a) Successive Mohr circles as the differential stress (σd) increases over time (t) as the hydraulic jack is applied. (b) Physical space and Mohr space at time of failure. Based on the principal stresses and the orientation of the shear fractures, the values for σn and τ can be determined from the Mohr circle. (c) Plots of successive Mohr circles for the four experimental runs in Table 5–1 taken to rupture. Failure envelope connects the stress state at failure for the successive experiments. (d) Mohr diagram showing unfailed (stable) and failed (unstable) regions. Stress | 121 τ τ 6,000 n 4,000 τ= σn kg cm–2 2,000 + (τ 0 + σn φ) 2 2θ φ σ3 τ= + (τ + σ n ta n –6,000 0 σn σ1 σ1 + σ3 2 0 –4,000 φ = 45° σ1 – σ3 2α τ0 –2,000 (a) ta φ) 2,000 6,000 10,000 (b) 14,000 kg cm–2 τ τ 3,000 τ= 2,000 σn kg cm–2 1,000 + + (τ 0 n φ) 22° σ n ta φ = 22° – 43° 2θ 2α 0 2α 2α σ3 σ1 + σ3 σn σ1 2 –1,000 –2,000 –3,000 0 (c) (d) 2000 4000 6000 8000 kg cm–2 FIGURE 5–13 Mohr diagrams for brittle [(a) and (b)], and more ductile [(c) and (d)] materials. Mohr diagrams for Oil Creek sandstone (b) and Blaine anhydrite (d), deformed at 24° C and 0–2,000 atmospheres pressure. (From M. K. Hubbert and D. G. Willis, 1957, American Institute for Mining, Metallurgical, and Petroleum Engineers Transactions, v. 210.) Several relationships within Mohr diagrams are summarized in Figure 5–14. Note that the τ axis separates compressional from tensional normal stress fields (Figure 5–14a). Materials with no tensile strength, such as dry sand, have an envelope that terminates at the origin (Figure 5–14b). Most geologic materials have compressive strengths (breaking strength under compressive stress) much greater than their tensile strengths (Figure 5–14c). Very few materials have tensile and compressive strengths even approximately the same, but mild carbon steel (Figure 5–14d) is one that does, and a horizontal envelope results that closes in the tensile field. Amontons’ Law and the Coulomb–Mohr Hypothesis French physicist Guillaume Amontons suggested at a scientific meeting in 1699 that a direct proportional relationship exists between F, the shear force necessary for sliding along a contact surface, and W, the force perpendicular to the surface, expressed as an equality F = μs W, (5–20) 122 | Mechanics: How Rocks Deform τ τ Tension Zero tensile strength Compression –σn σn σn (a) τ (b) τ σn σn (c) (d) FIGURE 5–14 (a) Axes for Mohr diagrams showing extensional (−σn) and compressional (+σn) fields. (b) Mohr diagram for quartz sand, a material with no tensile strength. (c) Mohr diagram for an average rock that exhibits tensile strength at low stress, and greater compressive strength and possibly some ductility at higher stress. (d) Mohr diagram for a mild carbon steel, where tensile and compressive strengths are about the same, yielding an almost horizontal Mohr envelope that ultimately closes into the tensile field. and today known as Amontons’ first law, where μs is the coefficient of sliding friction along the surface (Jaeger et al., 2007). The coefficient of sliding friction is a measure of the resistance of a material to sliding along a surface. If we divide both sides of equation 5–20 by the surface area (A), it becomes τ s = μ s σn . (5–21) Another French physicist, Charles A. Coulomb, recognized the linear relationship between shear and normal stress implied by Amontons’ first law. From that, he derived another relationship that today bears his name, the Coulomb criterion of failure, proposed in 1773. It states that the absolute value (either a positive or negative number) of shear strength τs is the sum of the inherent shear strength S0 and the coefficient of internal friction μi, or static friction, multiplied by the normal stress σn‑, |τs| = S0 + μi σn. (5–22) Equation 5–22 predicts that fracturing will occur when the shear stress on a plane (such as a fault plane) reaches a critical value. The Coulomb equation is an equation of a straight line that approximates straight-line segments of the Mohr envelope (Figure 5–12c). It is commonly expressed today as |τs| = τ 0 + σn tan ϕ or |τs| = τ 0 + σn μi. (5–23) Here, τ 0 is the cohesive strength of the material at zero normal stress, and μi = tan ϕ; ϕ is the angle of internal friction, and tan ϕ is the coefficient of internal friction. In 1900, Mohr generalized that shear strength is a function of normal stress, |τs| = f(σn), (5–24) where |τs| is the absolute value of shear strength—the resistance of a material to shear stress. The location of the Mohr envelope in σnτ space is directly related to the strength of the material. Mohr’s hypothesis and the derivation of the equations for resolved shear and normal stresses on a plane (equations 5–14a and 5–14b) are both incorporated in the Mohr construction (Figure 5–9). Stress Stress Ellipsoid 123 σ3 = σz A graphic means of showing the relationships between the principal stresses is the stress ellipsoid (Figure 5–15). It is a triaxial ellipsoid in which the greatest, intermediate, and least principal axes are σ1, σ2, and σ3. Principal planes in the stress ellipsoid contain the principal axes. The σ1 − σ2, σ2 − σ3, and σ1 − σ3 planes are principal planes. The σ1 − σ3 plane represents the maximum stress difference. All nonprincipal planes are shear planes. Having considered stress on a plane in two dimensions, we can now consider stress in three dimensions. Principal normal stresses, designated σ1, σ2, and σ3 (σ1 ≥ σ2 ≥ σ3), may be thought of as oriented parallel to coordinate axes x, y, and z, so that σ1 corresponds to σx, σ2 to σy, and σ3 to σz (Figure 5–16). These normal stresses may also be considered parallel to the edges and normal to the faces of a cube. If the cube is reduced to infinitesimal size, a stress σ applied to one of the planes that defines the cube may be considered as being applied at a point 0 (Figure 5–17a). We may also assume, using Newton’s third law of motion, that the stresses on all sides of the cube balance and cause no rotation or translation, regardless of the size of the cube and regardless of whether or not the stresses are normal or shear stresses. The cube should be very small so that both shear and normal stresses balance. The stress σ defines a second-rank tensor that may be expressed in both normal and shear components, σn and τ for any plane. In three-dimensional space, nine components (Figure 5–17b) are required to describe the stress σ at point 0. They include the three components of normal stress, σxx, σyy, and σzz, oriented parallel to the three coordinate axes, and six Shear plane z σ σ1 = σx x σ2 = σy y FIGURE 5–16 Principal normal stresses oriented parallel to the edges of a cube in x-y-z space. Note the position of the cube relative to the positive ends of the axes. Stress at a Point σ1 | components of shear stress lying within the three faces of the cube defined as planes xy, yz, and xz. The symbol σxx, for one of the principal normal stresses, indicates that this is a normal stress acting perpendicular to the yz plane and parallel to the x-axis. The components of shear stress are then expressed as τxy, τyz, τxz, τyx, τzy, and τzx. Any direction in the three-dimensional space is defined by the normal to the plane that contains the direction and a line in the plane. Thus, two lines define the orientation in three dimensions. Similarly for the cube, the notation xz means in the plane normal to x in the z direction; yx means in the plane normal to y in the x direction. A tensor is a mathematical tool for defining and manipulating a group of quantities, where each quantity is represented by a magnitude, and most have an +z σ 0 +x σ1 +y (a) +z σzz τzx τzy σ3 σ3 σ2 σ2 τxz τyz σyy σ τxy σxx +x τyx +y (a) (b) FIGURE 5–15 (a) The stress ellipsoid, a triaxial ellipsoid in which the axes are the principal stresses σ1, σ2, and σ3. (b) Planes of maximum shear stress are always parallel to σ2 and ideally at 45° to σ1 and σ3. (b) FIGURE 5–17 (a) Randomly oriented stress σ applied to an infinitesimally small (point size) reference cube in x-y-z space. (b) Enlarged reference cube shows resolution of nine shear and normal stress components. 124 | Mechanics: How Rocks Deform accompanying “direction.” (Note that the direction does not have to be related to real coordinates in space or time.) Tensors have the same magnitude in any coordinate system, but the values of the components depend on the choice of coordinate system or “space.” Tensors have different ranks: a zero-rank tensor is a scalar and has only one component; an example is air temperature at a particular time. A firstrank tensor is a vector and has three components; a wind current is a first-rank tensor if it is thought of as a single tensor quantity at a point. A second-rank tensor relates sets of vectors to each other and has nine components. As we saw earlier components of shear and normal stress at a point form a second-rank tensor. Tensor rank describes the minimum number of directions necessary to describe the dimensions under consideration. Thus the number of components for a particular rank depends on the number of dimensions in the space being considered. For a firstrank tensor, the number of components equals the number of dimensions in the space (2D = 2, 3D = 3, 4D = 4, . . .). A tensor may be used to describe a physical quantity by referring it to an appropriate coordinate system. The elastic constants relating stress and strain (Chapter 6) comprise a fourth-rank tensor. The number of components in a tensor may be determined from 3n, where n is the rank, and the rank equals the number of letters or numbers in the subscript for a particular element of the tensor. The symbol τyz for a shear stress tells us that it is part of a second-rank tensor. All nine components of the second-rank tensor for stress at a point σij, where i and j take the values of x, y, and z, may be arranged in matrix form as  σ   σxxxx ττxyxy ττxzxz    (5–25) σyyyy ττyzyz   ττyxyx σ    ττ  σzzzz   zxzx ττzyzy σ   This matrix contains the components of a stress tensor in terms of axes x, y, and z. The rows (horizontal) from top to bottom refer to stresses on a face normal to a particular coordinate axis, and columns (vertical) refer to stress directions parallel to coordinate axes (Figure 5–17b). The columns (vertical) from left to right represent the directions of stress components parallel to the x, y, and z-axes, respectively. The left column represents stresses acting parallel to the x-axis, the middle column the stresses acting parallel to the y-axis, and the right column the stresses acting parallel to the z-axis. If we designate the elements of the tensors i and j—again with i and j taking values of x, y, and z—we can state that the tensor in equation 5–25 is symmetric because τij = τji (that is, elements i and j may be reversed without changing the values of the components, a requirement of the condition of equilibrium; the subscript ij also indicates that this is a second-rank tensor). Symmetry is a requirement of the condition of force balance, or equilibrium, assumed at the beginning of this discussion. If the x-y-z coordinate system is oriented parallel to the principal stresses, no shear stress will be present on the faces (all values of τ = 0). The same result can be accomplished by rotating the cube in the stress field until only normal stresses are present on the faces. The stress tensor for zero shear stresses may be written as  σ  xx   0   0  0 σ yy 0   σ    xx     0  =  σ yy  .    σzz   σzz     0 (5–26) The three normal stresses are thus called the principal stresses, with σxx = σ1, σyy = σ2, and σzz = σ3. They act perpendicular to planes so that the tensor is transformed from second to first rank. Measuring Present-Day Stress in the Earth Knowledge of the orientation and magnitude of presentday stress in the Earth is important because it provides clues about the nature of active faults, information about what structures might become more active in the future, and insight into the kinematics of plate motion. Knowledge of stress orientations bears directly on our understanding of seismic activity and its causes (Zoback and Zoback, 1980; Zoback et al., 1980). Present-day stress in the Earth can be measured by placing a strain gauge in rock and recording the in situ elastic strain. Such measurements are most frequently carried out by drilling a hole into bedrock, inserting the instruments, and recording the amounts and orientations of elastic strain. Two techniques are commonly used for measuring in situ stress: overcoring and hydraulic fracturing, although other data, such as well-bore breakouts, can provide stress orientation. Overcoring involves drilling a hole 3 to 4 cm in diameter, and then drilling a larger core (12 to 15 cm) with the same center as the smaller hole (Figure 5–18; Hooker and Bickel, 1974). Before coring the larger hole, an instrument called a dilatometer (a stain gauge) is inserted into the smaller hole to permit measurement of the expansion (relaxation) of the rock mass as the larger hole is cored. Changes in shape of the small hole are recorded as it is overcored by the dilatometer. The orientation of the small hole is known, so changes in shape are measured as the cross section relaxes from a circle to an ellipse. This provides a measure of the orientation of the present-day stress ellipsoid. If several measurements can be made at right angles at the same locality of overcores in different orientations—as is possible in a mine, tunnel, or quarry—a very good measure of the orientation of the stress ellipsoid may be obtained. Stress Overcore Inner hole (drilled first) Rock 15–20 cm 125 FIGURE 5–18 Overcoring technique for measuring in situ stress. The strain gauge rests inside the small borehole and measures in situ stress—while the overcore is being drilled—by recording the amount and direction of change from a circular to an elliptical borehole. 3–4 cm 3-4 cm Rock Strain gauge Attempts have also been made to calculate the magnitude of the principal stresses using this technique. Hydraulic fracturing involves drilling a vertical hole, sealing off a part of the hole with packers, and increasing the hydraulic pressure in the sealed-off part of the hole until the wall of the hole fractures (Figure 5–19; e.g., Zoback and Haimson, 1982). Both the amount of pressure needed to produce fractures and the orientations of hydraulic fractures are measured to provide values of both the magnitude of minimum horizontal stress at the site and the orientation of maximum and minimum horizontal principal stresses. It is possible to make several measurements in the same hole if it is drilled to a minimum depth of 300 to 400 m. The hydraulic fracturing method requires that the hole drilled be nearly vertical, for it is assumed that one of the principal normal stresses is vertical and that the hydraulic fracture in a vertical borehole propagates perpendicular to σ3 (Hubbert and Willis, 1957.) Zoback and Zoback (1980) concluded that field data also support the relationship between hydraulic fracture propagation and σ3. Numerous measurements of in situ stress using different techniques around the world have been compiled into a worldwide stress distribution map (Heidbach et al., 2008). Such maps permit identification of areas or domains of common maximum principal stress orientation (Figure 5–20). In situ stress in a tectonically active area has been measured by Zoback et al. (1980) in a series of wells about 240 m deep drilled as far as 34 km from the San Andreas fault. They also made several measurements in a 1 km deep well about 4 km from the fault. Their goal was to evaluate variations in the magnitude of the principal stresses with depth and to calculate the magnitude of shear stress along the fault. They used hydraulic fracturing to measure stress and obtained the magnitudes of Shmax (maximum horizontal stress = σ1) and Shmin (minimum horizontal stress) by modifying an equation originally derived by Hubbert and Willis (1957): Pb = 3Shmin− Shmax− Pp + T, (5–27) Hydraulic line for injecting fluid Packer Bedrock Hydrostatic pressure Cable to recorder | Pressure is increased until the rock fractures Packer 3–5 cm drillhole FIGURE 5–19 Hydraulic fracturing method for measuring in situ stress. Larger diameter drill holes can be used but the pressures required to fracture the rocks increase as the radius of the drill hole increases by a power-law relationship. (Modified from R. O. Kehle, Journal of Geophysical Research, v. 69, © 1964 by the American Geophysical Union.) where Pb is breakdown (fracture formation) pressure, Pp is pore pressure, and T is the tensile strength of the rock mass. Pb is measured directly as the pressure necessary to hydraulically break the rocks. Pp is calculated from the pressure of a column of water (using ρgh) at the depth at which hydraulic fracturing was carried out, assuming that 126 | Mechanics: How Rocks Deform Crustal Stress Regime Method Normal fault (extensional) Breakouts Strike-slip fault Focal mechanism Thrust fault (compressional) Overcoring, hydrofracturing Unknown 0 400 800 kilometers FIGURE 5–20 Partial data set for measurements and estimates of orientations of principal stress directions in the continental United States, northern Mexico, and southern Canada. Heavy dashed lines indicate areas of common orientation of present-day maximum (compressional) and minimum (extensional) principal stress. Arrowheads of large red arrows indicate whether stress produces strike-slip, extensional, or compressional structures. (Modified from O. Heidbach, M. Tingay, A. Barth, J. Reinecker, D. Kurfeß, and B. Müller, The World Stress Map database, 2008, http://www.world-stress-map.org/.) the pores in the rocks are interconnected and communicate with the surface. The tensile strength of the rock mass can be estimated (as here) or measured on core samples obtained from the well. The magnitude of Shmax is measured directly, and its orientation (compass bearing) is obtained from orientations of hydraulic fractures in the well. The value of Shmax is then calculated from equation 5–27 and is assumed to be horizontal. Results of measurements in the two areas studied (Table 5–2) indicate that the maximum principal horizontal stress, Shmax, is oriented about 45° from the strike of the San Andreas fault. Shear stress, determined by plotting the maximum and minimum principal stresses on a Mohr diagram, increases from about 2.5 MPa (25 bars) at depths of 150 to 300 m to about 8.0 MPa (80 bars) at 750 to 850 m. Studies by Zoback et al. (1987) based on in situ stress measurements in the Cajon Pass scientific borehole, other stress measurements along the fault nearby, and orientations of folds in Pleistocene sediments immediately adjacent to the fault indicate that Shmax is oriented nearly perpendicular to the San Andreas fault northeast of Los Angeles. Thus, there is almost no shear stress along the fault near the surface in this area: shear stress equals zero. Plotting principal stress orientations on a map enables us to relate the present-day stress in the Earth to plate motion (Figure 5–20). The nearly uniform N 70° E orientation of stress fields in the eastern United States is thought to be related to “ridge push” from the MidAtlantic Ridge, and the markedly different orientations Stress TABLE 5–2 | 127 Hydrofracture Data along the San Andreas Fault DISTANCE SAN DEPTH ANDREAS WELL (M) FAULT (KM) FRACTURE BREAKDOWN OPENING PORE PRESSURE PRESSURE PRESSURE (BARS) (BARS) (BARS) Shmin (σ3) Shmax (σ3) σ2 TENSILE τmax STRENGTH (BARS) (BARS) DIRECTION OF MAXIMUM COMPRESSION 1 167 4 200 69 17 73 133 45 131 30 N 4° W 1 196 4 209 74 20 77 138 53 135 31 N 1° E 2 338 4 109 63 34 74 125 91 46 26 N 43° W 2 561 4 163 130 56 150 264 152 33 57 N 20° W 2 787 4 192 124 78 183 346 213 68 82 N 19° W 3 80 2 144 24 8 23 38 18 120 8 N 20° W 3 185 2 250 73 19 56 73 43 177 6 N 23° W 4 167 4 139 47 17 51 89 45 92 19 N 83° E 4 230 4 164 85 23 83 140 62 79 29 N 14° W (From Zoback, Tsukahara, and Hickman, Journal of Geophysical Research, v. 85, © 1980 by the American Geophysical Union. Used by permission.) in western states are related to interaction between the Pacific and North American plates (Figure 1–2; Richardson et al., 1979). In addition to direct measurements of stress, the orientation of maximum and minimum principal horizontal stresses can be obtained from well-bore breakouts (elongations) that form after a hole is drilled. A hole changes shape and fractures as the walls relax, producing curved fractures and causing rock to spall from the walls of the hole. These fractures form parallel to the orientation of the principal stress directions, but the magnitude of stress cannot be determined. Mount and Suppe (1987, 1992) used breakouts from drill holes near the San Andreas fault to independently conclude that σ1 is perpendicular to the fault, and that shear stress along the fault surface is zero. Interest in the stress and other properties of the San Andreas fault has resulted in a major part of the EarthScope Project being dedicated to study of this fault in the Plate Boundary Observatory, which consists of an array ESSAY of seismic monitoring equipment, GPS stations, and a scientific drill hole (SAFOD—San Andreas Fault Observatory at Depth). Numerous stress measurements have been made on the surface and several were made in the SAFOD pilot hole, a 2 km deep hole drilled southwest of the San Andreas fault near Parkfield, California, into a region near the fault that produces frequent small earthquakes. Stress measurements in this hole again indicate low shear stress parallel to the fault, but large mean stress—approximately twice the lithostatic stress there (Chéry et al., 2004). The high angle made by Shmax with the fault (85°) near San Francisco is consistent with an average angle of 68 + 7° over 400 km of the fault in California, again suggesting the San Andreas has low frictional strength throughout this region (Townend and Zoback, 2004). We end our survey of stress and its mechanical basis. We turn in the next several chapters to a discussion of strain— the presumed effect of stress. The Earthquake Cycle Whenever a large earthquake (ML ≥ 7) occurs somewhere in the world, that earthquake probably occurs on a fault that has been known to have produced large earthquakes for hundreds or even thousands of years. Large active faults produce earthquakes of different magnitudes and frequencies. These faults frequently form plate boundaries that separate two plates that are colliding head-on, grinding past each other, or pulling apart from each other (see Figure 1–2). Earthquakes occur along segments of large active faults like the San Andreas in California, the North and East Anatolian faults in Turkey, and the Cascadia subduction zone in the Pacific Ocean off Washington and Oregon. For an earthquake of any magnitude to occur, stress has to accumulate and be released suddenly, producing elastic rebound and 128 | ESSAY Mechanics: How Rocks Deform continued earthquake waves. Once the accumulated stress—elastic strain energy—is released, the fault begins to accumulate stress to a point where movement will occur again. This is the simplest statement of the earthquake cycle, but this process is not simple or we would today be able to predict when and where earthquakes will occur. The period of stress accumulation is commonly a quiet time along the fault lasting many years to centuries, although small earthquakes may occur during this period. As stress continues to accumulate over months to years, however, the frequency and magnitude of earthquakes increases. The larger earthquakes may or may not be “foreshocks,” depending on whether or not 125°W 120°W Cascadia subduction zone JUAN DE FUCA PLATE 115°W OR ID Mt. Shasta (4317 m) Basin and Range 40°N NORTH Province Sie GORDA PLATE NV rra tns aM vad Ne ey all tV ea CA AMERICAN PLATE Gr SF 1 2 40°N UT Mt. Whitney (4418 m) Death Valley n Sa (–86 m) LV An dr 35°N California and Vicinity Earthquakes (1769–2007) Magnitude (ML) 6.0–6.4 6.5–7.4 3 PACIFIC PLATE 7.5–9.0 0 125°W 50 100 kilometers eas s k f. rloc Mojave Ga Desert faul t 4 LA 35°N AZ Salton Trough C bo alifo rd er rnia lan d Mexico Gulf 200 120°W 115°W FIGURE 5E–1 San Andreas and related faults in California and adjacent region, together with ML = 6.0 and larger historical earthquakes. The San Andreas fault terminates to the northwest into one or more transform faults and the Cascadia subduction zone; to the southeast it joins the remnants of the East Pacific Ridge in the Gulf of California. Note that the San Andreas also has a splay, the Garlock fault, that trends eastward and terminates in the Mojave Desert. 1—1906 ML = 7.8 San Francisco earthquake. 2—1989 ML = 6.9 Loma Prieta (“World Series”) earthquake. 3—1994 ML = 6.7 Northridge earthquake. 4—1971 ML = 6.6 San Fernando earthquake. Despite the smaller magnitude of earthquakes 2, 3, and 4, they produced major damage in the populated areas where they occurred. SF—San Francisco. LA—Los Angeles. LV—Las Vegas. Lines with solid teeth are active subduction zones. Lines with open teeth are dormant or inactive subduction zones. Lines without ornamentation are strike-slip faults. (Modified from J. C. Crowell, 1987, Episodes, v. 110.) they culminate with a larger earthquake. During the weeks and even months that follow a major earthquake, there will be numerous “aftershocks,” commonly of smaller magnitude than the largest event. Aftershocks frequently bring down poorly constructed buildings and other structures weakened during the major earthquake. The fault then returns to another period of quiescence as stress and elastic strain energy build along the fault once more. A number of different factors influence the time interval between large earthquakes along a fault. These include the rate of stress (elastic strain) accumulation, presence of water or weak materials like clay along the fault that may weaken a particular segment of the fault, orientation of the fault relative to the maximum principal stress, σ1, and other factors that we do not understand. The time or “recurrence” interval between large earthquakes may range from a few tens of years, or even less, along some major active faults in the world to several centuries along some faults located in the interiors of continents far from plate boundaries. Large earthquakes (ML ≥ 7) occur at a rate of approximately 18 per year worldwide (USGS Earthquake Statistics website; http://earthquake.usgs.gov), and commonly not on the same fault or even the same part of the same fault. There has not been a large earthquake in the San Francisco area since the ML = 7.8 earthquake in 1906. The 1989 Loma Prieta earthquake located just to the south had a magnitude of 6.9, and it, with its accompanying aftershocks, filled in an area along the San Andreas fault (a “seismic gap”) where there had been relatively few historic earthquakes, indicating that part of the San Andreas had completed the earthquake cycle in 1989 (Figure 5E–1). Other parts of the San Andreas in southern California are thought to be “locked” (still accumulating stress as elastic strain energy), despite the damaging ML = 6.6 San Fernando earthquake in 1971 and the ML = 6.7 Northridge earthquake in 1994 in the Los Angeles area (Smith and Sandwell, 2006). An important exception to the point made here occurred in 1811 and 1812 in eastern Arkansas, southeastern Missouri, and western Tennessee where the four large New Madrid earthquakes occurred over a period of less than two months (U.S. Geological Survey) (Figure 5E–2). An estimated ML = 7.9 earthquake occurred here on December 16, 1811, an estimated ML = 7.0 earthquake on December 17, 1811, an estimated ML = 7.6 earthquake on January 23, 1812, and then a fourth earthquake on February 7, 1812, with an estimated magnitude of 8.0 (Johnston and Schweig, 1996). These magnitudes are estimates because the modern seismograph had not been invented yet, and additional analysis by Hough (2001, Table 1) has estimated these earthquakes to have slightly lower magnitudes. Nonetheless, never before or since have there been four major earthquakes occurring so close together in time or space. Other anomalous facts about this Stress 90°W Charleston New Madrid 2/7/1812 MO KY AR TN Earthquakes 1811–2012 12/16–17/1811 Marked Tree Magnitude (ML) <1.0 1.0–1.9 Memphis 0 25 kilometers TN 50 AR MS 129 series of earthquakes are that the earthquakes did not occur close to a plate boundary, there is no identifiable fault that actually broke the surface, and subsequent measurements of the continued seismicity in this area indicate the earthquake source is more than 5 km below the surface. The New Madrid seismic zone continues to be the most active in the eastern United States, although there have been no large (ML ≥ 7) earthquakes since the 1811–1812 series. Estimates of large earthquake recurrence in this zone are on the order of 400 y (e.g., Tuttle and Schweig, 1995; Johnston and Schweig, 1996). The New Madrid earthquakes fall into the general class of intraplate earthquakes—in other words, those not associated with plate boundaries. References Cited Mis si p sis 36°N lfo ot rif t MO AR er Blytheville Caruthersville Re e Boo thee l lin eam ent ift tr Reelfoot fault pi 36°N TN 1/23/1812 Riv Re elf oo Reelfoot Lake | Hough, S. E., 2001, Triggered earthquakes and the 1811–1812 New Madrid, Central United States, earthquake sequence: Bulletin of the Seismological Society of America, v. 91, no. 6, pp. 1,574–1,581. 2.0–2.9 Hough, S. E., Armbruster, J. G., Seeber, L., and Hough J. F., 2000, On the 3.0–4.9 modified Mercalli intensities and magnitudes of the 1811–1812 New Madrid 5.0–6.9 earthquakes: Journal of Geophysical Research, v. 105, pp. 23,839–23,864, doi: ≥7.0 10.1029/2000JB900110. 90°W Johnston, A. C., and Schweig, E. S., 1996, The enigma of the New Madrid FIGURE 5E–2 Distribution of earthquakes in the New Madrid earthquakes of 1811–1812: Annual Reviews of Earth and Planetary Science, seismic zone. Note that the earthquake array defines several fault segments, with only the northwest-trending Reelfoot (a thrust with the teeth on the hanging wall) identified on the map. The brown normal faults (ticks on the hanging wall) belonging to the Reelfoot rift are early Palezoic faults that have been identified using aeromagnetic data (Chapter 4). Earthquake data from the National Earthquake Information Center (NEIC) of the U.S. Geological Survey. Locations of lineaments and rifts from Johnston and Schweig (1996). Location of Reelfoot fault from Hough et al. (2000). v. 24, p. 339–384. Smith, B. R., and Sandwell, D. T., 2006, A model of the earthquake cycle along the San Andreas fault for the past 1000 years: Journal of Geophysical Research, v. 111, B01405, doi: 10.1029/2005JB003703. Tuttle, M. P., and Schweig, E. S., 1995, Archeological and pedological evidence for large earthquakes in the New Madrid seismic zone, central United States: Geology v. 23, pp. 253–256. Chapter Highlights • Stress in the Earth’s crust produces deformation; when stress exceeds the strength of a material permanent deformation occurs. • Compressional stress can be thought of as “pushing together,” resulting in a decreased volume, whereas tensional stress involves “pulling apart,” frequently producing a volume increase. • The state of stress at a point can be resolved into three mutually perpendicular principal stresses (σ1, σ2, and σ3) that define the stress ellipsoid. • The Mohr circle is a powerful and simple graphical tool for determining normal (σn) and shear stresses (σs) acting on planes. • Experimental deformation of materials leads to a failure envelope that separates states of stress in which a material will deform vs. not deform. • Stress can be measured in situ using a variety of techniques such as overcoring and hydraulic fracturing. Questions 1. Why do we commonly deal with stress, rather than force, in the earth sciences? 2. Calculate the lithostatic value of stress on a fault plane inclined at 30° and located at a depth of 7 km in oceanic crust (ρ = 3,000 kg m−3). 130 | Mechanics: How Rocks Deform 3. Given principal stresses with magnitudes of 90 and 50 MPa, what will the state of stress be (σn and τ) on a joint surface (Chapter 9) oriented 40° to σ1? 4. Use the data presented below to determine the values of σ1 and σ3 and σn and τ acting on the two planes oriented 80° and 30° with respect to σ1. Physical Space σ1 a = σ1 30° a = 80° σ3 σ3 σ3 σ3 σ1 σ1 𝝉 Mohr Space 20 10 –σn 10 30 5. What does the shape of the Mohr envelope tell us about the strength of the material being deformed? 6. At low to moderate differential stresses, materials typically do not fail along planes that experience the highest shear stress (θ = 45°). Why might that be the case? 7. What is actually happening in materials that produce straight Mohr envelopes? 8. A mine adit is opened at a depth of 2 km to extract gold from quartz veins in granite. Experimental data indicate that the cohesive strength (τ 0) of the granite is 20 MPa, its coefficient of internal friction (μi) is 0.6, and its density (ρ) is 2,600 kg m−3. What is the state of stress in the gold mine? Use the Coulomb fracture criterion (|τs| = τ 0 + σn μi) to determine if there is a danger of rock bursts in the mine adit. 9. Why are earth materials generally much stronger under compression than tension? 10. Hydrofracture measurement of principal stresses along the San Andreas fault at a depth of > 600 m in a drill hole by Zoback et al. (1980) yielded a value for σ3 of 141 bars and for σ1 of 258 bars. Determine the value of maximum shear stress at that point. σn 50 10 20 –𝝉 units in MPa Further Reading De Paor, D. G., 1986, A graphical approach to quantitative structural geology: Journal of Geological Education, v. 34, p. 231–236. A graphical method is described for use in structural geology, determining normal and shear stress without trigonometry. Engelder, T., 1994, Deviatoric stressitis: A virus infecting the earth science community: EOS, v. 75, p. 209–212. A tongue-in-cheek discussion of deviatoric stress that is both educational and entertaining. Fuchs, K., and Müller, B., 2001, World stress map of the Earth: A key to tectonic processes and technological applications: Naturwissenschaften, v. 88, p. 357–371. Discusses the world stress map and the techniques by which these data were collected. Hubbert, M. K., 1951, Mechanical basis for certain familiar geologic structures: Geological Society of America Bulletin, v. 62, p. 355–372. This is a classic study relating experimentally produced structures to both theory and real tectonic structures as observed in the field. It also presents a clear, simple, and concise derivation of the Mohr circle equations. Means, W. D., 1976, Stress and strain: New York, Springer-Verlag, 339 p. A clearly written introduction to the concepts of stress and strain through the principles of continuum mechanics. Mathematical concepts and derivations are presented understandably, using problems (with solutions) related to geologic situations. Emphasizes elastic and viscous strain. Means, W. D., 1990, Kinematics, stress, deformation and material behavior: Journal of Structural Geology, v. 12, p. 953–971. An excellent summary of the relationships between stress and strain in experimentally deformed rocks. Mohr circles are presented as two-dimensional tensor quantities. Also includes a useful glossary of terms. Zoback, M. L., 1992, First- and second-order patterns of stress in the continental United States: Journal of Geophysical Research, v. 97, p. 11,703–12,013. Contains a number of papers on stress patterns in different parts of the world, along with a map by Mary Lou Zoback depicting the worldwide state of stress from measurements on all the major plates. 6 Strain and Strain Measurement Structural geology is largely the study of deformation. Figure 6–1 dramatically illustrates how earth materials may be deformed. Sometime after these brachiopods were deposited and buried by younger sediment, stresses within the Earth’s interior were sufficient to permanently distort their shapes. Careful inspection of the brachiopod shapes, especially when compared to undeformed brachiopods, reveals that anatomical features that were originally perpendicular are now oblique to one another. Furthermore, these brachiopods are greatly elongated in one direction and significantly shortened in another. What happened at the microscopic or atomic scale to accomplish this deformation? These distorted brachiopods are vivid reminders of strain, but many other geologic features (folds, foliations, etc.) also are the products of strain. Stress conditions within the earth’s crust change during the progress of time, and these changes often lead to permanent deformation of crustal rocks. One of the prime aims of the structural geologist is to determine the nature and amount of these displacements. JOHN G. RAMSAY, 1967, Folding and Fracturing of Rocks FIGURE 6–1 Deformed brachiopods on a bedding plane in Ordovician limestone, Gander Lake, central Newfoundland. (Robert B. Neuman, U.S. National Museum, and R. Frank Blackwood, Newfoundland Department of Mines; U.S. National Museum specimen). 131 132 | Mechanics: How Rocks Deform As discussed in Chapter 5, permanent deformation or strain is the result of stress, but, in many situations, the stresses that caused rocks to deform have long since dissipated and structural geologists are left to unravel the strained puzzles in rocks—folds, foliations, and so on—to attempt to reconstruct ancient stresses. So, understanding strain is fundamental to structural geology. This chapter provides an introduction to strain; we will consider the measures of strain in one, two, and three dimensions and the nature of progressive deformation. The last half of the chapter illustrates strain measurement techniques and their utility for the structural geologist. Lo Lf Lf Definitions Deformation is a general term used to describe the changes in shape, position, volume, or orientation of a rock mass in response to the physical and chemical processes that may affect the rock mass. In a more abstract sense, deformation is the displacement field for tectonically driven particle motion(s) and involves the processes by which the particle motions are achieved (Figure 6–2). Body motions include: (1) distortion or strain, a change in shape, (2) rotation, a change in orientation, and (3) translation, a change in position. Deformation differs from strain, because it encompasses rigid body rotation and rigid body translation. In a strict sense, strain is a shape change in a material that includes line length changes, angular relations changes, and/or volume changes. The term strain, however, is often loosely applied to describe displacements along faults and the tilting of rock layers when they are folded. With regard to homogeneous strain, lines that are straight and parallel before deformation remain straight and parallel after deformation (Figure 6–3). With inhomogeneous strain, straight or parallel lines before deformation do not remain straight or parallel after deformation. Lines may also be broken during inhomogeneous deformation. Whether strain is homogeneous or inhomogeneous is sometimes a matter of scale. Rock masses several Lf (a) tion Rota (a) sla n Tra n tio (b) FIGURE 6–2 (a) Strain as a distortion of initially parallel and perpendicular lines involving a change in length, shape, or volume of a rock mass. Lo is the undeformed length; Lf is the deformed (final) length. (b) Rigid-body translation or rotation of a mass without accompanying distortion. (b) FIGURE 6–3 Homogeneous (a) and inhomogeneous (b) strain. Note that after deformation, originally parallel or straight reference lines remain straight and parallel with the body undergoing homogeneous strain. Similar reference lines in the body undergoing inhomogeneous deformation are either not parallel or straight or are broken. Strain and Strain Measurement 133 | cubic kilometers in size are likely to have deformed quite inhomogeneously, although there may be situations in which it is useful to consider the strain at that scale to be homogeneous. It is commonly assumed, at the scale of a hand sample or thin section, that a rock mass deforms in a homogeneous fashion, but invariably the differences in strength between mineral phases and within individual minerals produce inhomogeneties during deformation, even at that scale. Measures of Strain Consider the feldspar grain in the deformed granite illustrated in Figure 6–4a. This feldspar formed as a phenocryst when the granitic rock crystallized. Later deformation fractured the original feldspar grain into a series of fragments separated by quartz-filled veins. Individual fragments can be “put back together” and, as such, serve as markers for the amount of linear strain that occurred in one dimension (Figure 6–4b). Elongation (e), stretch (S), quadratic elongation (λ), and natural or logarithmic strain (ε), are all measures of linear or longitudinal strain. (a) A Deformed Lf Lf = 8.2 mm Af Elongation: e= ( L − L ) (6–1) f A o Lo Undeformed ( )    L f − Lo  % Elongation =   × 100   Lo   Lo Af Stretch: S= Lf Lo Ao Lo = 6.7 mm Elongation (e) = 22% Stretch (S) = 1.2 Quadratic elongation (λ) = 1.44 Natural strain (ε) = 0.18 (b) = (1 + e ) (6–2) Quadratic elongation:  L f 2 λ =   = (1 + e )2 = S 2  Lo  (6–3) Natural (logarithmic) strain: ε = ln (1 + e) = ln (S) FIGURE 6–4 (a) Photomicrograph of fractured and elongated feldspar phenocryst in granitic mylonite, Virginia Blue Ridge. q—quartz. f—feldspar. m—muscovite. (CMB photo.) (b) Sketch of the deformed and undeformed state with linear strain measurements calculated for A to Af. (6–4) where Lf is the final length of a deformed object and Lo is its original length. If ε > 0 or positive, material was extended; if ε < 0 or negative, material was shortened. All of these linear strains are related to each other and, if one is known, the others can be calculated. Furthermore, these quantities are all dimensionless because they are ratios. Later in the chapter these different measures of linear strain will be employed for a variety of purposes. The feldspar grain in Figure 6–4 was elongated 22 percent during deformation. It is important to remember that the linear strain estimate is for the feldspar grain, not necessarily the rock as 134 | Mechanics: How Rocks Deform X Vf ψ FIGURE 6–5 Shear strain. The angular shear (ψ) is 32°, and the shear strain (γ) is 0.63 (from equation 6–5). Vo +ΔV a whole, as the original feldspar may be more competent than the surrounding matrix. The rock matrix likely experienced significantly more strain than the feldspar. Angular shear (ψ) and shear strain (γ) are measures of orientation changes during deformation. For example, in Figure 6–5, line X rotates 32° clockwise during deformation; this rotation is angular shear. Shear strain is related to angular shear by Vf −ΔV FIGURE 6–6 Positive dilation (+ΔV) and negative dilation (−ΔV) of a sphere. Vo is the original volume, and Vf is the final volume. γ = tan ψ.(6–5) Shear strain can be utilized to determine the amount of displacement in deformation zones (Chapter 10) and to reconstruct the original geometry of contacts. Changes in material volume may occur during deformation. The dilation (Δ) of a material may be either positive or negative (Figure 6–6). A finite volumetric strain or dilational strain (Δ) is given as ∆= (V − V ) f o Vo Voids 0 1 mm (a) Pressure-solution zones (6–6) where Vo and Vf are the original and final volumes, respectively. In earth materials, volume change occurs by a number of mechanisms, including: (1) closing of voids between grains as material is compacted; (2) dissolving away parts of the rock mass by dissolution—both producing negative dilations; and (3) fracturing and veining a rock mass to produce a positive dilation (Figure 6–7). 0 1 mm (b) Fractures Strain Ellipse and Ellipsoid Let us homogeneously deform a box by shearing it into a parallelogram (Figure 6–8a). Notice that the deformation conserves area, and most lines in the box rotate clockwise. Some lines lengthen (e.g., line A) whereas other lines shorten (e.g., line B). Because we can measure the original and final length for each line, the stretch of each line can be quantified. When the stretch values and 0 1 cm (c) FIGURE 6–7 Three ways to accomplish volume change: (a) closing voids between grains; (b) dissolving part of the rock mass by pressure solution, here showing the zones of pressure solution “pulled apart” to make them more visible; and (c) fracturing the rock body. Note (a) and (b) produce negative volume changes, whereas an increase in volume occurs in (c). Strain and Strain Measurement ORIGINAL Bo Co Ao Eo Fo FINAL Af Do Ff Ko Ho Io Go Ef Gf X Df Z Kf Jf Mf Ao Af Lo = 1.4 cm Rs = Lf = 1.8 cm / SX SZ = 1.37 = 1.87 0.73 FIGURE 6–9 The strain ellipse, characterized by the maximum principal stretch (X) and the minimum principal stretch (Z). Strain ratio (Rs) is given by the ratio SX /SZ. / StretchA = Lf Lo = 1.8 cm 1.4 cm = 1.3 Bf Bo Lo = 0.5 cm (a) 135 Hf If Jo Mo Bf Cf | Lf = 0.4 cm / / StretchB = Lf Lo = 0.4 cm 0.5 cm = 0.8 SG SD SJ SB SC SI SA SE SF SK S H SM (b) FIGURE 6–8 Derivation of the strain ellipse. (a) Deformation of a box and set of lines, illustrating the stretch for various lines. Ao . . . Mo—original line lengths. Af . . . Mf—deformed line lengths. (b) Plotting all the stretch vectors (SA . . . SM) from a common point produces the strain ellipse. final line orientations are plotted from a common point (Figure 6–8b), a very clear pattern emerges. Collectively, the ends of the stretch vectors define an ellipse; this ellipse is a graphical representation of the stretch in all orientations and is the strain ellipse. The strain ellipse is an elegant concept that is vitally important for structural geology students to grasp and understand. Ellipses are characterized by two principal axes that are perpendicular to each other. For a strain ellipse, the long axis (X) is the direction of maximum stretch or greatest principal strain and the short axis (Z) is the direction of minimum stretch or least principal strain (Figure 6–9). The directions of maximum and minimum stretching are always perpendicular to each other. Another important consideration is that although the Z-axis is the direction of minimum stretching, it is also the direction of maximum shortening. The strain ratio or ellipticity (Rs) is given as RS = SX SZ (6–7) where SX and SZ are stretches in the X and Z directions. In an undeformed state, material has neither been shortened nor lengthened in any direction; thus SX = SZ = 1, so the strain ratio is 1. In the deformed state the strain ratio is always greater than 1. Deformations are more commonly three-dimensional and as such the three dimensional state of strain is graphically illustrated by the strain ellipsoid with its three mutually perpendicular principal axes X, Y, and Z, where SX ≥ SY ≥ SZ (Figure 6–10). The Y-axis is the intermediate principal strain axis. Two-dimensional sections through a strain ellipsoid are typically ellipses, although for triaxial ellipsoids (SX > SY > SZ) there are two circular sections (Figure 6–10b), that represent planes along which material has neither been elongated nor shortened. The shape of the strain ellipsoid is highly variable depending on the type of three-dimensional strain. If a material is shortened in one direction and extended in the other two (SX = SY ≥ 1 ≥ SZ), the ellipsoid is oblate with a shape something akin to a pancake or a hamburger (Figure 6–11), whereas extension in one direction and shortening in the other two (SX ≥ 1 ≥ SY = SZ) produces a prolate ellipsoid with a shape similar to a link sausage or a hot dog (Figure 6–11). Perfectly oblate and prolate ellipsoids have only one circular section. The shape and magnitude of the strain ellipsoid is commonly portrayed on a Flinn diagram, which plots the 136 | Mechanics: How Rocks Deform ratios of the principal stretches (SX /SY and SY /SZ) to one another (Figure 6–11). The distance from the graph origin is a measure of the overall strain magnitude. Perfectly oblate ellipsoids plot on the abscissa, whereas perfectly prolate ellipsoids plot on the ordinate. Oblate ellipsoids are characteristic of flattening strain and prolate ellipsoids are the product of a constrictional strain. In a Flinn diagram, the fields of apparent flattening and constriction are separated by the line of apparent plane strain. In the special case of plane strain, SX /SY and SY /SZ are equal and SY = 1, which means there is no shortening or elongation in the intermediate direction. Plane strain ellipsoids are triaxial and look something like an enchilada (Figure 6–11). A measure of the shape of the strain ellipsoid is given by Flinn’s k where X Principal planes Z Y (a) X Circular section Circular section k= A perfectly oblate ellipsoid has a k-value of 0, plane strain equals 1, and a perfectly prolate ellipsoid has a k = ∞. Another measure of ellipsoid shape is given by the Lode’s parameter (ν): Z Y ν= (b) X Z Y Y X >Y > Z Plane strain 3.0 = (k in ra st an e Z X Pl 2.0 Constriction (k = ∞) SX 1) 2.5 SY 1.5 Y Flattening (k = 0) 1.0 1.0 1.5 2.0 SY SZ 2.5 3.0 (6–9) FIGURE 6–11 Flinn diagram illustrating prolate, plane, and oblate strain ellipsoids. X X>Y=Z Prolate ellipsoid (εX − εZ) − (εX − εY) (εX − εZ) − (εX − εZ) where (εX, εY, ε Z) are the principal natural strains. The Lode’s parameter provides a symmetric measure of FIGURE 6–10 Strain ellipsoid with principal axes X, Y, and Z (a) and circular sections (b). Z ( SX SZ − 1) .(6–8) ( SY SZ − 1) X =Y > Z Oblate ellipsoid Strain and Strain Measurement strain ellipsoid shape with ν = −1, corresponding to a perfectly prolate ellipsoid (k = ∞), while ν = 1 corresponds to a perfectly oblate ellipsoid (k = 0). The overall amount of distortion (d) recorded by the strain ellipsoid is defined as d= 2 2 ( RXY − 1) + ( RYZ − 1) (6–10) which, in essence, is a measure of the distance from the origin of the Flinn diagram. Volume change or dilational strain can be estimated if the three principal stretches are known by the following relationship SX • SY • SZ = (Δ + 1).(6–11) If no volume change occurs (Δ = 0) during deformation, the product of the principal stretches equals 1. As we shall see later in this chapter and throughout the book, many geologic structures are directly related to the principal strains. In many situations, the penetrative lineation | 137 (Chapter 19) is parallel to the X-axis and the prominent cleavage or foliation characteristic of most slates forms parallel to the XY plane (Chapter 18). Simple, General, and Pure Shear Although the strain ellipse characterizes the state of twodimensional strain, not all strain ellipses develop in the same way. If we homogeneously deform an original unit square by shortening it in the vertical direction and elongating it in the horizontal direction, the result is a rectangle (Figure 6–12). Compare that to deformation in which the original unit square is differentially displaced by horizontal translation, such that a parallelogram is created (Figure 6–12). Both deformations produced strain ellipses with identical ratios, although the orientation of the principal axes is different (Figure 6–12). In the first deformation, the principal axes remain in the same Pure shear General shear Simple shear Wm = 0 0 < Wm < 1 Wm = 1 Shape and orientation Strain ellipses Particle paths Kinematic vorticity number FIGURE 6–12 Pure, general, and simple shear illustrating the shape and orientation of the deformed material, the corresponding strain ellipses, particle paths, and kinematic vorticity number (Wm) for each. 138 | Mechanics: How Rocks Deform orientation throughout (a coaxial strain accumulation), whereas the principal axes rotate during the second deformation (a non-coaxial strain accumulation). These are special two-dimensional deformations referred to as pure shear and simple shear, respectively. Intermediate cases are called general shear (Figure 6–12). The paths traced by individual particles in the deforming material are different for pure, simple, and general shear. In pure shear a particle is translated along a curved path, whereas in simple shear the particles are translated horizontally. There is symmetry to the particle flow and the boundaries between flow fields are eigenvectors. In pure shear, the eigenvectors are 90° apart; in general ESSAY shear, the angle between the eigenvectors becomes progressively less as simple shear is approached such that in simple shear the two eigenvectors have merged into a single eigenvector (Figure 6–12). A quantitative measure that relates the rotation of the principal strain axes to the overall stretching is the kinematic vorticity number (Wm) given by Wm = cos υ(6–12) where υ is the acute angle between the two eigenvectors (Figure 6–13). For pure shear, Wm = 0 and for simple shear, Wm = 1, with general shear between 0 and 1 (Figure 6–12). Daubrée and Mead Experiment A classic experiment involving formation of fracture sets in plate glass was made first by Auguste Daubrée (1879), a French geologist and mineralogist. The experiment was repeated several decades later by W. J. Mead (1920), using a paraffin-coated rubber sheet in a square frame. The two men produced almost identical fracture sets within the glass or paraffin by applying a shear stress in the form of a couple (oppositely directed shears; Figure 6E1–1). On shearing, a reference circle was deformed into a strain ellipse. In addition, four sets of fractures were easily recognized. One set paralleled the long axis of the strain ellipse (X), another paralleled the short axis (Z), and two conjugate sets formed about an acute angle with the X-axis as a bisectrix. Considering the work by Daubrée and Mead, it is easy to see that a fracture set parallel to the short axis of the strain ellipse results from extension. Extension fractures are known to form parallel to the YZ plane of the strain ellipsoid and perpendicular to X. We can also see that these fractures formed perpendicular to X and parallel to Z in the essentially twodimensional strain model. The conjugate set of fractures parallel to the edges of the glass plate are readily explained as shear fractures. If we consider that the stresses were applied parallel to the edges of the frame in Figure 6E1–1, they must be considered shears, for they are oblique to the orientation of the normal stresses. The fracture set parallel to the X direction is more difficult to explain. The set formed perpendicular to σ1 and Z—assuming that the stress field did not rotate during deformation—and formed parallel to a different oriented shear plane. If so, such fractures could be considered thrust faults (Chapters 10, 11, and 12), especially because they frequently form inclined to the surface of the glass Z r1 r'1 r2 X r'2 r'2 > r'1 r1 = r 2 (a) Z X Z X 1 2 Shear planes Z (b) X 3 FIGURE 6E1–1 Daubrée–Mead experiment and interpretations of fracture sets in terms of the strain ellipse. (a) Four fracture sets in glass or paraffin. (b) Separating fracture sets. 1. Set parallel to Z, therefore composed of extension fractures (joints). 2. Possible shear planes. 3. Set parallel to X, may(?) be thrust faults. Strain and Strain Measurement 139 | Shear fractures Extension fractures Shear plane X Extension plane Y (a) (b) Z (c) FIGURE 6E1–2 (a) Fragment of safety glass from a wrecked car (unfortunately Hatcher’s) illustrating a fracture pattern almost identical to that produced by Daubrée and Mead. U.S. quarter indicates scale. (b) Sketch of the fracture pattern in (a). (c) Strain ellipse with principal and shear planes oriented parallel to most of the fractures in the glass. Deformation of the window glass probably occurred by clockwise (dextral) homogeneous simple shear, indicated by arrows. or paraffin—not perpendicular to σ1. Otherwise, they are called “compression fractures.” Any homogeneous material of approximately the same shape, strained in similar fashion, would yield about the same fracture pattern (Figure 6E1–2). References Cited Progressive Deformation, Strain Symmetry, and Strain Path clockwise (Figure 6–14c). The final or finite strain ellipse has an aspect ratio of 5.2 and can be divided into distinct fields in which materials were either elongated (field of extension) or shortened (field of shortening) (Figure 6–14b). The boundaries between the two fields are lines (lines of no finite elongation) that are the same length as they were before deformation. A few other observations come from this exercise: the fields of shortening and elongation change their orientation during deformation and materials rotate toward the field of elongation such that some lines (i.e., line C) are shortened first and then elongated. Progressive deformation in three dimensions is a bit more complex, but leads to the idea of strain symmetry. Consider a two-dimensional, homogeneous progressive deformation by general shear (Figure 6–14). Lines A, B, C, and D in Figure 6–14 are all deformed but in different ways: line A does not rotate but progressively elongates, line B progressively shortens and slowly rotates counterclockwise, line C shortens and then elongates all while rotating clockwise, and line D is greatly elongated and rotates Daubrée, A., 1879, Études synthétiques de géologie expérimentale: Paris Nabu Press, p. 306–314. Mead, W. J., 1920, Notes on the mechanics of geologic structures: Journal of Geology, v. 28, p. 505–523. 140 | Mechanics: How Rocks Deform υ = 20° Eigenvectors Wm = cos υ Wm = 0.94 FIGURE 6–13 General shear deformation. Flow eigenvectors are used to determine the kinematic vorticity number (Wm). Rs = 1.0 B C 90° Rs = 1.3 Rs = 2.1 Rs = 5.2 D A 180° 0° The concept of strain symmetry is broadly similar to the symmetry of mineral crystal structures, but there are important differences. Imagine a unit sphere and unit cube that undergo progressive pure shear. With increasing strain the cube is transformed into an elongate box and the characteristic strain ellipsoid develops (Figure 6–15a). In this case, the angles between the sides of the box all remain perpendicular to one another and the principal axes of the strain ellipsoid parallel the sides of the box (Figure 6–15a). This is orthorhombic strain symmetry. Now deform the unit sphere and cube by simple or general shear (Figure 6–15b); in this situation, the cube is transformed into a parallelepiped and the X- and Z-axes of the strain ellipsoid progressively rotate (the Y-axis remains in a fixed orientation). This is monoclinic strain symmetry. The most complex case involves the progressive rotation C B A D (a) Lines of no finite elongation S S S E E E E E S S E S (b) D C 1 B (c) 1 2 3 Strain ratio 4 Extension Shortening 5 Orientation (°) Stretch of line D A 0 A 180 2 C 90 B 0 1 2 3 4 Strain ratio FIGURE 6–14 Progressive deformation. (a) Strain ellipse and orientation of marker lines for progressive deformation. (b) Illustration of the fields of shortening and elongation separated by lines of no finite elongation. Note lines of no finite elongation rotate with progressive deformation. S—field of shortening. E—field of extension. (c) Plots of line length and orientation with progressive deformation. 5 Strain and Strain Measurement Z Z X X Y Y (a) Orthorhombic symmetry Z X X Z Y Y | 141 FIGURE 6–15 Progressive eformation with orthorhombic d (a), monoclinic (b), and triclinic (c) symmetry. X, Y, and Z are principal strain axes. Note that while the strain ellipsoid in all cases has the same degree of symmetry, the final shape of the original cube differs in shape and orientation. Also note that orthorhombic symmetry is characterized by three axes of unequal length that meet at 90°, monoclinic symmetry is characterized by two axes that meet at 90°, and a third that is not at 90° to the other two, and triclinic symmetry is characterized by three axes that are not at 90° angles to each other. All axes are of unequal length. (b) Monoclinic symmetry Z X X Z Y Y (c) Triclinic symmetry of all three principal strain axes producing triclinic strain symmetry (Figure 6–15c). Because strain symmetry is directly linked to progressive deformation, it is a difficult quantity to visualize or understand. Remember that the shape of all finite strain ellipsoids is characterized by orthorhombic symmetry (that is, all the principal axes are at right angles to one another). Rather, it is the progressive strain path that determines the strain symmetry. Structural geologists have only recently recognized that triclinic strain geometries occur in naturally deformed rocks, and their significance is still debated. Finite strain is the sum of all the intermediate strain steps (incremental strain). The nature of the incremental strain is referred to as the strain path; two different strain paths are illustrated in Figure 6–16, and although the strain paths are different (steady-state general shear vs. pure shear followed by simple shear), both yield the same finite strain. As we shall soon see, geologists can often quantify the finite strain, but resolving the strain path is more difficult. The very smallest possible increment of deformation is called the infinitesimal strain. Mohr Circle for Strain Just as we used a Mohr circle to describe the states of normal and shear stresses acting on a rock mass, a Mohr circle for strain can be constructed. In Mohr space, the axes are the reciprocal quadratic elongations (λ') and the modified shear strain (γ') where λ' = 1 / λ(6–13) and γ' = γ / λ.(6–14) 142 | Mechanics: How Rocks Deform FIGURE 6–16 Incremental strains (Wn) lead to finite strain. (a) Incremental general shear (Wn = 0.9) path. (b) Incremental pure shear (Wn = 0.0) followed by incremental simple shear (Wn = 1.0). Note the finite strain in both (a) and (b) are the same, but they followed a different strain path. Incremental strain 1 Rs = 1.44 Wn = 0.9 Incremental strain 2 + Rs = 1.44 Wn = 0.9 Finite strain = Rs = 2.06 Wm = 0.9 (a) Incremental strain 1 Rs = 1.37 Wn = 0.0 Incremental strain 2 + Rs = 2.16 Wn = 1.0 Finite strain = Rs = 2.06 Wm = 0.9 (b) These quantities are employed because they plot as a circle with a radius of (λ'X − λ'Z)/2 (Figure 6–17a). The values of λ' and γ' are given by the following equations  λλ'' + +λ λ''ZZ   λλ'' X − − λλ''Z  λλ'' =  X  −   cos 2φ' (6–15)     2 2 and  λλ'' − − λλ'' Z  γγ'' =  X  sin 2φ' (6–16)   2 where ϕ' is the angle between a material line and the X direction (Ramsay and Huber, 1983). Like with stress, equations 6–15 and 6–16 are the equations of circles. The original orientation of the material line (ϕ) may be found for any value of ϕ' from φ = tan−1  SX SZ tan φ'  .(6–17)   The terminology of the Mohr circle for strain is less intuitive than those for stress, and, as such, the Mohr circle for strain is less commonly used. The Mohr circle for strain, however, is a useful tool if we have knowledge of the finite strain (Figure 6–17). Consider the marker line in Figure 6–17b: what was its original orientation prior to deformation? We know the strain ratio, principal strains, and the orientation of the line (ϕ' = −14°). With this information we can plot this strain state in Mohr space (Figure 6–17a). Note the principal elongations are reciprocal values. The maximum elongation (λ'X) plots closer to the origin than the minimum elongation (λ'Z) (Figure 6–17a). From the Mohr circle (or equations 6–15 and 6–16), we can determine the elongation and shear strain for the marker line (λ' = 0.55, γ' = 0.42), and by solving e quation 6–17 we can determine the pre-deformation orientation of the marker line (−30°) (Figure 6–17c). Our example followed a coaxial strain path; if the progressive deformation had been non-coaxial, the center of the Mohr circle would plot off the λ' axis. Off-axis Mohr circles are more complex, although the kinematic vorticity number (equation 6–12) can be derived from this construction. Tensor Operations for Strain Strain is a second-rank tensor, and the state of strain can be represented and manipulated in matrix form. In matrix notation, the two-dimensional strain matrix or deformation gradient matrix is represented by four components:    Sxx  Fij =   γγ  yx  S  yy  γγxy   Sxx   .(6–18)  S yy    The first row represents stretch and shear strain along the x-axis in Cartesian space, and the second row represents shear strain and stretch along the y-axis in Cartesian space. The displacement of a point X by a deformation defined by the deformation gradient matrix Fij is simply X' = Fij X. For three-dimensional strain, the deformation gradient matrix has nine components to include stretch and strain Strain and Strain Measurement γ' 1.0 0.5 4 λ'Z 2ϕ' 0 −0.5 Pure shear λ' = 0.55 γ' = 0.42 λ'X 1 2 y 3 λ' Syy = Lf Lo Lf Lo 143 = 4 =2 2 γxy = tan(0) = 0 = 1 = 0.5 2 γyx = tan(0) = 0 2 2 0 0 0.5 ψ = 0° 0 −1.0 Sxx = | 0 2 4 x (a) (a) Deformed state ϕ' = −14 ° X SX = 1.50, λX = 2.25, λ'X = 0.44 4 SZ = 0.67, λZ = 0.44, λ'Z = 2.25 Simple shear RS = 2.25 y Z Sxx = 2 =1 2 γxy = tan(45) = 1 Syy = 2 =1 2 γyx = tan(0) = 0 2 Original state ϕ = −30 ° (b) 0 1 1 0 1 ψ = 45° 0 2 4 x (b) (c) FIGURE 6–17 Mohr circle for strain. (a) State of strain for strain ellipse illustrated in (b). (c) Undeformed state illustrating the original orientation of the marker line (magenta line). with respect to the z-axis, and it possesses a form similar to that of the stress tensor (Chapter 5). We will now explore how the deformation gradient matrix reacts in the cases of pure shear, simple shear, and general shear. In pure shear (Figure 6–18a), the value Sxx is in the direction of maximum elongation, Syy equals 1/Sxx such that area is maintained, and both off-diagonal components of the matrix are zero. In the case of simple shear in Figure 6–18b, the values of Sxx and Syy both equal 1, an off-diagonal component is non-zero, and Sxx and Syy are no longer the principal axes. The value of the off-diagonal component in this case equals γxy /Sxx = γxy. For general shear (Figure 6–18c), the value Syy equals 1/Sxx such that area is maintained, and an off-diagonal component is non-zero. In this case, the off-diagonal component equals γxy /Sxx . 4 General shear y Sxx = 4 =2 2 γxy = tan(45) = 1 Syy = 1 = 0.5 2 γyx = tan(0) = 0 2 0 2 0.5 0 0.5 ψ = 45° 0 2 4 x (c) FIGURE 6–18 Two-dimensional strain tensor for: (a) pure shear; (b) simple shear; and (c) general shear. Measuring Strain in Rocks Even a casual glance at the conglomerate in Figure 6–19 reveals the rock has been deformed, but just how much deformation did this rock undergo? What are the sectional 144 | Mechanics: How Rocks Deform FIGURE 6–19 Strongly deformed pebbles in the Neoproterozoic Bygdin conglomerate, southern Norway. The surface where the pocket knife is located is the direction of maximum elongation. The surface to the left of the pocket knife is vertical and is the direction of greatest flattening. Pocket knife is 10 cm long. (RDH photo.) strain ratios on the two exposed faces? What is the shape and magnitude of the strain ellipsoid? Did this rock undergo volume change during deformation? Did this rock follow a pure, simple, or general shear deformation path? Structural geologists endeavor to quantify the amount of deformation. This section focuses on strain markers and the techniques that enable us to quantify strain in rocks. To determine the amount of strain in a rock mass, we need a strain marker, a feature in which the original shape can be quantitatively compared to its deformed shape. Ideal strain markers should be common, with an readily identifiable original shape, and they should have similar mechanical properties to the surrounding rock. Passive strain markers are materials within a rock mass that have no mechanical contrast with the surrounding rock, thus faithfully recording the finite strain. In contrast, active strain markers are mechanically different from the surrounding materials. Consider quartzite pebbles in a shaly matrix: as the rock is strained, the weak matrix will deform much more than the pebbles. If we measure strain in the pebbles, our values will underestimate the strain in the matrix and the total strain in the rock mass. Active strain markers are more widespread than passive markers, but, in spite of these limitations, useful information about strain can be gleaned from these markers. Common strain markers include reduction spots, pebbles and other detrital clasts, ooids and pisolites, fossils, burrows, vesicles, pillows, columnar joints, and xenoliths. Reduction spots are small, mostly spherical features in fine-grained oxidized sediments (Figure 6–20). Chemically reducing conditions in the sediment can be produced around materials or grains with a different composition (such as disseminated sulfides or organic matter), causing the surrounding sediment to be chemically reduced to a greenish color from its oxidized reddish-purple-brown color. In essence, the only difference between a reduction spot and the rest of the sediment is its color, and thus it should behave as a passive marker. Unfortunately, not all reduction spots are originally spherical, and the timing of their formation relative to compaction and tectonic deformation may not always be evident. Pebbles and other detrital clasts are among the most frequently used strain markers. Originally, most clasts are ellipsoidal in shape such that, upon first consideration, we might consider them to be of little value in recording strain. As we shall see, however, by using a population of pebbles or detrital clasts, finite strain can be commonly measured. Oöids and pisolites, because of their nearly spherical original shape, are excellent strain markers (Figure 6–21). Fossils can make good strain markers. We commonly know the original shape, although not typically the original size, of organisms from specimens in undeformed samples. Most fossil groups, such as trilobites, brachiopods, graptolites, and echinoderms, possess a symmetry that will be distorted during deformation (Figure 6–22). Trace fossils such as Skolithos (nearly cylindrical burrows originally oriented normal to the sea bottom in sandy shallow marine environments) can be useful for determining both sectional strain in the bedding plane and shear strain parallel to bedding (Figure 6–23). Because of their originally circular cross sectional shape, Skolithos form visually distinctive strain markers, but frequently are of limited value since they are two-dimensional strain markers. Nevertheless, classic studies of strain have been made in the Pipe Rock Sandstone in Scotland (e.g., Coward and Kim, 1981). Strain and Strain Measurement | 145 Reduction spot (a) FIGURE 6–20 (a) Reduction spots in Metawee Slate from near utland, Vermont, viewed oblique to the cleavage plane. Length R of specimen is 29 cm. (RDH photo.) (b) Relationship between reduction spots and slaty cleavage (also see Figure 2–19). FIGURE 6–21 Deformed oöids in Cambrian onococheague Limestone, Valley and Ridge C province, near Hagerstown, Maryland. (Charles M. Onasch, Bowling Green State University.) FIGURE 6–22 Deformed trilobite (Angelina) from Ordovician slate, north Wales. Simple shear deformation produced top-to-the right asymmetry. (W. Stuart McKerrow, Oxford University.) Reduction spot Cleavage surface (b) 146 | Mechanics: How Rocks Deform (a) (b) FIGURE 6–23 Deformed Skolithos. (a) Plan view (almost parallel to the axes of Skolithos, along a bedding surface) with nearly u niformly oriented tectonically flattened elliptical tubes (Rs = 1.5 to 1.7) in Cambrian Antietam sandstone, Virginia Blue Ridge. (CMB photo.) (b) Vertical section through a bed (subhorizontal) with deformed and curving Skolithos, indicating greater shear strain toward the top of the bed. (Michael P. Coward, Imperial College of Science and Technology.) Vesicles (gas bubbles) in volcanic rocks may be used as finite strain indicators—provided they were not strongly deformed during eruption. Vesicles are mechanically different from the surrounding rock, but mineral-filled vesicles (amygdules) may also serve as reasonable strain markers (Figure 6–24). Pillows commonly develop in submarine lava flows, and these approximately equidimensional masses with downward-pointing bases may be used to determine finite strain (Figure 6–25). In subaerial lava flows, columnar joints form during contraction as the flow solidifies and cools; these columns typically develop an equant hexagonal shape in cross section (Chapter 9). When deformed, the equant hexagons are transformed and, as such, serve as a two-dimensional strain marker (Figure 6–26). The usefulness of both pillows and columnar joints is limited, however, because their original shapes are not always uniform. (a) (b) Strain Measurement Techniques Linear Markers Earlier in the chapter we discussed measures of linear strain. If a sufficient number of linear strain markers in different orientations are present, they can be used to FIGURE 6–24 (a) Deformed amygdules filled with quartz and epidote in Neoproterozoic Catoctin greenstone, Virginia Blue Ridge. (CMB photo.) (b) Deformed amygdules filled with calcite in Neoproterozoic greenstone, Maryland Piedmont. (Charles M. Onasch, Bowling Green State University.) Strain and Strain Measurement 147 FIGURE 6–25 (a) Deformed pillow from the Grenville province, Québec. Pillow was shortened from bottom to top. Note parts of other pillows around the pillow in the center. The tops of the pillows are to the right. The bands enclosing the pillows are hyaloclastite. (b) Hypothetical pillows shortened by 60 percent pure shear (flattening) strain. (c) Shortening of the same pillows as in (b) by dextral simple shear to a ψ of 60°. Shear strain (γ) is thus 1.73. (d) A more complex, realistic(?) alternative is to have the pillows oriented at an angle other than 90° to the deformation, here 15°. S0 is bedding or primary layering. In this scenario, a dextral simple shear strain results in a shortening of only 40 percent. (Photo and diagrams courtesy of Dr. Réal Daigneault, Québec Geological Survey and Université du Québec à Chicoutimi, Canada.) (a) 60% A Primary layering S0 S0 X (b) ψ = 60° A' A S0 S0 X (c) A' A S0 (d) | 15° 40% S0 X 148 | Mechanics: How Rocks Deform that have been elongated; if grains had instead been shortened and buckled, they could be utilized in this analysis as well. Two-dimensional strain estimates have been made using both boudinaged and folded dikes, veins, feldspars, and rutile needles. It is important to remember that competent (strong) materials (such as tourmaline crystals or belemnites) are likely much stronger than the matrix in which they are embedded and therefore were strained less than the matrix. (a) (b) Initially Elliptical Markers FIGURE 6–26 (a) Schematic view of undeformed hexagonal Rf /ϕ METHOD columnar joints viewed parallel to long axis of the column. (b) Columns deformed by simple shear, indicated by arrows. As noted earlier, initially elliptical markers are common in rocks but present challenges for determining finite strain. Consider the four clasts in Figure 6–28; in the undeformed state, each clast has its own original ellipticity (Ri) and orientation (ϕ). When a strain ratio of 2 (R s), with its maximum principal elongation oriented horizontally (ϕ' = 90°) is applied, the clasts are transformed to a final ellipticity (Rf) and orientation (ϕ'). The deformation increases the ellipticity of some clasts, but one clast becomes less elliptical (Figure 6–28). The final state e estimate the two-dimensional strain. Consider boudinaged tourmaline fragments in a foliated quartzite (Figure 6–27). When the linear strain (stretch) and orientation of each boudinaged tourmaline is plotted, a pattern emerges (Figure 6–27c), and an ellipse can be fitted to the data (Figure 6–27d). The ellipse is defined only by grains 1.0 lia tio nt rac S 63 S = 1. Fo 1.0 S = 1.63 ϕ = 48° (a) 0 1.0 ϕ = 48° 1.0 Rs = 3.0 ϕ = 55° S (b) (c) (d) FIGURE 6–27 (a) Boudinaged tourmaline grains in Cambrian Setters Quartzite, Maryland Piedmont. (CMB photo.) (b) Schematic view of boudinaged tourmaline grains (thick black lines) in foliated quartzite. (c) Plot of stretch versus orientation (ϕ) for tourmaline grains in (b). (d) Ellipse fit to those data with an Rs = 3.0 and ϕ = 55°. FIGURE 6–28 Population of initially elliptical clasts (a) that undergoes a strain of 2.0 resulting in elliptical final shapes (b). Note some grains become more elliptical, whereas one grain becomes less elliptical. Undeformed state Ri = 1.2 ϕ = −45° Ri = 2.0 ϕ = 10° + (a) Ri = 1.5 ϕ = 30° Deformed state Rf = 2.06 ϕ = −82° R = 2.0 S ϕ' = 90° Rf = 1.28 ϕ = 46° = Rf = 1.85 ϕ = 72° Ri = 1.7 ϕ = −70° (b) Rf = 3.18 ϕ = −82° Strain and Strain Measurement R f max R f max RS = where Rf max and Rf min are the maximum and minimum aspect ratios of the clast population, respectively. The second and opposite case occurs when the strain ratio is greater than the maximum original ellipticity (Rs > Ri) and the population of ellipses forms a symmetric −90° ϕ 0° Ri = 2.0 Rs = 1.0 −90° 1 2 3 2 3 (a) ϕ' 4 5 6 4 5 6 4 5 6 Ri −90° RS ϕ' 0° Rs = 1.5 −90° (b) 1 Rf −90° ϕ' RS F ϕ' 0° Rs = 3.0 −90° (c) 1 2 R f max ⋅ R f min .(6–20) This method was first introduced by Ramsay (1967) and further developed by later workers. Lisle (1977, 1985) devised a series of Θ curves for different values of Rs that can be used with plots of Rf and ϕ' values, but this technique is tedious, time consuming, and the curve-fitting can be subjective. De Paor (1988) developed a more rapid technique for Rf /ϕ analysis by combining the complete set of Θ curves for all Rs values onto a single diagram known as the hyperbolic net (Figure 6–31a) with two hemispheres R and ε (natural strain). We will use the upper or R hemisphere that is divided into a set of hyperbolae that represent the Θ curves for Rs values of 1 to 10. The Rf and ϕ' of individual clasts are plotted as points on the hyperbolic net, where the ,(6–19) ϕ 149 closed curve. The range of ϕ' values is the fluctuation (F) (Figure 6–29c) and, with increasing strain, the fluctuation decreases so the curves become more closed and onion-shaped (Figure 6–30). In this case, the strain ratio is given by of an individual clast is a function of its original ellipticity and orientation as well as the strain it underwent. Our ultimate goal is to measure the strain (R s) that the rock underwent, and, to accomplish this, we use a population of clasts. Consider a population of clasts all having an original ellipticity of 2 in a range of different orientations (Figure 6–29a). If the strain ratio is less than the maximum original ellipticity (Ri > Rs), the population of ellipses forms a symmetric curve with a range of ϕ' from 90° to −90° (Figure 6–29b). The strain ratio is given by the following relationship RS = | 3 Rf FIGURE 6–29 Relationship between initial ellipticity (Ri) and orientation (ϕ), final orientation (ϕ'), and final ellipticity (Rf) in an array of markers. (a) Undeformed (Rs = 1) markers with an initial ellipticity of 2. (b and c) Deformed state with strain ratios of 1.5 and 3.0, respectively. Dots represent the aspect ratio (Ri or Rf) and orientation of individual markers. F is the fluctuation. (Modified from Ramsay and Huber, 1983). 150 −90° 0° | Mechanics: How Rocks Deform 0.0 1.3 ln Rf 1.0 1.5 2.0 2.0 3.0 Rs = 1.5 3.0 4.0 Ri −90° 0.0 ln Rf 1.0 3.0 2.0 Rs = 4.0 4.0 3.0 ϕ' 0° 2.0 1.5 50% data 90° 90° −90° −90° Rs = 2.0 3.0 4.0 2.0 1.5 0° 4.0 ϕ' 0° 90° 90° −90° −90° Rs = 3.0 4.0 3.0 2.0 1.5 0° 90° 1.0 Rs = 5.0 5.0 10.0 20.0 30.0 90° 2.0 1.5 Rs = 6.0 4.0 ϕ' 0° 1.5 2.0 2.5 3.0 3.0 1.0 3.0 2.0 1.5 1.5 2.0 2.5 3.0 5.0 Rf (a) min. −90° 10.0 20.0 Rf ln Rf max. min. −90° A A ϕ' 0° ϕ' 0° 90° 90° ln Rf max. F (b) FIGURE 6–30 Rf /ϕ' plots showing different relationships between Ri and Rs and the resulting curves. (a) Rf /ϕ' reference curves for different values of initial ellipticity and the strain ellipse. (b) Features of the Rf /ϕ' plots used for calculating strain. Note the symmetry of the fluctuation (F) about the orientation of the strain ellipse (A). In the left diagram Ri > Rs; in the right, Rs > Ri. (From Ramsay and Huber, 1983). 30.0 Strain and Strain Measurement | 151 R ϕ' = 0 10 − ϕ' 5 + ϕ' 4 3 2 Rf = 2.7 ϕ' = 15° (b) Rf = 1.4 ϕ' = −31° ε (a) ϕs = 10° − ϕ' + ϕ' Rs = 1.6 (d) (c) FIGURE 6–31 (a) Hyperbolic net: R is aspect ratio and ε is natural strain. (From De Paor, 1988). (b) Hyperbola for various strain ratios with the Rf and ϕ' of two clasts from (c) plotted. (c) Population of deformed clasts. (d) Data points from (c) with ϕs (10°) and hyperbola for a Rs of 1.6 bisecting the data. center of the net equals an Rf of 1 (Figure 6–31b). In practice, a population of clasts is plotted on the hyperbolic net, and the geometric mean of that population obtained by bisecting the data with a ϕs line and the appropriate hyperbola that represents the strain ratio (Figure 6–31d). Ideally, the plot should have bilateral symmetry. The hyperbolic net is a more convenient and simpler method to use than the standard Rf /ϕ technique. CENTER-TO-CENTER METHOD When a material is deformed, the distance and angle between the centers of objects changes in a predictable manner that can be used to determine the orientation of the strain ellipse (Figure 6–32). Prior to deformation, the distance between centers should be uniform, while after deformation the distance between centers becomes nonuniform. Fry (1979) devised a graphical method in which the centers of grains are marked and then an overlay is moved to all grain centers (Figure 6–33). The procedure is repeated until all the grains have been overlain and plotted. The result should be a vacant area surrounded by a cloud of dots, revealing the shape of the sectional strain ellipse, if the particles were uniformly distributed and homogeneously deformed (Figure 6–33). Dividing the center-to-center distances between grains by the sum of the average radii eliminates variations due to particle size and sorting, producing a better-defined vacant field. 152 | Mechanics: How Rocks Deform FIGURE 6–32 In the undeformed state, the distance between the centers of adjacent grains is similar, whereas after deformation by flattening, the distance between grain centers increases (AB) in some directions and decreases (AC) in others. C C B A A B Initial position of reference point A A (a) (b) B Reference point moved to second position (c) FIGURE 6–33 Stepwise plotting of a Fry diagram. The reference point is moved through successive positions (a and b) and the centers of the grains (on underlay) until a vacant area appears (c). This is known as the normalized Fry method (Erslev, 1988). The manual plotting of points is tedious and time consuming, but computer applications employing this technique have greatly facilitated the use of this procedure. DISCUSSION Which of the two methods is better for determining the strain from a population of originally elliptical clasts? The best method depends on the situation. For the center-to-center method to effectively record the finite strain, grains must originally be anticlustered with a uniform distribution. Well-sorted, equigranular grain-supported sedimentary rocks are ideal for centerto-center strain measurements, whereas poorly sorted, matrix-supported sediments with a heterogeneous grain size are better suited for the Rf /ϕ methods, because it is the shape and orientation of clasts that is most important, not their position relative to one another. The specific deformation mechanisms (Chapter 7) by which a rock changes its shape also play a role; for instance, pressure solution commonly removes soluble minerals from high-stress grain boundaries, producing truncated grain boundaries perpendicular to the direction of maximum shortening. For a pressure-solution dominated deformation, the center-to-center method should more faithfully record the overall strain than the Rf /ϕ method. Deformed rocks containing elliptical particles are very common, but how many grains need to be measured or digitized to accurately characterize the state of strain in a rock? Consider a grain-supported sandstone with an average grain diameter of 1 mm. In a standard petrographic thin section (4 × 2.5 cm) there could be 1000 grains, but do we need to measure every grain? For center-to-center analysis, 50 to 100 grains commonly yield a sufficiently dense cloud of points to accurately define the vacancy ellipse. The hyperbolic net yields an R s and ϕs value with as few as 16 grains, whereas traditional 153 | Strain and Strain Measurement Rf /ϕ methods require 50 or more grains to accurately estimate the strain. In the past decade, a number of statistical treatments for resampling data (bootstrapping) have been employed to better evaluate the uncertainty and error associated with strain analyses. fossils, the better defined the resulting strain ellipse will be. Other techniques for measuring strain in bilaterally symmetric fossils involve the Mohr circle for strain and orthographic projection of fossil shapes onto a stereonet. BILATERALLY SYMMETRIC FOSSILS From Two to Three Dimensions Wellman (1962) introduced a simple geometric method for determining the strain ellipse using deformed fossils. The method is based on the angular distortion of reference lines originally aligned at 90° to one another. Consider the distorted brachiopods in Figure 6–34, with an arbitrary reference line AB drawn. Lines are also drawn along the hinges and symmetry lines of each fossil. A pair of lines is then drawn for each fossil parallel to both the hinge line and symmetry line that pass through points A and B. If there is no strain in the plane containing the fossils, the result is a rectangle. Strained brachiopods yield a parallelogram. This procedure is repeated, creating a parallelogram for each fossil, and the corners of the parallelograms outline an ellipse (Figure 6–34). The greater the number of individual 1 Measuring strain in two dimensions has its complications, but accurate estimates of sectional strain are achievable. As noted earlier in this chapter, finite strain is commonly three dimensional, but how can strain be measured in three dimensions? If sectional strains are measured on any two of the principal planes (XY, YZ, XZ), the magnitude and shape of the strain ellipsoid can easily be determined. In many geological settings, the foliation or cleavage plane is the XY plane and many lineations develop parallel to the X-axis (Figure 6–35a; Chapters 18 and 19). At low finite strains, however, rocks may not possess an identifiable 1 2 2 7 2 3 3 3 6 A B 4 5 4 4 5 1 8 A B 5 5 4 6 3 6 6 1 8 2 7 (c) 7 (a) 7 8 8 (b) FIGURE 6–34 Determination of strain in fossils, using Wellman’s method. Note that neither of the axes of the best-fit ellipse in (c) are parallel to the arbitrarily chosen line AB in (b). The ratio of the ellipse records a strain of 1.3. 154 | Mechanics: How Rocks Deform Foliation r; ula dic Z) en (X rp lel pe al n- ar tio -p lia tion Fo nea li (a) (XY) L in e a ti o n (X) lar; erpendicu Foliation-p ndicular (YZ) erpe lineation-p (b) FIGURE 6–35 (a) Schematic of deformed rock with well-developed foliation and lineation. Foliation corresponds to the XY plane. The aspect ratio of the deformed pebbles (dark gray ellipses) is greatest on the foliation-perpendicular/lineation-parallel plane (XZ). Threedimensional strain could be determined from sectional measurements on any two principal planes. (b) Schematic of weakly deformed rock with elliptical clasts; it is not clear if any of the faces are principal planes. Determination of three-dimensional strain requires sectional strain measures from all three faces. cleavage or lineation. In situations with no prior knowledge about the orientation of the principal planes, sectional strains must be determined in at least three different orientations (Figure 6–35b) and converted to three dimensions using tedious tensor operations. Fortunately, there are modern computer applications that make quick work of the process. A further caution comes from the calculation of sectional and three-dimensional strains using ratios, as the ratios, in and of themselves, do not uniquely define the amount of elongation or shortening. Consider the sectional strain estimated from a deformed quartz sandstone in the Virginia Blue Ridge (Figure 6–36). The sample is foliated with a distinct lineation defined by elongate quartz grains; Fry analysis of quartz grain centers from micrographs yield sectional strain ratios of 2.8 on the foliationperpendicular/lineation-parallel face (assumed to be XZ plane) and 1.4 in the foliation plane (assumed to be XY plane) (Figure 6–36a). Based on these ratios, the sample plots in the field of apparent flattening in the Flinn diagram (k = 0.22, d = 1.84) (Figure 6–36b). If we assume there has been no elongation or shortening parallel to the Y-axis (SY = 1), stretch both in the X and Z directions can be calculated (SX = 1.4, SZ = 0.5), implying the sandstone was shortened by ~50 percent normal to foliation. As noted earlier in the chapter, with no volume change, the product of the principal stretches equals 1. In this case, however, the product equals 0.7 or an apparent volume loss of 30 percent (Δ = −0.3) (Figure 6–36c). What if there was elongation or shortening parallel to the Y-axis? The principal stretches can be recalculated (although the ratios of 2.8 and 1.4 remain the same) such that there is no apparent volume change. For this case, SZ = 0.6 (40 percent shortening) and there is ~20 percent elongation parallel to the Y-axis. Without other information, either model (plane strain with volume loss or flattening strain) could be correct; independent measures of stretch (not simply ratios) or volume change are needed. The Utility of Strain Analysis What can we learn from strain analysis? Two- and three- dimensional strain data, when plotted in the correct orientation and magnitude on geologic maps or cross sections, readily portray the nature of strain across an area or even an orogenic belt. In order to properly restore or “retrodeform” materials to their original orientation and position they must be “unstrained.” Although geologists first measured strain in rocks during the mid-nineteenth century, it was pioneering strain studies of Cloos (1947, 1971) across the South Mountain fold in the central A ppalachians that brought strain analysis to the fore. Cloos analyzed the shape of thousands of distorted oöids and was able to quantitatively measure the amount of shortening and elongation (Figure 6–37) in the region. He recognized that the principal strain axes are geometrically related to cleavage and lineation in the rocks and that the deformation intensity decreases toward the foreland (northwest) (Figure 6–37). Ramsay and Wood (1973) presented strain data for nearly 1,000 slates from northwestern Europe and the Appalachians (Figure 6–38). These strains generally record maximum principal elongations that range from 0 to Strain and Strain Measurement Foliation parallel XY section 3.0 155 Field of apparent constriction (k > 1) 1) Foliation perpendicular, lineation parallel XZ section | X ne st ra i n (k = 2.5 Field of apparent flattening (k < 1) Ap p ar en tp la 2.0 Y 1.5 X k = 0.22 d = 1.84 X Z Rs = 2.8 Y 1 Rs = 1.4 (a) 1 1.5 2.5 3.0 Y Z (b) (c) 2.0 Assume no elongation or shortening parallel to the Y-axis Allow SY ≠ 1.0 SX = 1.4 SX = 1.67 SY = 1.0 SY = 1.19 SZ = 0.5 SZ = 0.6 SX • SY • SZ = 0.7 SX • SY • SZ = 1.0 ∆ = −0.3 ∆=0 FIGURE 6–36 (a) Photomicrographs of deformed quartz sandstone from the Virginia Blue Ridge. Ellipses illustrate the XZ and XY strain ratios respectively, as determined from Fry analysis of quartz grain centers. Field of view ~2 × 4 mm, cross-polarized light with gypsum plate. (b) Flinn diagram with sample plotted. (c) Derived ratios of stretch parallel to X, Y, and Z and apparent volume change (Δ). If Y is assumed to be 1, there is an apparent volume loss of 30 percent; with no volume loss there is ~20 percent elongation parallel to Y. 200 percent and maximum principal shortenings of 20 to 80 percent. Remarkably, all of these strain ellipsoids are oblate and plot in the field of apparent flattening. Ramsay and Wood also considered the geometric effect of volume change during deformation. Using the principal natural strains (ε), dilation (Δ) can be expressed as εX + εY + εZ = ln(1 + Δ).(6–21) Strain ellipsoids that represent true constriction (εY < 0, SY < 1) are separated from true flattening (εY > 0, SY > 1) by plane strain ellipsoids (εY = 0, SY = 1) that are defined on a logarithmic Flinn diagram (Figure 6–38) by ln(SX /SY) = ln(SY /SZ) + ln(1 + Δ),(6–22) a straight line with a slope of 1. If volume change occurs, the line of plane strain maintains its slope but is shifted either upward for a volume gain (+Δ) or downward for a volume loss (−Δ). The plane strain line for a volume loss of 50 percent (Δ = −0.5) roughly bisects the Ramsay and Graham (1970) data set for slates. Did these rocks undergo significant volume loss during deformation, or are true flattening strains common in orogenic belts? Ramsay and Huber (1983) plotted XZ strain ratios along a down-plunge profile through a stacked set of five fold/ thrust nappes in the Swiss Alps (Figure 6–39). Strains are highest in the structurally lowest nappes and along overturned limbs near the basal thrusts. X-axes tend to parallel the thrust near the base of the nappe, whereas higher up in the nappe, X-axes plunge more steeply, an observation consistent with differential non-coaxial (simple or general) shear through the nappe (Figure 6–39). The larger strain at deeper crustal levels is consistent with the observation that material strength decreases as temperature increases. Bailey (2003) reported three-dimensional strains from a deformed granitic pluton in the Virginia Piedmont. These granitic rocks were deformed at greenschist to amphibolite facies conditions during the late Paleozoic Alleghanian orogeny. Strain ratios vary across the pluton 156 | Mechanics: How Rocks Deform 78° W 77°30' W 77° W 76°30' W Harrisburg ale Su Carlisle sq u sh 40° N 40° N York R insb I urg McConnellsburg PA T Mar t Gettysburg G Hagerstown Westminster 39°30' N iv er R I D R ac Clear Spring E MD Potom Boonsboro B L U E 78° W 39°30' N WV Frederick Baltimore MD 40 VA 77°30' W 0% (b) 50% NW 2,000 ding n Bed sectio ter Y tio n( X X) Cl X ea pla vag ne e Clea vea ge Z ea meters 1,000 In 100% SE Monument Knob SL −1,000 −2,000 (c) 77° W Boonsboro (a) Lin Rive r A Chambersburg na n S eh a S Shippensburg C I (d) 0 1.5× Vertical exaggeration 2 4 kilometers FIGURE 6–37 (a) Generalized geologic map of the South Mountain region, Maryland and Pennsylvania. Magenta arrows denote orientation of the maximum oöid axes at a given location; most samples are orientated normal to the South Mountain trend. Heavy black line near Boonsboro indicates location of cross section in (d). (b) Oöids at varying degrees of elongation. (c) Relationship between cleavage, lineation, and principal strain axes. (d) NW to SE cross section with strain ellipses (orange) illustrated. Strain decreases toward the northwest. [(a)–(d) From E. Cloos, 1947, Oölite deformation in the South Mountain fold, Maryland: Geological Society of America Bulletin, v. 58, p. 843–918]. 0) Strain and Strain Measurement = (∆ in st ra e ) = Pl an ln (SX /SY) 1.0 0 (∆ 0 1.0 ln (SY /SZ) Concluding Thoughts 2.0 FIGURE 6–38 Logarithmic Flinn diagram (modified by Ramsay) illustrating the strain state of nearly 1,000 slates from northwestern Europe and the Appalachians. All samples plot in the field of apparent flattening. (Modified from Ramsay, J. G., and Wood, D. S., 1973, The geometric effects of volume change during deformation processes: Tectonophysics, v. 16, p. 263–277.) (Figure 6–40a and b); the maximum principal elongation (X) direction consistently plunges gently northeast (Figure 6–40c), whereas the maximum shortening (Z) direction is highly variable and plots along a great circle distribution on a stereonet (Figure 6–40c). The three- dimensional shape of the strain ellipsoid is quite variable, ranging from strong constrictional strains (ν < −0.5) to UH 157 strong flattening strains (ν > 0.5) (Figure 6–40d). These rocks experienced multiple deformation events, and the nature of the cumulative strain produced regions of overall constriction and flattening. An important conclusion drawn from these data is that, although these rocks were shortened in a northwest-southeast direction, they were also elongated northeast-southwest, parallel to the overall trend of the Appalachians. Modern strain studies reveal that orogen-parallel elongation is common in the deeper parts of contractional tectonic belts (mountain chains). .5 −0 | Understanding two- and three-dimensional strain is critical to the structural geologist. Although we’ve introduced many terms and numerous equations and discussed the difficulties of measuring strain in rocks, the concepts discussed in this chapter will be relevant throughout the rest of the book. As we consider brittle fractures, refolded folds, and foliations later in the text, be mindful of what those structures record in terms of strain at scales from the thin section up to mountain belts. Over the last two chapters, we have developed concepts about stress and strain with only passing mention that with sufficient stress earth materials become strained. In the next chapter we explore, in more depth, the relation of stress to strain in materials and consider the deformation mechanisms by which rocks become strained. UH Wildhorn nappe Diableretes nappe UH NW SE UH 0 Ultra-Helvetic nappes thrust contact top of Cretaceous top of Jurassic unit circle strain ellipse (XZ) 1 2 Morcles nappe Aiguilles Rouges massif kilometers FIGURE 6–39 Down-plunge cross-sectional view of nappes (thrust sheets) in the Swiss Alps near Valais with XZ strain ellipses plotted. Note that the strain increases near the base of each nappe. (From Ramsay and Huber, 1983.) | Mechanics: How Rocks Deform 1.7 = XZ 22 = XY .5 1 1.6 XZ = .1 =2 XY 1.2 1.2 2 1. 8 2.0 0 11 3.2 3.0 C' Ocv 3 kilometers (b) A' 26 18 1.5 2.6 = .8 3.3 2.0 37 2.4 = XZ = Ocv .9 =2 31 3 2. = =1 Aspect ratio of fabric ellipse with direction and plunge of X-axis 36 .2 =2 N 26 .7 34 XZ XZ XZ 18 = 3 2. 20 B' 0 5 kilometers 0.5 XZ XZ XZ 0 3. XZ = XZ = 10 12 XY C = XZ 30 = 32 20 3.2 2.4 Ocg C' 31 XZ 2.7 2.9 Ocv 2.7 XZ 27 4 2. 34 6 = XY 2.1 3. Ocg 16 17 =2 1.5 Ocg C 14 30 8 1. = XY XZ .6 34 6 1. .7 22 20 B XY = B' 1.7 = 37° 45' W 13 6 2. 2. 2 1.6 25 1. XY 1. = 3 = = 10 .7 =1 = XY 1.4 = XZ 21 XZ Oa XZ Oa XZ = 2 13 16 B XY 1.1 = .2 XY = 1.2 XZ 5 XZ 1.2 = 32 18 6 1. = 1.2 1.0 Ocg Oa 28 XZ= 2 XZ = 1 .9 7 1.3 XZ 1. = 3 XY = 1.4 X 1. Z = 5 10 1.7 6 2. 18 A N 11 A' Ocv Oa 1 .1 XY 1.2 = 17 VA Ocv A 1.9 Piedmont XZ 158 (a) 0 N Z X Z Z Z ZZ Z ZZ Z Z Z Z Z Z Z Z Z X Z X (c) Z ZZ X X Z Z sample (n=38) Z ZZ Z 0 XX X X XX XX X XXXX X XXXX X X XX XX X XX 0 X Z Z ZZ −0.5 X Z Z X = 38, Z = 38 0.5 Z Z Z Z 0 0 5 kilometers −0.5 ν-value contour (interval 0.5) S-tectonite SL-tectonite LS-tectonite L-tectonite (d) FIGURE 6–40 (a) Simplified geologic map of the Ordovician Columbia pluton, Virginia Piedmont, with strain ellipses. Note long axes of ellipses define a trend oriented northeast-southwest. Oa—Arvonia Fm. Ocg—Columbia granitoid. Ocv—Chopawamsic Fm. (b) Cross sections A–A', B–B', and C–C' with strain ellipses. (c) Equal-area stereographic projection of the orientation of the maximum elongation direction (X) and maximum shortening direction (Z) for 38 samples. Note the X-axes form a cluster plunging gently northeast (green dot is mean orientation), whereas the Z-axes are spread along a great circle (dashed line). (d) Fabric shape map of strain ellipsoids contoured based on Lode’s parameter (ν), illustrating dramatic changes in ellipsoid shape across the pluton. A tectonite is a penetratively deformed (foliated or lineated) rock (see Chapter 21). (From Bailey, 2003.) Strain and Strain Measurement ESSAY 5 10 15 Inner Piedmont (Cat Square terrane) 20 81° 30' 35° 15' kilometers .m o N . NC SC tu Clover pluton su D nt mo York pluton 35° Ce ntra l CP S d Pie FIGURE 6E2–1 Simplified geologic map of the region including the study area along the North Carolina–South Carolina border (compiled from numerous sources). D—Draytonvlle metaconglomerate localities studied (in red). CPS—Central Piedmont suture. S. Z.— shear zone. This segment of the Central Piedmont suture is both a thrust and a dextral strike-slip fault. 81° 15' 35° 15' re qz therefore traditional Rf /ϕ and center-to-center techniques cannot be employed to estimate the finite strain. The ratios of the long to intermediate axes versus the intermediate to short axes of individual pebbles can be plotted on a diagram akin to a Flinn diagram, the difference being that each data point is a clast (and its aspect ratios) rather than three- dimensional strain (Figure 6E2–3). The pebbles display a variety of shapes that range from prolate to oblate, although the majority of the pebbles are prolate with a mean value of 2.1 for the long/intermediate axes and 1.7 for the intermediate/ short axes. The mean value may approximate the finite strain for the pebbles, assuming the original clast population was nearly spherical, as field data suggest, and not highly elliptical with a strong preferred orientation. If the mean values of the aspect ratios are treated as the X/Y and Y/Z axes of the finite strain ellipsoid, the k-value equals 3.2 indicating an apparent constrictional strain in the Draytonville metaconglomerate. It is, however, worthwhile to consider both the assumptions and sources of error that are inherent in this method of strain analysis. Kings Mountain belt ite on nz .Z .S ill e v k y r C r gs Ch e Kin . .Z n. S Mt s g Kin NC SC 81° 45' 35° 159 Finite Strain from Deformed Pebbles As part of a senior research project at Clemson University, Baylus K. Morgan measured deformed pebbles eroded from the Draytonville metaconglomerate in the Kings Mountain belt in the southern Appalachian Piedmont of South Carolina (Figure 6E2–1). The metaconglomerate consists of recrystallized vein quartz pebbles (up to 16 cm long) in a matrix of predominantly recrystallized quartz (Figure 6E2–2a). Long axes of pebbles measured from bedrock exposures cluster about N 55° E with a 15° plunge (Figure 6E2–2b), and are approximately parallel to the axes of upright folds in a major syncline (Figure 6E2–1). Morgan collected more than 100 intact pebbles that had been eroded from weathered outcrops of the Draytonville metaconglomerate, measured the major axes of individual clasts with a caliper, and then determined the volume of each pebble using an immersion-displacement technique. Based on the pebble volume, the diameter of the undeformed pebble can be back-calculated, assuming the pebble was originally spherical. The orientation of the pebbles cannot be determined because they were eroded from the rock; 0 | Carolina exotic superterrane Bald Rock pluton Lowrys plutonic complex 34° 45' 81° 45' 81° 30' 81° 15' 34° 45' 160 ESSAY | Mechanics: How Rocks Deform continued 0 (a) 5 centimeters N FIGURE 6E2–2 (a) Representative pebbles measured during a senior research project. Most are composed of vein quartz. Planar surfaces on pebbles are joints, which introduce small errors into measurement of pebble dimensions and estimates of strain. (RDH photo.) (b) Orientations of the long axes of 143 pebbles, measured in exposures of Draytonville metaconglomerate in the field, plotted on a lower hemisphere, equal-area net. + (b) Strain and Strain Measurement | 161 te /S h or t 3.5 /In te rm ng 2.5 Lo Long axis Intermediate axis ed ia te = In te rm ed ia 3 2 1.5 (n = 117) 1 1 1.5 2 2.5 3 3.5 Intermediate axis Short axis FIGURE 6E2–3 Plot of ratios of long to intermediate vs. intermediate to short axes of 117 pebbles from the Draytonville metaconglomerate. The large diamond (red) is the average value of all measurements, and the dashed lines through it represent the possible error range (standard deviation). Chapter Highlights • Strain describes changes in shape or distortion of a rock mass. • The strain ellipse in two dimensions, and strain ellipsoid in three dimensions, is a graphical representation of the stretch in all orientations of a deformed material, and is an important concept in structural geology. • In homogeneous deformation, material is both shortened and elongated, and the principal strain axes are normal to one another. • Three-dimensional strain can vary between constrictional strain (elongation in one direction, and shortening in two directions) and flattening strain (elongation in two directions, and shortening in one direction). • Different deformation paths, such as simple, general, or pure shear, cause material to flow in different ways during deformation. 162 | Mechanics: How Rocks Deform • Strain markers, such as reduction spots, ellipsoidal clasts, and distorted fossils, can be used to estimate strain in one, two, and three dimensions. • Strain analysis is useful because the amount of shortening and elongation of strain markers in a rock mass or region can be quantified. Questions 1. What is the value of having so many different measures of linear strain? 2. The College of William & Mary recently unveiled a new logo. Unfortunately, not all of the geology students were happy with the logo so they took matters into their own hands and homogeneously deformed (improved!) the logo: Ao New Logo Bo “Improved” Logo Co Af Do −90° 0° 90° Cf Bf Df a. Determine the linear strain (stretch) between points AC, AD, and BC. b. What is the angular shear and shear strain experienced by the line connecting CD? c. What is the approximate shape (Rs) and orientation (in degrees) of the X-axis of the strain ellipse? d. Estimate the kinematic vorticity number of the deformation. e. Estimate Δ for the deformation. f. What type of strain did the logo undergo? 3. Following is an exposure of Tallulah Falls Quartzite in northeastern Georgia intruded by a thin pegmatite dike. The dike, however, was displaced along successive bedding surfaces, so that it does not line up the way it was originally emplaced. Calculate the amount of shear strain involved in displacement of the dike. 4. Why are some strain markers passive and others active? 5. Use the aspect ratio of the markers in Figure 6–35a to calculate the values for k, ν, and d. What is the shape of the finite strain ellipsoid? 6. What geologic structures could be used to determine whether a deformation had orthorhombic, monoclinic, or triclinic symmetry? 7. We frequently see rippled asphalt pavement where vehicles stop at traffic lights, like the following example (both sides of the lane). Think about what happens when a vehicle, particularly a heavily loaded truck, brakes to stop for the red light. How does the strain accumulate? Of the deformation processes we have discussed in this chapter, which one would best explain this phenomenon? (Photo courtesy of Morgan M. Strissel, Maryville, TN.) 8. Describe a scenario, involving either natural or artificial materials, where strain begins with increments of pure shear and is followed by simple shear. 9. For a sectional strain ratio of 3:1, calculate the amount of elongation (as a percent) parallel to the X-axis and shortening parallel to the Z-axis. Assume no volume change. 10. Strain measured in a conglomerate immediately above an unconformity dipping 30° to the west has principal quadratic elongations of λX = 4, oriented horizontally (0°) Strain and Strain Measurement and λ Z = 0.25, oriented vertically (90°). Based on these values, calculate the percent elongation parallel to the unconformity and the orientation of the unconformity prior to deformation. What assumptions are made in this reconstruction? 11. Using reduction spots in a slate, principal strain ratios were measured as Rs = 1.3 in the plane of foliation and Rs = 2.8 in the plane perpendicular to foliation/parallel to lineation. a. Determine the k value for this deformation. b. Assuming SY = 1, what is the percent shortening parallel to the Z-axis? c. What is the apparent volume change (Δ) (assuming SY = 1)? d. If this deformation involved no volume change, what is the stretch parallel to the X, Y, and Z axes? 12. Why does the plane strain line on the Flinn diagram shift its orientation when deformation involves volume change? 13. What primary depositional processes can add difficulties to determining the finite strain using elliptical markers? 14. Two planar sections of deformed conglomerates. (a) Neoproterozoic matrix-supported quartz pebble conglomerate from the Sheeprock Mountains, Basin and Range province, Utah. (b) Neoproterozoic cobble-pebble metaconglomerate from the Virginia Blue Ridge. (CMB photos.) | 163 (b) a. What strain analysis technique would be best to employ for each example? Explain. b. Use your preferred method to estimate the two- dimensional strain for each conglomerate. (Note: a larger color version is available with the ancillary materials from the publisher’s website). 15. Following is an image of a sample from a 3 cm thick vein of calcite. Calcite crystals frequently record a history of opening and filling in veins like this. Describe the history of opening and filling of this vein by the calcite crystals. Did this vein open strictly by extensional separation along the crack that filled with calcite, or was there a component of simple shear involved with opening and filling of this vein? Explain the reasoning behind your conclusion. (a) Further Reading De Paor, D. G., 1988, Rf /ϕ strain analysis using an orientation net: Journal of Structural Geology, v. 10, p. 323–333. Introduces the hyperbolic net, a very useful but under-utilized tool for strain analysis. Ferguson, J., 1994, Introduction to linear algebra in geology: London, Chapman and Hall, 203 p. A straightforward introduction to matrix operations, eigenvectors, and eigenvalues. Numerous solved problems. Jessup, M. J., Law, R. D., and Frassi, C., 2007, The rigid grain net (RGN): An alternative method for estimating mean kinematic vorticity number (Wm): Journal of Structural Geology, v. 29, p. 411–421. Summarizes the methods of measuring kinematic vorticity in deformed rocks and presents a new, simplified method for estimating kinematic vorticity from thin-section data. 164 | Mechanics: How Rocks Deform Lin, S., Jiang, D., and Williams, P. F., 1998, Transpression (or transtension) zones of triclinic symmetry: Natural example and theoretical modelling, in Holdsworth, R. E., Strachan, R. A., and Dewey, J. F., eds., Continental transpressional and transtensional tectonics: London, Geological Society Special Publication 135, p. 41–57. Brings out the concept of triclinic deformation symmetry both in theory and from field examples. Lisle, R. J., 1985, Geological strain analysis: A manual for the Rf /ϕ technique: Oxford, Pergamon Press, 99 p. The complete guide to traditional Rf /ϕ strain analysis. Means, W. D., 1976, Stress and strain: New York, Springer- Verlag, 339 p. A well-written introduction to the concepts of stress and strain. Mathematical concepts and derivations are presented in an understandable fashion. Problems (and solutions) related to geological situations. Ramsay, J. G., and Huber, M. I., 1983, The techniques of modern structural geology, Volume 1: Strain analysis: London, Academic Press, 307 p. A detailed, well-illustrated classic treatment of strain and strain analysis. Many concepts are presented by means of solved and illustrated problems. Some of the strain nomenclature is different from the treatment in this text. Simpson, C., 1988, Analysis of two-dimensional finite strain, in Marshak, S., and Mitra, G., eds., Basic methods of structural geology: Englewood Cliffs, New Jersey, Prentice Hall, p. 333–360. A simple and well-illustrated introduction to strain analysis with solved problems. Simpson C., and De Paor, D. G., 1993, Strain and kinematic analysis in general shear zones: Journal of Structural Geology, v. 15, p. 1–20. Clear discussion of general shear and recognizing it in naturally deformed rocks. Tikoff, B., and Fossen, H., 1999, Three-dimensional reference deformations and strain facies: Journal of Structural Geology, v. 21, p. 1497–1512. Discusses an array of different three-dimensional strain geometries resulting from general shear and transpressional deformation. Introduces the infamous “wheel of strain.” 7 Mechanical Behavior of Rock Materials The effects of the mechanical behavior of materials are visible all around us, in deformed rocks and in the technology that produces many of the conveniences of everyday life. In any automobile, the metals used in the body panels and engine block display contrasting physical properties due to their differing compositions and the physical conditions involved in their manufacture. Steel or aluminum may be used for both, but for fenders a more ductile steel is rolled into sheets and stamped (deformed) into shape. The engine block is cast in molten form roughly with more brittle steel or aluminum and cooled under conditions that produce the needed strength and temperature resistance, then machined into shape. Plastics and ceramics are quite different from metals, but they, too, are pertinent here. Modern plastics are mostly artificial polymers made from hydrocarbons manufactured at temperatures high enough to soften— make them plastic—but not melt them. Ceramic materials in common use today—bricks, semiconductors, glasses, fine china, and ceramic internalcombustion engines—all exhibit elastic properties at room temperature, but are made from different geologic raw materials at high temperatures, where they behave plastically or as viscous melts. Much of the theory we use in structural geology to explain the behavior of rocks was originally developed to explain the behavior of common materials under a wide range of conditions. Idealized mechanical models that simulate the behavior of rocks, soils, concrete, steel, and ceramics have been used for many years, because they enable us to simplify and thereby understand the response of these real materials to stress (Figure 7–1). The three ideal end-member behavior models—elastic, viscous, and plastic (to be discussed shortly) can be defined mathematically. The study of the interrelationships between the different end members, particularly viscous and plastic behavior, is collectively referred to as rheology. Some rocks and minerals approach ideal behavior under particular conditions; others exhibit more complex behavior under all conditions. Few exhibit ideal behavior, but frequently respond to stress in ways that approach one of the ideal types. The discussions of stress and strain in Chapters 5 and 6 set the stage for us to look at the behavior of rocks under various conditions, thus enabling us to better understand the physical conditions that produce many geologic structures, as well as infer some of the bulk mechanical properties of rocks. The fact that rock does show marked differences in behavior in natural deformation provides the geologist with an unusual opportunity to learn more about the conditions of deformation. . . . FRED A. DONATH, 1970, American Scientist 165 Mechanics: How Rocks Deform Elastic Viscous Piston in liquid σ σ ε Constant σ ε Plastic Sliding block time (b) (c) Elasticoviscous σ σ Weight gravity σ ε ε Elasticplastic σ Weight gravity time Elastic s Upper crust tic as El –p tic las Properties of homogeneous materials are the same throughout any sample regardless of size; those of inhomogeneous materials vary with location, either in a hand specimen or in a region. This inhomogeneity leads to scale-dependent behavior of rocks. Isotropic materials have the same properties in all directions, contrasting with anisotropic materials, wherein properties vary with direction. Some rocks, such as thinly bedded shale and strongly foliated gneiss, may behave as strongly anisotropic materials on the scale of a hand specimen, but they may behave isotropically on a scale of a rock mass of tens to hundreds of meters across. Large rock masses, such as many stocks or batholiths, may be homogeneous and isotropic in response to stress. The uppermost crust of eastern North America displays a very uniform distribution of present-day stress and thus is said to behave homogeneously with respect to the present-day stress field (Figure 5–20); but earthquakes do occur in the East, and so there must be local inhomogeneities that interrupt the stress field, concentrate stress, or include regions that are relatively weak and allow the crust to rupture. Layered rocks are strongly anisotropic to stress, but the degree to which the anisotropy is expressed depends on the direction in which the stress is oriented. The crustal rupture that produces earthquakes in eastern North America probably occurs as a result of localized stress concentrations at suitably oriented anisotropies. These anisotropies may consist of old fault or fracture zones, or rock bodies of contrasting composition and density (for example, granite and gabbro). Thus, an old fault zone may be inherently weak and provide a lower threshold for movement—lower strength than unbroken rock. We commonly think of deformation in terms of three end-member behavior types: elastic, plastic, and viscous (Figure 7–2). Strain that is recovered instantaneously on removal of stress is called elastic strain. The elastically deformed object returns to its original undeformed shape after the stress is removed. No other behavior mode exhibits this reversible property or “material memory.” Plastic strain behavior involves permanent strain that occurs without loss of cohesion and results from the rearrangment of chemical bonds in crystal lattices in minerals by one of the creep mechanisms described in Chapter 8; some materials behave plastically after exceeding a threshold or yield differential stress. Obviously, it is a pervasive strain that affects the entire rock mass. (NOTE: This definition of plasticity is the same as the frequently employed terms crystal plasticity, or crystal-plastic behavior.) Viscous behavior is the behavior of fluids such as water or magma or of any other substance with little internal structure. Viscous deformation is pervasive and permanent, and the strain rate depends on the stress. Although most rocks do not behave as viscous materials, some of their properties may be approximately explained by assuming viscous behavior. ou Definitions ε (e) isc σ ov (d) tic FIGURE 7–1 Ideal Spring mechanical models and stress-strain or straintime curves for material behavior. Think about the mechanical models in terms of how a spring, a piston in (a) a liquid, and a sliding block behave independently or in combination. Strain is plotted versus time for viscous (b) and elasticoviscous (d) materials because strain in viscous materials (liquids) is time dependent. as | El 166 Lower crust Rock salt Magma Viscous Viscoplastic Plastic FIGURE 7–2 Material behavior-modes triangle. Most rock materials do not exhibit ideal behavior, although their behavior plots outside the circular vacant region of the diagram. Mechanical Behavior of Rock Materials Combinations of the three end-member types produce elastic-plastic, viscoplastic, and elasticoviscous behavior (Figure 7–2). Other combinations may approximate the behavior of most geologic materials. Fortunately, plots of the behavior of most rock types fall close to one of the end members or to an edge of the triangle—not in the middle— and so the end-member behavior models discussed in the next sections approximate the behavior of rock masses under a variety of conditions. Elastic (Hookean) Behavior We say a material exhibits linear elastic behavior if it deforms in direct proportion to the applied stress and, after the stress is removed, immediately returns to its original shape. Linear elastic behavior in an isotropic homogeneous material is described by Hooke’s law—named for an English physicist, Robert Hooke (1635–1703)—which states that the strain (ε) in the material is directly proportional to the applied stress (σ) (Figures 7–1a and 7–3a): (7–1) σ ∝ ε. Equation 7–1 is converted to an equality by inserting a proportionality constant, here E, which is Young’s modulus (E): 167 E is an experimentally determined elastic constant where F σ E= = A ∆l ε l0 (7–3) where F is force, A is area, Δl is the change in length of a reference line, and l0 is the initial length of the line. Because strain is a dimensionless number, the unit for Young’s modulus is the same as that for stress in (Pa). Young’s modulus is a measure of the “stiffness” of a material. A foam ball is easily deformed when squeezed, whereas a baseball is much stiffer and for the same amount of stress would change its shape much less than the foam ball. When stress-strain data are plotted against one another, the slope of the line is determined by the elastic constant for the material used in the experiment (Figure 7–3). Note that the strain referred to in equations 7–1, 7–2, and 7–3 is the elongation strain. For elastic behavior under shear stress, (7–4) τ = G γ, where τ is shear stress, γ is shear strain, and G is another experimentally determined elastic constant, the rigidity modulus, or shear modulus (G), defined as the ratio of shear stress to shear strain τ G= . γ (7–2) σ = E ε. | σ (7–5) Rupture point ε = ∆l = l – l0 Ultimate strength σ σ Slope = ε = Young’s modulus ε (b) l0 l Nonelastic behavior Ultimate strength Elastic limit Rupture point σ Yield point A Ideal elastic behavior (a) Area (c) ε FIGURE 7–3 (a) Relationships between stress, σ, and elastic strain, ε, in a cylinder of rock in a test apparatus. The ends of the cylinder have a known area, A. (b) and (c) Stress-strain diagrams for an ideal elastic material (b) and a real elastic material (c). The real elastic material exhibits ideal behavior initially but begins to deviate and become nonelastic at higher strains. 168 | Mechanics: How Rocks Deform A linear relationship exists in ideal elastic behavior between the application of stress and the resulting strain. Below the elastic limit, an elastic material rebounds instantaneously to its original shape when the stress is removed. The stress-strain curve for an elastic material begins at the origin and abruptly changes slope at the yield point (Figure 7–3c), where Hooke’s law no longer holds: so nonelastic, permanent deformation behavior begins, or the material begins to fail and ruptures. Brittle behavior, as defined in Chapter 1, implies failure in the elastic range, actually at the elastic limit for the material. Permanent strain occurs by rupture in an ideal elastic material. A change in slope of the stress-strain curve also indicates that the direct proportionality between stress and strain no longer exists. The highest point on the curve is the ultimate strength for the material. The elastic limit, here the same as the yield point, is the point on the curve beyond which the material begins to undergo permanent deformation or ruptures (or both), although the elastic limit is reached in many rocks at about half the ultimate strength (the ability of a material to withstand stress). Brace et al. (1966) showed that microcracks begin to form, the rock begins to expand (dilate), and permanent deformation begins at a value of approximately half of the ultimate strength. In another stress-strain curve for elastic materials (Figure 7–3c), the slope decreases before reaching the ultimate strength of the material. This point where the decrease in slope occurs is both the yield point and the elastic limit. Above the elastic limit, the material exhibits nonelastic behavior. When a material is elastically shortened by compression in a test cylinder it also elongates laterally (at right angles to σ1); the ratio of elastic elongation to the elastic shortening of the material is given by Poisson’s ratio (ν) defined as σ1 ε3 Cylinder shortened Dimension increases ε1 FIGURE 7–4 Definition of Poisson’s ratio. The unconfined rock cylinder is compressed parallel to σ1 and expands perpendicular to σ1. Poisson’s ratio is the ratio of shortening parallel to σ1 to the extension perpendicular to σ1. ratio for cork is near zero; metallic lead, 0.45; aluminum, 0.33; most steels, 0.27; and polymers, 0.1 to 0.4 (Lakes, 1987). Recall that all stresses measured at depth in the Earth’s crust are compressional (Chapter 5) and the vertical (lithostatic) stress at a particular depth is given by the product of TABLE 7–1 ROCK TYPE oisson’s Ratios (𝜈) for P Common Rock Types LOCALITY POISSON’S RATIO Quartzite Baraboo, WI 0.10 Granite Westerly, RI 0.25 Eclogite Healdsburg, CA 0.26 where ν is Poisson’s ratio, and ε1 and ε3 are linear elastic strains derived from changes of length measured in uniaxial compression experiments (Figures 7–4 and 7–5). Values of ν are positive because one strain (ε1) is negative and it thus cancels the negative sign in equation 7–6. Table 7–1 contains representative values of Poisson’s ratio for a variety of common rocks calculated from compressional (VP) and shear (VS) wave velocity measurements, where Amphibolite Bantam, CT 0.26 Felsic granulite Saranac Lake, NY 0.26 Sandstone Berea, OH 0.26 Shale Thorn Hill, TN 0.26 Peridotite Cypress Island, WA 0.27 Tonalite gneiss Torrington, CT 0.27 Diorite Mount Rainier, WA 0.28 Dunite Twin Sisters, WA 0.28   1 1  vν = 1 −  2 2 − V V 1 ( P S )   Dolostone Thorn Hill, TN 0.29 Mafic granulite Adirondack Mountains, NY 0.29 Gabbro Duluth, MN 0.30 Slate Poultney, VT 0.30 Anorthosite Adirondack Mountains, NY 0.31 ε ν = − ε1 3 (7–6) (7–7) at 200 MPa confining pressure. Most rocks have a Poisson’s ratio of less than 0.5, indicating that the volume of the material decreased under elastic strain. Water, although not an elastic solid, is an incompressible material with a Poisson’s ratio of 0.5; halite has a very low compressibility and has a Poisson’s ratio of less than 0.5. Soft biological tissues and rubber have a Poisson’s ratio of about 0.5; the Quartz mica schist Thomaston, CT 0.31 Limestone Thorn Hill, TN 0.32 Serpentinite Burro Mountain, CA 0.35 (Data provided by Nicholas I. Christensen, University of Wisconsin–Madison). Mechanical Behavior of Rock Materials ε3 Potential shear surface ε1 ε2 FIGURE 7–5 Cylinder of rock in an axial compression experiment showing orientation of strain axes, with ε1 = ε2 and ν = –(ε1/ε3). The conical areas inside the cylinder are locations of potential shear surfaces. the average rock density (ρ), the acceleration due to gravity (g), and the depth in meters (h) (recall the discussion of force and stress in Chapter 5). In most settings the vertical stress likely approximates σ1, thus rocks are elastically shortened vertically and attempt to expand laterally (in the horizontal direction). But in the Earth’s crust, the adjacent rocks “push” back on the other rocks, generating a compressional horizontal σh. In essence this horizontal stress is a consequence of the Poisson’s ratio. Knowledge of Poisson's ratios is important to engineers in estimating the behavior of earthquake (elastic) waves in the crust, which is useful in estimating the amount of damage that might occur where a planned (or existing) building or power plant is located. If the subsurface geology is known down to a few kilometers, the design of a new building or power plant can be modified (and existing structures possibly retrofitted) to accomodate the seismic hazard. | 169 deformation occurs in solids below their melting points. Rutter (1986) maintained that ductility should reflect the capacity for large amounts of nonlocalized homogeneous strain. He would include all flow processes, including brittle mechanisms, in the usage of the term “ductile,” and restrict the use of the term “plastic” to rocks that have been deformed by diffusion processes that deform crystal lattices (Chapter 8). In a strict sense, solids also can behave as fluids, so the definitions become a bit unclear. Scale dependence is important when considering deformation of a rock mass, because the kind of deformation occurring in a few cubic centimeters of rock may not be the same as that occurring in several cubic kilometers of rock, even if the larger mass includes the smaller. Consequently, the term “ductile” will be used here for deformation in which plastic or viscous flow dominates over brittle processes. For example, in very fine-grained fault rocks formed under near-surface conditions, handspecimen to outcrop-scale deformation may appear to have involved ductile flow, but microscopic examination reveals that the fine-grained material still consists of uniformly pulverized original rock without any internal deformation of individual microscopic grains. The fault rock is still brittle (not ductile), but when the uniform very fine grain size is reached, the material will flow like wheat flour or dry cement. Viscous Behavior Viscous behavior is fluid-like behavior (Figure 7–1b). Natural fluids, including water, magma, gases, and the molten part of the Earth’s core, are all viscous materials. We can also argue, for purposes of simplification, that the mantle is a viscous material, using the example in Chapter 1 for calculating mantle viscosity from glacial rebound rates. Stationary fluids will not transmit shear stresses and are called perfect fluids. Moving fluids undergo shear stresses on all planes of differential motion (non zero shear-strain rate), including the fluid-rock boundaries. Shear stress exists in a fluid only when it is in motion. Fluids in which there is a linearly proportional relationship between differential shear stress (τ) and shear-strain rate (γ̇) are Newtonian fluids, expressed as τ ∝ dτ dt (7–8) τ = η˙γ, (7–9) or Permanent Deformation—Ductility Permanent strain in the form of viscous or plastic deformation occurs in a material beyond its elastic limit. Viscous behavior occurs in fluids, whereas plastic where γ is shear strain and t is time, so that dγ/dt, or γ̇, is the shear-strain rate, and η is both the viscosity of the fluid and the proportionality constant. (The SI unit for viscosity is the poise, and 10 poise equals 1 Pa s.) The reciprocal of viscosity, 1/η, is called the fluidity, which is the ability of a fluid to move, rather than the resistance to 170 | Mechanics: How Rocks Deform motion measured by the viscosity. Stress-strain curves for viscous materials are not as useful as strain-time curves (Figures 7–1 and 7–6), because of the dependence of strain on time as well as on stress. Rocks at high temperatures near their melting points behave in a nearly viscous fashion, but their behavior is better described as plastic (to be discussed), because they are still crystalline solids. Useful models of crustal dynamics can, however, be formulated assuming viscous behavior. Plastic (Saint-Venant) Behavior Ideal plastic behavior (Figure 7–1c) involves permanent (nonrecoverable) deformation that affects the entire rock mass and begins at a yield stress. Ideal plastic behavior is also known as Saint-Venant behavior in honor of Adhemar-Jean-Claude Barre de Saint-Venant (1797–1886), a French physicist, who in the nineteenth century wrote mathematical expressions to attempt to relate various stress components in materials exhibiting plastic behavior. τ (a) γ In natural materials, plastic behavior is generally preceded by elastic behavior, with plastic behavior beginning at the elastic limit of the material being deformed (Figure 7–7). Total strain in a plastic material also depends on the deformation path. It thus depends on the sequence of stresses applied to the body rather than the final stress, as in an elastic material. After the yield point is passed, the material flows at a constant stress unless one of two things occurs. The first is strain hardening (increased resistance to deformation as strain increases), such that more stress is required to produce a given strain. The second, and opposite, is strain softening (Figure 7–8), in which even with less stress the material deforms further. Materials that either strainharden or strain-soften should probably be described as non ideal plastic, because they exhibit a more general property of non ideal behavior. Stress-strain curves for the limestone in Figure 7–8b indicate that at relatively low confining pressure, the limestone deviates from ideal elastic behavior at moderate differential stress values before rupturing; at higher confining pressure, it still deviates but enters a realm of strain softening (decreasing slope) beyond the ultimate strength. At still higher confining pressure, the limestone exhibits almost ideal plastic behavior beyond the yield point. Plastic behavior is thought to dominate at depths in the crust and mantle where temperature reaches several hundred degrees Celsius and confining pressure reaches several kilobars. Presence of water or other fluid may lower threshold temperatures and pressures for ductile behavior, but also may promote brittle behavior if there is a rapid increase in fluid pressure. Different minerals undergo plastic behavior at different temperatures and pressures. Recrystallization processes, grain-boundary sliding, calcite twinning, and some effects of pressure solution in metamorphic rocks (Chapter 8) are commonly associated with ductile deformation on the microscopic scale. The effects Rupture point γ Yield point Ela sti c σ (b) Ultimate strength ic last P Elastic limit t FIGURE 7–6 (a) Stress-strain and (b) strain-time diagrams for a viscous material at constant τ. The stress-strain curve is uninformative and even somewhat misleading, because the strain rate depends on stress in viscous materials. A plot of shear strain vs. time (t) yields a more meaningful curve. ε FIGURE 7–7 Stress-strain curve showing general properties of an elastic-plastic material (with strain hardening) and inflection points in the curve. Mechanical Behavior of Rock Materials | 171 plastic rdening Ideal plasti c a Strain h Strain so ftening plastic σ ε (a) 7 7,500 Differential stress in kg/cm2 × 103 6 5 5,000 4 FIGURE 7–9 Strongly foliated Neoproterozoic biotite gneiss containing coarse feldspar layers on the Yadkin River near Siloam, North Carolina. Quartz and micas (black) were plastically deformed, and feldspar (white) was deformed brittlely during the middle Paleozoic. (RDH photo.) 7,000 4,000 3 2 Denotes fracture 1 2 (b) 4 6 8 Strain in percent 10 12 14 FIGURE 7–8 (a) Strain hardening and strain softening in an elastic-plastic material. (b) Experimental deformation of Solnhofen Limestone. Curves represent deformation at different confining pressures. Rupture occurs at differential stress indicated (in kg/cm2). (From H. C. Heard, 1960, Geological Society of America Memoir 79.) pervade the entire rock mass or, in some instances, are confined to tabular zones of ductile deformation (ductile shear zones; Chapter 10). Laboratory experiments designed to duplicate ductile deformation must be carried out at high temperature and pressure to attain strain rates sufficiently rapid to complete many experiments during a human lifetime. Consider a test cylinder that is permanently shortened by 10 percent (0.1): if the experiment lasted an hour (3,600 seconds), the strain rate is 2.8 × 10−5 s−1 (because strain is dimensionless, strain rate is given in reciprocal seconds, 1/s or s−1); if the experiment lasted a week (6.05 × 105 seconds), the strain rate is 1.7 × 10−7 s−1. Structures in metamorphic and many fault rocks form under ductile conditions, but at timescales of hundreds of thousands to millions of years (Figure 7–9), which yield strain rates of 10−14 to −15 s−1. In glacial ice and rock salt, ductile behavior may be initiated under surface conditions, so these rocks serve as useful analogues for rocks deformed deep in the crust. Several models have been proposed to explain plastic behavior, but none fully succeeds in quantifying it because of the inherent complexity of the process. The mathematics describing plastic deformation is also complex, particularly that describing the plastic behavior of anisotropic crystalline solids like most rocks (Nicolas and Poirier, 1976). So, in order to communicate about the nature of deformation processes, we derive flow laws to express the relationships between strain rate and stress. An example of a relatively simple flow law is (7–10) ε̇ = Aσn, where ε̇ is strain rate, A is a material constant, σ is normal stress, and n is another constant that depends on the flow mechanism. A creep (flow) law for shear-strain rate is ψP γ̇ = Aτne RT , (7–11) where γ̇ is shear-strain rate, τ is shear stress, ψ is another material constant, P is pressure in MPa, R is the gas constant (1.987 cal deg−1 mol−1), and T is absolute temperature. The two additional models that follow were chosen because of their simplicity and historical significance. Tresca’s criterion states that plastic yield will begin when the maximum shear stress (τmax) reaches a critical value (Cy), specific for each material. This is half of the initial stress difference (σ1 – σ3) where yielding begins, or τ max = C = y ( σ1 − σ3 ) , 2 (7–12) 172 | Mechanics: How Rocks Deform (σ1 – σ2)2 + (σ2 – σ3)2 + (σ3 – σ1)2 Reference length l d Undeformed rod New length l + ∆l d Extended rod d' FIGURE 7–10 Extensional ductile “necking” of a metal rod. d and d' are the initial and deformed diameters of the rod, respectively. where σ1 and σ3 are the principal stresses at yielding. It predicts that the material will yield when this maximum shear stress is reached regardless of the specific values of σ1 and σ3 . This criterion was intended to account for some properties observed in metals where the constant maximum stress difference, Δσ (= σ1 – σ3), indicates that yield stresses in both tension and compression have approximately the same magnitude. This relationship probably can best be used to explain the plastic behavior of metal rods in extension experiments (Figure 7–10), but, because rocks are stronger in compression than in tension, it does not adequately describe the plastic behavior of rocks. Another model is based on the Von Mises criterion, which proposes that yield will occur under any combination of principal stresses that will produce the same distortional strain energy that existed in a previous uniaxial test of the same material at the yield point. When the sum of the squares of the principal stress differences equals 2(σ3)2, commonly expressed as where Cy is the yield constant, the criterion is satisfied. The Von Mises criterion does explain some plastic deformation in metals, but, again, not in rocks. Elasticoviscous (Maxwell) Behavior A combination of viscous and elastic behavior called elasticoviscous behavior was studied by a Scottish physicist, James Clerk Maxwell (1831–1879)—hence the alternative name—and depends on both stress and strain rates (Figure 7–11). Thus, equations 7–1 and 7–7 must be combined to express relationships between stress and strain in an elasticoviscous material. Total strain in the material is given by the sum of elastic and viscous strains, Elastic Limit Elastic Viscous (7–14) γ = γe + γv , where γe is the elastic shear strain and γv is the viscous shear strain. From equations 7–4 and 7–7,  τ   τt  γ =   +  .  G   η  (7–15) Thus, the elasticoviscous strain (γ) equals the sum of the elastic strain and viscous strain components. G is the shear modulus, τ is shear stress, t is time, and η is viscosity. Here, we must consider time dependence of deformation, an important factor in geologic processes. Rocks that deform brittlely over a short time (milliseconds to a few years) will deform ductilely over periods of thousands to millions of years. The problem of why deep-focus earthquakes occur (see Essay in this chapter) is a good example of the time dependence of geologic processes. Viscous ε σ (or τ) (7–13) = 2(σ3)2 = 6Cy , (or γ) Elastic (a) ε (b) t FIGURE 7–11 Stress-strain (a) and strain-time (b) diagrams for an elastico viscous material. The same problems exist here with stressstrain curves as for ideal viscous materials (Figure 7–6). Mechanical Behavior of Rock Materials Controlling Factors Many factors affect and control the behavior of rock materials, including composition, texture, temperature, confining pressure, fluid (pore) pressure, rate of stress increase and strain rate, and character and spacing of anisotropies such as bedding or foliation. Temperature, composition, strain rate, confining pressure, and fluid content typically have a greater effect than others. Given proper conditions, any of these variables may play a major role in the behavior of a rock mass being deformed. For example, most rocks deform elastically at low temperature, but will deform ductilely at high temperature and low strain rate. At high strain rate, the same rocks may deform brittlely. Increased fluid pressure may produce ductile behavior at lower temperatures than those at which it would occur in a dry rock mass, although increased fluid pressure has also been shown by Handin et al. (1963) to lower the threshold of brittle deformation. Behavior of Crustal Rocks The ideal mechanical behavior models discussed so far approximate the behavior of rock materials in the Earth. Some geologic materials exhibit almost ideal model behavior (Figure 7–2). Thin sheets of muscovite and biotite | 173 exhibit elastic behavior as they are flexed at room temperature and spring back to their original shapes. Muscovite and biotite sheets also have an elastic limit that can be exceeded. Some fluids upon and within the Earth approximate ideal viscous behavior, and we also have abundant evidence for occurrence of nonideal plastic deformation. Transitional behavior such as viscoelastic or elastic-plastic is also prevalent at certain temperatures and pressures. Ideal behavior models (Figure 7–1) are defined in large part by the shapes of stress-strain or strain-time curves (or both). Further discussion of deformation mechanisms in Chapter 8 will help in understanding these behavior modes in rocks. Ductile-Brittle Transition Brittle behavior generally dominates in the upper crust, with elasticity providing rigidity and permitting faulting and jointing to occur at the elastic limit. A transition zone occurs in the crust where brittle behavior is inhibited because increased ductility occurs as a result of increases in temperature and pressure with depth. This is the ductilebrittle transition (DBT) (Figure 7–12). Direct evidence of ductile behavior in crustal rocks is shown by “similar” folds (Chapter 14) that can form only in the ductile realm. Laboratory studies of minerals in these folded rocks indicate that temperatures of several hundred degrees Celsius and pressures of several kilobars were required Differential stress (rock strength) (MPa) 0 0 Threshold depth and thickness determined by heat flux and fluids Ductile-brittle transition Depth (km) Brittle upper crust (obeys Byerlee’s Byerlee's Law) 25 Stronger, ductile lower crust 50 Br ittl eb eh av ior 100 Upper crust (quartz model) DBT Lower crust Wet granulite Moho 50 Dry peridotite (olivine model) Upper mantle Upper mantle 75 FIGURE 7–12 Simplified concept of the ductile-brittle transition (DBT) in the lithosphere. The depth to the transition is determined by the amount of heat produced in that part of the lithosphere, the nature and amount of fluid present, and pressure variables. Simple, and expected, variations in layered structure (e.g., massive vs. foliated rocks), water content, local strain rate, and local shortening and lengthening directions relative to structure can all produce a much more complex geometry for the DBT. 174 | Mechanics: How Rocks Deform to form them deep in the crust. It would be incorrect to assume that there is no elastic behavior in the lower crust or the mantle well below the DBT. If the high pressure and temperature of the lower crust and mantle could suddenly be relieved, there would still be some elastic recovery, again illustrating the behavior of these elastic-plastic materials (Figure 7–7). The actual depth to the DBT in the lithosphere is determined by the geothermal gradient (rate of increase of temperature with depth determined by the amount of radioactive heat-producing elements U, Th, and K, intrusion of magma into the crust, and mantle heat flux). It is also controlled by the quantity of fluid present and close to other variables that determine pressure gradients. In tectonically inactive parts of the continents such as eastern North America, where thermal gradients are very gentle (15 to 25° C/km), depth to the DBT may be as much as 15 km, but in areas of steep geothermal gradients (30 to 40° C/km) in the continents, the depth to the DBT may range from 8 to 12 km. Depth to the DBT may be approximately estimated from the maximum focal depth of most earthquakes in an area (implying no elastic behavior below the DBT). In eastern North America, most earthquakes occur at depths of between 5 and 25 km; in the Great Basin in Utah and Nevada, where the thermal gradient is steeper, the foci of most earthquakes are within a few kilometers of the surface. Large active faults that accommodate displacement through the entire crust, such as the San Andreas in California, unquestionably exhibit brittle behavior in the upper crust, but probably involve ductile flow in the fault zones below the DBT (Figure 7–12). Large faults also exhibit a kind of elastic-plastic behavior—the upper-crustal segments exhibit pure elastic behavior, and the lowercrustal segments exhibit nearly pure plastic behavior— but segments of the fault within the DBT (and sometimes below it) exhibit elastic-plastic behavior (Figures 7–7 and 7–8). High strain rates favor brittle behavior, but high fluid and confining pressures may permit rapid plastic flow along the fault. Natural models for the DBT occur in glaciers, salt, and unconsolidated sediment. A definable brittle zone occurs in the upper parts of a glacier where crevasses and other brittle fractures form. The fractures close at depths rarely exceeding 60 m, giving way to a zone of ductile flow (Figure 7–13). Direct observations in the ductile zone in glaciers have been made by excavating a shaft through the upper brittle zone into the lower ductile deformation zone. Observers can enter the shaft and make observations because ductile flow closes the shaft at a very slow rate over several years. Salt structures afford similar opportunities to observe ductile behavior occurring near the surface in natural materials (Chapter 2). The unconfined parts of the salt yield brittlely; the confined parts yield ductilely (Jackson and Talbot, 1986). Other analogies of ductile or viscous behavior exist where folds have formed in slumped water-saturated sediments and in glacial silts deformed by slumping or ice movement (Figure 2–5a; Stone and Koteff, 1979). An everyday model for elasticoviscous or elasticplastic behavior is the silicone material called Silly Putty (polydimethyl siloxane). It behaves as a ductile (probably viscous) material if it is deformed slowly, but exhibits brittle-elastic behavior if it is strained rapidly (Figure 7–14). Pulled slowly, it stretches; hit with a hammer, it shatters. Crustal rocks, except magma (even though magma has a finite yield strength and is thus not Newtonian viscous), probably do not exhibit viscous behavior, except perhaps over geologically long periods of time, but for simplicity, viscous behavior is used as an approximation for flow in the mantle (Chapter 1). Ductile flow may occur in the mantle much of the time, but rapid accumulation of strain energy may provoke transformation to elastic behavior that produces fractures, elastic-rebound, and deep-focus earthquakes. Thus, the behavior of Silly Putty subjected to markedly different Creva sses Plastic zone Brittle zone DBT Thrustfaulted toe Flow o f ice Bedrock FIGURE 7–13 Cross section of a glacier showing deformation zones. DBT—ductile-brittle transition. Mechanical Behavior of Rock Materials FIGURE 7–14 Behavior of Silly Putty. Compare the behavior of this material with that of the metal rod in Figure 7–10. | 175 Extension fracture Pulled apart rapidly Pulled apart slowly Plastic necking Static flow (one hour) Struck with a hammer Sha tter ESSAY s J elly Sandwiches, Crème Brûlée, and the Mechanical Behavior of the Lithosphere Continental lithosphere is composed of the upper and lower crust, and the mantle down to approximately 100 km. We commonly think of the composition of these components as a granitic upper crust, a lower crust composed of granulite, and the upper mantle composed of peridotite. Mechanical models for the strength and behavior of crust and upper mantle rocks (Figure 7–12) are commonly based on the behavior of quartz and feldspar in the crust and olivine in the mantle. The upper crust becomes stronger with depth until the brittle/ductile transition is reached for quartz and feldspar; from that depth downward the strength progressively decreases. Under the ambient temperaturepressure conditions in the upper mantle olivine is strong, but its strength dramatically decreases below its brittle/ ductile transition (Figure 7–12). At depths of greater than 100 km, peridotite is sufficiently weak that it flows over time forming the mechanically weak asthenosphere. This model is probably an oversimplification, but, even with a simple mineralogy, the simplicity ends there. Additional variables include wet versus dry conditions, compositional variables, the nature of continental crust and subcontinental mantle in different parts of continents, and strain rate. The standard model for lithospheric behavior has been compared to that of a jelly sandwich, with the slices of bread being a strong upper crust and upper mantle, and the lower crust being the jelly. Several, however, have questioned the validity of this model based on modern earthquake, gravity, and other data from active collision zones—like the Himalayas—and continental interiors composed of Precambrian rocks, such as the Canadian Shield (Jackson, 2002; Afonso and Ranalli, 2004; Burov and Watts, 2006; Hartz and Podladchikov, 2008). Several additional models have been devised based on other combinations of the basic strength, fluid, and compositional variables (Figure 7E–1). The “crème brûlée” model involves a strong upper crust and a weaker lower crust and mantle. These additional models provide more realistic options for mechanical behavior of the different major components of the lithosphere, but do not begin to account for the heterogeneous nature of the crust and upper mantle. For example, the contrasts in anisotropy (e.g., foliated rocks versus nonfoliated, massive rocks) of parts of the crust to which we have easy access reveal greater complexity than can be accounted for by any of these models. Presence of significant volumes of melt in the crust or upper mantle, produced by decompression melting or some other mechanism, would locally lower the strength of these components. While these models account for the structure and mechanical behavior of most of the lithosphere, and plate tectonics theory predicts the occurrence of most earthquakes, none of Mechanics: How Rocks Deform continued them account for the occurrence of deep-focus earthquakes (Figure 7E–2). These earthquakes occur in the mantle far below the lithosphere at depths where only plastic behavior should occur, with the mantle deforming ductilely at an average strain rate of 10 –15s–1. Earthquakes, however, occur on a timescale of seconds, and most geoscientists agree that earthquakes involve an elastic-rebound mechanism that produces a suite of seismic waves that travel on the surface of and inside the Earth. Moreover, a rule of thumb regarding deep-focus earthquakes is that the largest deep-focus earthquakes are always smaller than the largest earthquakes in the shallow crust. The reason for this is that, with the mantle yielding continuously by ductile processes, it would be more difficult to accumulate enough elastic strain energy for a large earthquake to occur in the mantle. Much of this concept went out the window on June 9, 1994, when a magnitude 8.2 earthquake occurred some 630 km beneath northern Bolivia (Figure 7E–2). How could such a huge earthquake occur so far down in the mantle, even near a plate boundary where a cooler slab of oceanic lithosphere (crust plus upper mantle) is descending into the mantle beneath the western margin of South America? Even if subduction of cold brittle lithosphere is a viable alternative explanation, generation of earthquakes requires sudden release of elastic strain energy, a very rapid strain rate. Relatively few ML > 8 earthquakes are on record in the brittle crust above the ductile-brittle transition, compared with the overall numbers of ML > 6 earthquakes worldwide. The relatively shallow December 26, 2004, ML = 9 earthquake in the Indian Ocean just west of Sumatra is one of the largest earthquakes, if not the largest to be recorded in historical times. This earthquake is relatively easy to explain in terms Differential stress (MPa) WET lower crust DRY upper mantle 10 Load 20 DBT 30 DBT Wet granulite Lower crust Depth (km) Jelly sandwich Moho Quartz 0 200 400 40 Upper mantle Differential stress (MPa) 3000 Dry olivine 50 ε = 10 Moho 600 s–1 (b) Moho ε = 10 s –15 –1 800 Differential stress (MPa) 3000 WET lower crust WET upper mantle Quartz 0 200 DBT 400 DBT Wet granulite Moho 600 10 Depth (km) 2000 20 30 50 0 1000 2000 3000 DRY lower crust WET upper mantle Quartz 200 DBT 400 Dry diabase 40 Wet olivine (e) 600 Dry olivine 800 Temperature ( ° C) Depth (km) 30 1000 40 Upper mantle 200 Dry diabase r vio ha w) be ’s la e ittl lee Br yer (B Moho 20 0 r vio ha w) be ’s la e ittl lee Br yer (B Lower crust 10 Load DRY lower crust DRY upper mantle (d) 0 Upper crust 3000 400 30 50 –15 2000 DBT 20 Differential stress (MPa) Crème brûlée 1000 Quartz 40 DBT (c) (a) 0 10 Depth (km) 2000 Temperature ( ° C) 1000 r vio ha w) be ’s la e ittl lee Br yer (B Upper crust 0 r vio ha w) be ’s la e ittl lee Br yer (B 0 Temperature ( ° C) ESSAY | DBT Moho 600 Wet olivine 50 ε = 10 –15 s–1 ε = 10 800 –15 s–1 800 (f) FIGURE 7E–1 Variations on the basic “jelly sandwich” and “crème brûlée” models (a and b) of behavior of different components of the upper lithosphere. (c) is the standard model; dry diabase in (d) produces a strong layer that encompasses parts of the lower crust and upper mantle. Introduction of a dry lower crust into the crème brûlée model in (f) essentially converts the crème brûlée model to the standard (jelly sandwich) model (c). Variables are composition, depth-temperature, and differential stress (rock strength). Strain rate (ε̇) is constant (10 –15s–1), as is Moho depth (40 km). Various combinations of wet and dry conditions in different components produce marked changes in behavior. The behaviors depicted in (c) through (f) are predicted from laboratory experiments on the materials indicated, with an attempt to apply the results to simplified lithospheric models in (a) and (b). Curved arrows indicate flow in the ductile portions of each model. DBT—ductile-brittle transition. (Modified from diagrams in J. Jackson, 2002, GSA Today, and E. B. Burov and A. B. Watts, 2006, GSA Today). Temperature ( ° C) 176 Mechanical Behavior of Rock Materials 85° 10° N 80° 75° 70° 65° 60° W 10 | W 177 E A 0 10 kilometers 5° 0° A 22° 100 200 47° 300 400 5° 500 600 700 10° 0 10 15° 1,500 kilometers W E B 0 10 kilometers 20° 25° 100 23° 200 58° 300 400 500 30° 600 B 35° 40° 0 500 kilometers 45° S 700 Trench 0 Volcano Line of volcanoes kilometers 1,500 ML = 6.0 – 6.9 ML = 7.0 – 7.7 ML = 7.75 – 8.6 ML = 8.2 deep-focus earthquake FIGURE 7E–2 Depth distribution of earthquakes beneath western South America. Note that few occur at depths greater than 250 km, and that all of the earthquakes with foci > 300 km, with the exception of the 1994 ML = 8.2 Bolivian earthquake, have lower maximum magnitudes than most large shallow earthquakes. (Modified from H. Benioff, 1954, v. 65, Geological Society of America Bulletin.) of elastic-rebound theory, but the 1994 deep-focus Bolivian earthquake remains difficult to explain. So, how can we explain deep focus earthquakes at all, and the huge 1994 ML = 8.2 Bolivian earthquake, with our current knowledge? References Cited Afonso, J. C., and Ranalli, G., 2004, Crustal and mantle strengths in continental lithosphere: Is the jelly sandwich obsolete?: Tectonophysics, v. 394, p. 221–232, doi: 10.1016/j.tecto.2004.08.006. Benioff, H., 1954, Orogenesis and deep crustal structure—additional evi- Burov, E. B., and Watts, A. B., 2006, The long-term strength of continental lithosphere: ”Jelly sandwich” or “crème brûlée?”: GSA Today, v. 16, no. 1, p. 4–10, doi: 10.1130/1052-5173(2006)016<4:TLTSOC>2.0.CO;2. Hartz, E. H., and Podladchikov, Y. Y., 2008, Toasting the jelly sandwich: The effect of shear heating on lithospheric geotherms and strength: Geology, v. 36, p. 331–334. Jackson, J., 2002, Strength of the continental lithosphere: Time to abandon the jelly sandwich?: GSA Today, v. 12, no. 9, p. 4–10, doi: 10.1130/1052-5173(2002)012<0004:SOTCLT>2.0.CO;2. dence from seismology: GSA Bulletin, v. 65, p. 385–400. strain rates may be a useful analogue comparative model for understanding the behavior of mantle rocks, and it also helps to answer the question: why do earthquakes occur there at all? Other possible answers include dehydration reactions that produce brittle rock and phase changes, in addition to the strain rate changes suggested by the Silly Putty analogue. Strain Partitioning Behavior of rocks may vary in space as well as in time; concentration of deformation into specific parts of a rock mass by different behavior or mechanisms is called strain partitioning. This phenomenon may be related to differences 178 | Mechanics: How Rocks Deform in flow rate for a ductilely deforming mass (Lister and Williams, 1983), with the change in behavior type resulting from different physical properties of different rock types or (occasionally) conditions (Figure 7–15). Plastic strain may be localized in narrow ductile deformation zones along deep crustal faults, leaving adjacent rocks mostly unaffected. Different strains result from the bulk properties of the rocks being deformed. Relatively weak rocks (shale, salt, and schist, for example) commonly exhibit styles of deformation that contrast with those of stronger rocks (sandstone, gneiss, and amphibolite, for example) in the same deforming mass at the same depth in the Earth. Layers of different thickness in the same rock type may also cause partitioning of mechanical behavior. Shapes and wavelengths of folds are strongly influenced by layer thickness (Chapter 16). For example, folding of thinly bedded sandstone/shale layers in a sequence of massively bedded sandstone will result in strong contrasts in mechanical behavior. In massive layers, folds of longer wavelength and less curvature will be produced; in the thinly bedded weaker layers, folds will have very short wavelengths (Figures 7–15b and 7–16). This may be explained by differences in the original Rotating rigid feldspar or garnet porphyroclast 1m Thicker, more gently folded layer 1 mm Flowing ductile groundmass (a) (c) Complexly folded thin layer (b) Weak groundmass FIGURE 7–15 Strain partitioning at different scales and involving different variables of rigidity, layer thickness, and other properties. (a) Microscale deformation involving a strong object in a weak groundmass. (b) Outcrop-scale folding of layers with differing strength in a ductile groundmass. (c) Road-cut exposure of a sedimentary sequence of several rock types that exhibit different styles of behavior in different parts of the layered sequence. 10 m Original Anisotropy [bedding, foliation(s)] Viscous—regular folds FIGURE 7–16 Relationships between original (intrinsic) anisotropy and tectonically induced anisotropy, producing different kinds of structures in rocks and an opportunity for strain partitioning. Return to this diagram after considering fold mechanics (Chapter 15) for a better understanding of both folds and strain partitioning. (Reprinted from Journal of Structural Geology, v. 7, J. P. Latham, p. 237–249, © 1985, with kind permission from Elsevier Science, Ltd., Kidlington, United Kingdom.) Induced Anisotropy [foliation(s)] Viscous—irregular, passive folds Viscous—shear zones* Elastic—faulting * Strain softening Elastic—regular, similar folds Elastic—kinking Mechanical Behavior of Rock Materials anisotropy of the sequence or by tectonically induced anisotropy (such as fractures and foliations) in the rock mass (Latham, 1985). Other factors, including local variations in fluid pressure, confining pressure, temperature, and strain rate, may create conditions under which strain will be partitioned in different parts of a rock mass. | 179 Now that we have discussed the principles and problems of mechanical behavior in materials, we can apply these principles not only to ideal materials but also to crustal rocks. In an attempt to round out our discussion of rock mechanics, we turn to an introduction to the nature of microstructures in minerals. Chapter Highlights • Rheology concerns the deformation and flow of materials under stress. • Earth materials can behave in an elastic, viscous, and plastic manner, and their rheology is controlled by temperature, pressure, and strain rate. • The strength of Earth materials increases at higher pressures, but eventually Earth materials become weaker and ductile at high temperatures. Questions 1. Why do many rocks exhibit nearly ideal behavior? 2. What factors control the depth to the ductile-brittle transition in the crust? How do these factors accomplish this? 3. Construct a hypothetical stress-strain diagram for inflation to rupture of a new (previously uninflated) balloon. If, instead of rupturing the balloon, you deflate it and then inflate it again, would the stress-strain curve be different before rupture? 4. Poisson’s ratios for most natural and synthetic materials are positive. Predict the properties a material must have to exhibit a negative Poisson’s ratio. See Roderic Lakes, 1987, Science, v. 235, p. 1038–1040, for a discussion of synthetic materials with negative Poisson’s ratios. 5. Why do so many rock cylinders break along planar shear planes in uniaxial experiments, although the shear surfaces in a cylinder compressed from the ends are expected to be conical? Think about the way the experiments are designed, with σ1 ≠ σ2 = σ3. Are the principal stresses really so if planar shear surfaces form? 6. The stress-strain data set tabulated here is from a loading experiment made by adding successive weights to the end of a 1 m length of steel wire 3 mm in diameter, producing an elongation strain (~1). • The ductile-brittle transition occurs at depths between 10 and 25 km, and is an important mechanical boundary in the Earth’s crust. • A number of different models have been proposed to characterize the strength of the crust and upper mantle with differing implications for crustal flow and tectonics. (kgcm –2) σ Δl (mm) (kgcm –2) 0.00 0.00 3.84 4.63 0.63 0.15 4.11 5.30 1.23 0.33 4.40 7.34 2.45 0.60 4.36 8.08 2.79 0.47 4.17 8.70 2.39 2.45 3.88 9.17 3.17 3.33 3.51 9.49 3.55 4.00 σ Δl (mm) Using these data, and assuming uniform strain along the entire wire, calculate the stresses in MPa, plot the data on stress-strain axes, and interpret the kinds of behavior exhibited by the wire throughout the experiment. Note that the load needed to produce the next increment of strain may actually decrease at some stages. Calculate Young’s modulus for the wire from the elastic region of the curve. 7. Consider an experiment where standard axial compression experiments were run on shale, limestone, and sandstone at near-surface conditions to obtain stress-strain curves. Instead of discarding the broken rocks after failure, a second run was made on each confined rock to failure again. Would you expect the stress-strain curves to be different for each rock this time, or the same? 180 | Mechanics: How Rocks Deform Further Reading Bayly, B., 1992, Mechanics in structural geology: New York, Springer-Verlag, 253 p. A concise book that presents in greater detail the concepts dealt with in Chapters 3 and 4, yet understandably with many solved problems. Discusses fundamental strain principles, then presents stress, and afterward discusses various modes of behavior of Earth materials. Donath, F. A., 1970, Some information squeezed out of rock: American Scientist, v. 58, p. 54–72. Relationships between experimental rock mechanics and structures we commonly observe in the field are presented, clearly, at the level of elementary structural geology. Laboratory techniques are explained in a way that clarifies the operation of rockmechanics experiments, the construction of stress-strain curves from experimental data, and the formation of many common structures. Jaeger, J. C., Cook, N. G. W., and Zimmerman, R. W., 2007, Fundamentals of rock mechanics, 4th edition: Oxford, England, Wiley–Blackwell Publishing, Ltd., 675 p. An excellent summary of the mechanical properties of rock materials presented somewhat as seen by an engineer, but is a very useful book for geologists. It contains numerous practical examples as well as clear discussions of behavior models for rock materials. Nicolas, A., and Poirier, J. P., 1976, Crystalline plasticity and solid state flow in metamorphic rocks: London, John Wiley & Sons, 444 p. This is a mathematically rigorous treatment of plastic behavior in rocks, but sections may yield some understanding of the plasticity of rocks without resorting to the mathematical statements. A feeling will also be gained of the inherent complexity of plastic deformation processes. Patterson, W. S. B., 1981, The physics of glaciers, 2nd edition: New York, Pergamon Press, 380 p. Shumskii, P. A., 1964, Principles of structural glaciology, D. Kraus translation of 1955 edition: New York, Dover Publications, 497 p. Both books survey glaciers and glacial ice, and each contains chapters on the ductile and brittle properties of ice. Shumskii includes photographs of glacial folds and other ice structures, the counterparts of which in rocks form only at great depths. Turcotte, D. L., and Schubert, G., 2002, Geodynamics: Applications of continuum physics to geological problems, 3rd edition: Cambridge, England, Cambridge University Press, 623 p. Mathematical treatment of elasticity and viscous behavior, written at a suitable level and with many worked problems. 8 Microstructures and Deformation Mechanisms Our discussion of stress and strain and ideal mechanical models for deformation in Chapters 6 and 7 provides a basis for exploring the microstructures and deformation mechanisms we actually observe in rocks (Figure 8–1), as well as some of the ideas that attempt to explain how The presence of dislocations in crystals was first proposed 30 years ago. . . . Today, an understanding of dislocations is essential for all those concerned with Starting material the properties of crystalline materials. Product Deformation mechanism Fragments of undeformed rock Cataclasis DEREK HULL, 1975, Introduction to Dislocations (a) Undeformed rock mass Slip along crystal boundaries Grainboundary sliding (b) Pressure solution Residues (stylolites or cleavage) (c) New, unstrained crystals Recrystallization (d) FIGURE 8–1 Common modes of deformation in rocks. (a) Cataclasis, involving crushing, fragmentation, and grain-size reduction of the original rock. (b) Grain-boundary sliding, producing deformation by grains sliding past each other. (c) Pressure solution, forming zones of residues where the rock has been dissolved. (d) Crystal-plastic deformation, involving partial to complete recrystallization of the rock, producing preferred orientation of minerals that may preserve old (but deformed) external boundaries, but internally consist of a mosaic of new unstrained crystals. 181 182 | Mechanics: How Rocks Deform deformation processes operate on the microscopic scale. Today we recognize the importance of temperature- and pressure-driven grain-scale mechanisms as we progress toward a more complete understanding of crust and mantle deformation processes. We have learned that rock deformation is also scale dependent; for example, microscopic-scale brittle fractures produce small incremental displacements of a layer that appears on the map scale as smoothly curved folds, giving the appearance of being the product of ductile deformation. The concepts related to the behavior of dislocations and deformation mechanisms developed in metallurgy, materials science, and solid-state physics have been successfully applied to geologic materials to enhance our understanding of rock deformation. The same deformation mechanisms identified in metals and ceramics occur in rocks, indicating that these phenomena are present in all crystalline solids. We have learned a great deal about deformation from studying simple monomineralic rocks (dunite, limestone, and quartzite), but most rocks are polymineralic. Rock mechanics structural geologists have the opportunity to add to the body of knowledge related to the behavior of defects and dislocations (imperfections) in polycrystalline anisotropic materials as well as the conditions that influence the behavior of deformation mechanisms, such as pressure solution. Although some studies of deformation processes have been made in polymineralic rocks, complete understanding of deformation processes in these materials remains in its infancy. In this chapter, we will see how rocks deform on a microscopic to submicroscopic scale, and then explore how microscopic-scale deformation is related to larger structures. When we understand the conditions that produce the variety of deformation mechanisms known to occur in natural rocks, we will be able to better deduce the conditions that affected an ancient rock mass that was deformed at great depths before erosion exposed it for us to study at the present surface. For example, some fault zones contain crushed and ground-up rocks (called cataclasite), whereas others may contain ductilely deformed rocks: the latter contain evidence of flow and reduced grain size (mylonite) and may be recrystallized. What different physical conditions produced fault zones that differ so markedly? What different behavior modes created these differences? Lattice Defects and Dislocations We commonly think of crystals in terms of groups of spheres in a convenient packing arrangement or as a series of lines wherein intersections are occupied by atoms, ions, or groups of atoms such as CO32− and SO42−, an obvious but convenient oversimplification. Regular geometric Unit cell (simple cubic lattice) (b) (a) Lattice FIGURE 8–2 (a) Crystal lattice (without atoms) and (b) simple cubic unit cell. Atoms or ions are red in (b). arrangement of atoms, ions, or groups in a compound is characteristic of a crystalline solid. A crystal lattice is a hypothetical representation of the arrangement of the constituents of a crystalline solid that permits us to describe the symmetry of the crystal structure (Figure 8–2). It consists of a three-dimensional array of intersecting lines that portrays the lattice as a series of parallelepipeds where the constituents (atoms, ions, groups) mostly occupy the intersections of lines (Hull and Bacon, 1984). These parallelepipeds form building blocks—repeat units—called unit cells. A crystal of a specific compound where all sites are filled with atoms, ions, or groups of the “correct” species, and which contains no interstitial atoms between lattice sites, is often called a perfect crystal. In the context of the hypothetical lattice, this is an orderly stack of unit cells. Ideally, perfect crystals exist only at 0° K (−273° C), where no thermal or other disturbances can affect the lattice. A halite lattice in which all the Na+ sites are occupied by Na+ ions and all the Cl− sites are occupied by Cl− ions at absolute zero is a perfect crystal. Such crystals are nonexistent in minerals and rocks; real crystals contain imperfections called defects. Defects are produced by: introducing different kinds of ions into the structure (such as K+ into Na+ sites or Br − into Cl− sites in halite), artificially making crystals in a laboratory or finding natural crystals with vacancies (unoccupied sites), changing the stacking order of layers, or otherwise distorting the lattice. Several kinds of defects have been described and categorized as point, line, surface (planar), and mixed defects. All these locally introduce imperfections to disturb the otherwise regular arrangement in a crystal. In the past few decades, technological uses of defects in crystal lattices have profoundly influenced the way we live. Mass-produced semiconductors made of high-purity silicon crystals manufactured (or “doped”) with carefully added compositional defects (such as phosphorus or boron) have led to universal adaptation of transistors, | Microstructures and Deformation Mechanisms Interstitial atom Vacancy Interstitial impurity Substituted impurity (a) 183 (b) FIGURE 8–3 (a) Vacancies and interstitial atoms. (b) Impurities in crystals. microprocessor chips, and other components of computers, smartphones, tablets, and other electronic systems that have become essential components of our modern world. In the natural world, knowledge of defects helps us to understand the varied ways rocks deform on microscopic and larger scales. Now we will examine crystal defects more closely. Point Defects Substitution or interstitial defects involving a foreign atom or ion in a lattice site, or a normal atom out of its proper place, may be introduced while a crystal is forming. Vacancies in a crystal may also be produced during ductile deformation, by irradiation by high-energy particles, and by sudden cooling of a crystal from high temperature 1 2 3 (Figure 8–3). An equilibrium concentration of vacancies will always occur at any temperature above absolute zero. In ionically bonded materials, substitution defects can be accommodated only if the charge balance is maintained, a factor relatively unimportant in metals, because of the nature of metallic bonding. Line Defects—Dislocations A dislocation is the line on a crystallographic slip plane that separates the slipped from the unslipped portion of a crystal (hence the name line defect). An edge dislocation is a line dislocation in which the slip sense across the crystallographic slip plane is perpendicular to the dislocation (Figure 8–4a). A screw dislocation is a line dislocation in which the slip sense across the crystallographic slip plane 1 4 B 5 6 A Sites of future dislocations (extra half planes) 2 3 B A C F C F D D E (a) (1) Unit cell 5 6 Positive edge dislocations (DC & EF) E H H G 4 (2) Reference lines G FIGURE 8–4 (a) Lattice before deformation showing (1) the site of a future edge dislocation and a unit cell (red line), and (2) simple shear-driven propagation of an edge dislocation outward produces a displacement equal to Burgers vector as the dislocation moves toward the margins of the crystal. (b) Right-handed screw dislocation, propagating downward. 184 | Mechanics: How Rocks Deform Screw dislocation slip direction Burgers vector Burgers circuit partial layer produces an edge dislocation (Figure 8–4a). The inserted layer is called an extra half plane. In real crystals, the extra half plane is produced by subjecting a crystal to simple shear, which is frequently encountered in nature, leading to distortion of the crystal so that part of a layer of atoms is isolated halfway between two undeformed layers. The dislocation nucleates as a small loop and propagates outward as the crystal is progressively deformed by simple shear (Figure 8–5). The term “line or edge dislocation” is derived from the location of the edge of the extra layer separating the dislocation from the undisturbed lattice. Edge dislocations are designated by if the dislocation is positive (the extra half plane lies above the reference line), and by T if the dislocation is negative (the extra half plane lies below the reference line). The other end-member type, called a screw dislocation, involves rotation about the dislocation line. The net result is that planes of atoms spiral around the dislocation line (Figure 8–4b). Screw dislocations are right-handed if the sense of rotation is clockwise (as seen looking down the screw axis from above; common wood screws have right-handed threads) and left-handed if the rotation is counterclockwise. A convenient means of describing either edge or screw dislocations is Burgers vector and Burgers circuit. Imagine a layer in a perfect crystal where a loop traverse is made from one site in the layer so that it returns to that site (Figure 8–6a). In a perfect crystal, the traverse should close precisely at the starting point. If the traverse encloses a dislocation, it will not close in the same distance as in the perfect crystal. The traverse, known as a Burgers circuit, requires that the traverse go an equal number of atomic units in each direction. The magnitude of the failure of the traverse to close in the same loop that surrounds a dislocation defines the unit shear or jump distance and direction of the dislocation, also defining a Burgers vector, b (Figure 8–6b). The Burgers vector of an edge dislocation is perpendicular to the line of dislocation; that of a screw dislocation (Figures 8–5a, 8–6, and 8–7) is parallel to the line of the dislocation (Hull and Bacon, 2001). Most dislocation lines are located at an angle to Burgers vector, giving them a mixed character, with an edge component and a screw component (Figure 8–5a). Dislocations in crystals may be best observed in extremely thin sections using the greater magnification of the transmission electron microscope (Figure 8–8). They were actually observed—but not understood—during the nineteenth century by examining etched surfaces of cleaved crystals with an optical microscope. Areas around dislocations are more soluble in acid because the crystal contains unrecovered elastic strain around the dislocation. A combination of grinding and etching steps (called “decorating”) T (b) FIGURE 8–4 (continued) is parallel to the dislocation (Figure 8–4b). Dislocations move sequentially and incrementally by displacing a single bond at a time in the crystal. A direct analogy with macroscopic faults exists where a fault propagates incrementally and recurrent motion occurs similarly. A comparison made by Price (1988) noted the similarity, although at vast scale difference, between a particular kind of dislocation with the generation, propagation of the tip, and subsequent motion of a thrust sheet. Small, outcrop-size faults may involve motion along the entire fault surface, but earthquake distributions on large faults clearly indicate that this motion occurs on only a small part of the entire fault. The larger the earthquakes, the larger the area of the fault surface is moved. All dislocations in crystals evolve from lines to closed loops. These loops have different characteristics ranging from nearly pure edge dislocations, described earlier, to uniformly mixed to nearly pure screw dislocations, depending on their propagation direction (Figure 8–5a). A dislocation begins as a line called a “Frank-Read source” that propagates with increasing shear stress until it forms a closed loop (Figure 8–5b). Loops formed in a common plane coalesce into edge, screw, or mixed dislocations and propagate through the crystal. A threshold length of a Frank-Read source exists at some critical shear stress τc, and the source is said to be activated at values of τ > τc. Making a hypothetical incision into a hypothetical crystal, partly separating two layers, and then inserting an extra Microstructures and Deformation Mechanisms Propagating screw dislocation 185 Displacement equal to Burgers vector Slipped crystal (no dislocations present) Propagating edge dislocation | Slip plane (a) τ τc τ > τc Time (b) (1) Edge Length Screw Screw lc Time (2) lc > l FIGURE 8–5 (a) Simple shear-driven propagation of slip in a mixed edge and screw dislocation. This process results in a displacement equal to Burgers vector as the dislocation moves through the crystal. Once the dislocation has propagated, the crystal lattice has slipped and it contains no dislocations in that region. (b) (1) Propagation of dislocations as Frank-Read sources. Think of this process as being analogous to blowing soap bubbles using a wire ring: the soap film stretches until it reaches a critical stress (τc) or length (lc). (2) The film forms an enclosed bubble that leaves the wire to become an independent feature, and the process is repeated. (Part b is modified from Jean-Paul Poirier, Creep of Crystals, 260 p., © 1985, reprinted with permission of Cambridge University Press.) made it possible to map the three-dimensional shapes of dislocations. Dislocations in some iron-bearing minerals, such as olivine, can be brought into view by heating at 900° C, long enough for some of the FeII to oxidize to FeIII along dislocations, making them visible under a standard petrographic microscope (Mackwell et al., 1985). Dislocation lines can end at crystal (grain) boundaries, but never within a crystal. They must either join or branch into other dislocations, or form lines or closed loops in the same crystal. Three or more dislocations meet at a point forming a node, and the Burgers vectors sum to zero at the node (Figure 8–8). 186 | Mechanics: How Rocks Deform Burgers vector (nonexistent here) Burgers circuit Point of emergence of edge dislocation Burgers vector b Undeformed crystal (a) Deformed crystal (b) FIGURE 8–6 (a) Cross section through a perfect crystal illustrating where Burgers vector would occur if the crystal were deformed. (b) Burgers vector in a crystal deformed by an edge dislocation. Note that to define Burgers vector, the traverse must involve an equal number of repeat intervals in each direction. Screw dislocation and slip direction Burgers vector Burgers vector = 0 b (a) (b) FIGURE 8–7 (a) Burgers vector for a screw dislocation. (b) Burgers vector for a perfect crystal for comparison (zero here). b2 b1 FIGURE 8–8 Several oppositely oriented Burgers vectors meet at a node and sum to zero. (Reprinted with permission from D. Hull and D. J. Bacon, Introduction to Dislocations, 3rd edition, © 1984, Pergamon Books Ltd.) b1 + b2 + b3 = 0 b3 b1 b2 b3 Microstructures and Deformation Mechanisms | 187 FIGURE 8–9 Dislocations in experimentally deformed synthetic quartz under the transmission electron microscope. Width of field is approximately 2 µm. Note the concentration (pinning) of some dislocations around fluid inclusions (red arrow). (John W. McCormick, SUNY College at Plattsburgh.) FIGURE 8–10 Dislocations piled up at a barrier (red arrow) in experimentally deformed synthetic quartz under the transmission electron microscope. Width of field is approximately 2 µm. (John W. McCormick, SUNY College at Plattsburgh.) Measuring dislocation density in a series of grains deformed by mostly dislocation glide (without climb) can be used to indicate the magnitude of differential stress affecting the crystal. Sometimes it is useful to construct dislocation maps of the distributions and kinds of dislocations in crystalline solids. A saturation limit can be reached in most crystals; then dislocations from several different slip systems, or planes, become entangled, and no more dislocations can form in that part of the crystal (Figure 8–9). Slip systems consist of combinations of specific crystallographic planes with crystallographic directions in each plane; active slip systems in crystals require minimum energy to cause displacement (Hobbs et al., 1976; Nicolas, 1987). Dislocations, after they are formed, may be thermally annealed out of a crystal by nucleation of new and unstrained crystals that replace the old strained configuration. Annealing is accomplished by the dislocation glide and climb, annihilation, and grain-boundary formation and migration mechanisms of recrystallization. Dislocation glide and climb, and annihilation may also be active without accompanying recrystallization. (Recrystallization mechanisms are discussed later in this chapter). Tangles and pileups of dislocations at impurities in the crystal may inhibit but not prevent complete annealing (Figure 8–10). Planar Defects—Stacking Faults Among the most common planar defects in isometric crystals are stacking faults, which consist of irregularities in the repeat order in a series of layers in a lattice (Figure 8–11). If a lattice has a repeat sequence between layers of ABAB (only two kinds of layers), the sequence can alternate in relatively few ways, and stacking faults can occur only if the repeat order is ABBA or BAAB. If the normal repeat sequence among layers is ABCABC (three kinds of repeat units), possibilities exist for locally changing the stacking order. If part of a layer is left out in a face-centered cubic lattice, so that part of the crystal has the stacking order ABCABABC . . . or ABCABACABC . . ., a local discontinuity results, giving rise to two kinds of stacking faults (Figure 8–11). Additional possibilities for stacking faults also exist. 188 | Mechanics: How Rocks Deform may be produced artificially in some crystals, such as Iceland spar calcite, by inserting a knife blade parallel to the 0112 plane of the negative rhombohedron (Figure 8–14). Mechanical twinning also occurs in plagioclase twinned on the albite and pericline systems (Borg and Handin, 1966; Borg and Heard, 1970). For a more complete discussion of mechanical twinning and slip systems, see Passchier and Trouw (2005). C B A B A C B A C A B A C Deformation Mechanisms FIGURE 8–11 Two kinds of stacking faults (red dashed). Translation (Dislocation) and Twin Gliding Deformation may occur in a crystal by homogeneous simple shear that causes movement of a dislocation located parallel to an existing crystallographic plane (Figure 8–12). This kind of deformation is called translation (dislocation) gliding, or mechanical crystal plasticity (Knipe, 1989), and the specific planes along which offset occurs are called “slip systems.” Slip may occur on the 0001, 1011 and other planes in quartz (Christie et al., 1964; Carter, 1971); the 1011, 0221, and other planes in calcite (Turner et al., 1954); the 010 plane in plagioclase (Seifert, 1965); the 001 plane in the micas (Etheridge et al., 1973); and the 0kl, 110, and 010 planes in olivine (Raleigh, 1965; Carter and Avé Lallemant, 1970). Deformation of crystals may also occur by homogeneous simple shear that produces deflection slip of less than one repeat interval along crystallographic planes, producing shear-induced twinning of the crystal—another form of translation, called twin gliding (Figure 8–13). Twin gliding Factors that determine which deformation mechanism will dominate are temperature, total stress, differential stress, fluid pressure, composition, grain size, texture, and strain rate (not all are independent variables). Deformation mechanisms (Figure 8–15) will be discussed here in order of dominance with increasing temperature. Structural geologists use microstructures that form under specific physical and chemical conditions as a guide to the active deformation mechanisms in particular minerals. Cataclasis Brittle deformation is concentrated in a rock mass along movement surfaces that have no cohesion—surfaces that separate undeformed parts of the rock mass. The product of this process is the cohesive rock cataclasite. This type of deformation, called cataclasis, is characterized by megascopic breccias (breccias with visible fragments), gouge (very fine-grained rock in a brittle fault zone), fractures and faults, microbreccias, and microfractures (Figure 8–16). Cataclasis produces brittle granulation of rock at low temperature and low to moderate confining pressure (near-surface conditions) but may be facilitated by high fluid pressure. Also, where strain rate is high, Glide plane FIGURE 8–12 Translation gliding. Twin band FIGURE 8–13 Twin gliding. 0112 plane FIGURE 8–14 Mechanical twin of a cleavage rhomb of calcite produced by inserting a knife blade parallel to the 0112 plane. The twin is the small upturned corner close to the pencil point (white arrow). Microstructures and Deformation Mechanisms Temperature (° C) High strain Differential Stress (σd) Fracture and cataclasis rate Dislocation creep Dissolution creep (pressure solution) w Lo High in rate stra Volume diffusion creep Grain-boundary sliding Low High Melting Low FIGURE 8–15 Generalized deformation mechanism map illustrating the relationship between temperature, differential stress, and deformation modes. failure occurs under brittle conditions by exceeding the elastic limit of the material. Cataclasis occurs mostly at low temperature within a few kilometers of the surface, but feldspars, garnets, and a few other minerals undergo cataclasis at high temperatures (500–1,000° C). In contrast, under conditions of moderate to low strain rate and temperatures of 300–800° C, feldspars (commonly above 450° C) and garnets deform by cataclasis, but quartz, calcite, and many other minerals deform ductilely and undergo recrystallization. Total volume of rock may be reduced by closer packing of grains (that closes larger Pure shear or 189 open spaces between grains) and by recrystallization that produces denser minerals. Fracturing and granulation, on the other hand, increase volume by creating pore space where none existed before, and also increase exposed surface area, making recrystallization and chemical/metamorphic reactions proceed more readily. Some map-scale fault zones contain rocks that resemble ductilely formed fault rocks (mylonite), but microscopic examination reveals that deformation was brittle and that the rock was granulated frictionally to a very fine powder of unaltered grains (Figure 8–17). Apparent flow of finegrained material produced by brittle deformation is called cataclastic flow. The process may also describe large-scale changes in shape due to small-scale brittle fracturing. Apparent megascopic ductile behavior shown to be brittle (cataclastic flow) on the microscopic scale is sometimes called triboplastic behavior; it has been observed at shallow depth where rocks have been ground to fine grain size (gouge) during motion along a fault. Dolomite or other rocks of high mechanical strength on both sides of a fault may produce triboplastic cataclasite at low temperatures. Creep Processes Creep processes depend on strain rate, but the amount of strain is not limited by strain rate. These are also known as diffusional mass transfer processes (Knipe, 1989). Creep mechanisms may involve mass transport or diffusion of atoms or ions at grain boundaries, including pressure solution, climb of dislocations within a lattice, and diffusion of point defects through lattices. Each is a separate mechanism that is most efficient over a particular range of temperature, Deformation occurs on discrete surfaces that separate undeformed rock Solid rock mass | Fragments preserve the original texture and composition of the starting material Low T Solid rock mass Simple shear P FIGURE 8–16 Cataclastic materials and behavior. Cataclasis is fundamentally a process of making larger objects into smaller ones through brittle deformation. 190 | Mechanics: How Rocks Deform 4 0 centimeters FIGURE 8–17 Mesozoic cataclasite from a brittle fault in sandstone in northern Virginia. The light-colored matrix between the darker sandstone fragments consists of fine-grained, pulverized quartz derived from decreasing the grain size of sandstone from the larger angular fragments by cataclasis. pressure, and grain size. These processes also overlap and compete with one another under the right conditions so that more than one mechanism may occur simultaneously, although one usually dominates. Creep is a slow process but may result in large strains if it occurs over a long time interval, as with mantle convection. Because these mechanisms occur over a range of conditions, it is useful to plot their occurrence on deformation maps (Figure 8–18). These maps contain experimentally determined ranges of occurrence of several mechanisms for particular rock types or minerals together with the boundaries calculated using the appropriate flow law governing each process that can be expressed in terms of differential stress, strain rate, and temperature, along with several constants. Note that all of the flow equations that follow relate strain rate to differential shear stress and temperature, and contain several constants that are specific for the material being deformed. Thus flow laws simply express the rate of strain relative to increasing temperature and differential shear stress. These mechanisms are sometimes referred to as s because they operate above threshold values of pressure and temperature. When initiated, they continue unchecked until a competing mechanism becomes more efficient as temperature or pressure—or both—increase, or the fluid supply is exhausted (for pressure solution), or until the energy supply is exhausted. They are also considered to be steady-state processes because we do not yet know about critical changes in variables such as dislocation density, unit cell size, and grain size during deformation, so they are assumed to cancel each other—hence, steady state. PRESSURE SOLUTION The phenomenon of pressure solution was first recognized in the mid-nineteenth century by Henry C. Sorby (1826–1908), the English geologist who pioneered microscopic petrography and made several important contributions to structural geology. Pressure solution consists of dissolution, under stress, of soluble constituents such as calcite or quartz, and is generally active at low to moderate temperature (< 350° C) in the presence of water. The process is limited by the requirement of water between grains. Microstructures and Deformation Mechanisms 2 4 11 12 Dislocation glide 13 4 0 Dislocation creep 2 4 8 6 10 14 Pressure solution Coble creep 15 6 2 7 15 16 0 400 Nabarro-Herring creep 13 12 11 10 800 T° C 9 8 0 KD gb ΩCo x 3kT ρ ττd , (8–1) where ε̇ is strain rate, K is a material constant, Dgb is the coefficient of grain-boundary diffusion, Ω is molar volume, Co is concentration of the solution outside the grain boundary, x is grain size, k is Boltzman’s constant, T is absolute temperature, ρ is density, and τd is differential (shear) stress. Raj (1982) modified Rutter’s flow law by assuming the solute is transported by diffusion through a σ1 191 FIGURE 8–18 Deformation mechanism map for calcite, showing the different mechanisms that affect it at various temperatures and stresses. Contours (gray lines) are negative log strain rate per second. Vertical axis is in units of (negative log of) differential stress (Chapter 5) divided by the square root of 3 times the shear modulus (left vertical axis) or (log of) differential stress divided by 105 Pa at 500° C (right vertical axis). Thus the left axis numbers decrease upwards as differential stress increases (contrast with the right axis). Note that differential stress increases upward, so the highest-numbered contours represent the slowest strain rates. (After E. H. Rutter, 1976, Philosophical Transactions of the Royal Society of London, v. 283.) 1200 After the water is lost, pressure solution ceases to occur. Pressure solution is commonly viewed as a stress-induced diffusion-flow process (Wheeler, 1991). Rutter’s (1976) flow-law equation attempts to define most of the variables related to the process, and assumes Newtonian behavior: ε̇ε = | liquid film along grain boundaries. It employs an “islandchannel” model for grain boundaries and the pressure solution process: ε̇ε = K ΠfhΩ Dc τdd(8–2) x 3kTb where Π is the mathematical symbol for product, f is the area fraction of grain boundaries occupied by islands, h is the grain boundary thickness, D is diffusivity of the solute in the fluid phase, c is mole fraction of solute dissolved in fluid, and b is the “jump distance” in the diffusion process. Parts of quartz, calcite, or other soluble mineral grains may be dissolved at points of greatest stress, where one crystal touches another. Dissolution begins at these points of high stress (Figure 8–19a). Minerals dissolved Points of high stress at contact points between sand grains Dissolved surfaces (stylolites) 0.05 mm (a) (a) (b) FIGURE 8–19 (a) Grains dissolve first at points of high stress. Note that the scale changes from before to after deformation. (b) Partly dissolved quartz grains along mica-rich slaty cleavage surfaces produced by pressure solution in Martinsburg Slate, Delaware Water Gap, New Jersey. Width of photograph is approximately 1.5 mm. Plane light. (Thin section courtesy of Timothy L. Davis, Marathon Petroleum Company.) 192 | Mechanics: How Rocks Deform by pressure solution are commonly precipitated in zones of lower pressure as overgrowths and fibers in pressure shadows, deposited in veins, or remain in solution and are completely removed from the region undergoing deformation. Parts of original grains, along with any reprecipitated material, may survive as evidence of pressure solution. In addition, residues of insoluble materials, including clays, micas, and opaque minerals, are commonly left behind on pressure-solution surfaces (Figure 8–19b). Pressure- solution surfaces appear to develop best in slightly impure carbonate rocks rather than in pure limestone (Marshak and Engelder, 1985). Fine (or mixed) grain size and impurities, because of greater surface area and compositional differences, initiate pressure solution more readily than coarser grain size and greater purity in carbonate or clastic rocks. Pressure solution occurs during diagenesis, particularly during compaction and cementation of carbonate sediments where stylolites—irregular surfaces coated with insoluble minerals—may form parallel to bedding (Figure 8–20), indicating that the maximum stress (overburden pressure) was vertical. Stylolites also form during deformation of carbonate rocks and sandstone perpendicular to the direction of applied tectonic stress, with the orientation of the “teeth” of the stylolites perpendicular to the plane of the stylolite, providing a more exact indicator of the orientation parallel to σ1. The dark irregular surfaces (lines resembling graphs in cross section) that mark stylolites are insoluble minerals that remain after soluble minerals have been dissolved by pressure solution. Tectonic stylolites (Figure 8–20c) may sometimes be distinguished from stylolites formed during diagenesis if one set is subparallel to bedding (generally diagenetic) and others are at moderate to high angles to bedding (generally tectonic). Pressure solution may proceed grain by grain without formation of stylolites if the rock mass is water- saturated and is sufficiently porous. Most porosity in a rock mass tends to be concentrated along bedding and fracture planes; pressure solution begins there, and stylolites form along existing surfaces. Preferential dissolution will occur along favorably oriented surfaces, perpendicular to the maximum principal stress. Pressure solution may occur at high confining pressure and elevated temperature in both fine clastic and carbonate rocks where carbonate minerals and quartz are dissolved. It can be the dominant process up to 300° C (Rutter, 1976, 1983) and can reduce rock volume by as much as 50 percent if the system is open and dissolved constituents can escape (Wright and Platt, 1982). In the past, it has been difficult to understand the transport mechanism of dissolved constituents, given the low solubilities of quartz and calcite at surface conditions. It is now known, however, that during an orogeny, huge volumes of fluid are forced by deformation to move outward from the hotter inner parts of an orogen toward the cooler external parts. In the process, large quantities of quartz, calcite, metals, and hydrocarbons are dissolved and transported (Oliver, 1986). Veins composed of fibrous calcite, quartz, or other lowtemperature minerals developed on bedding or foliation planes (Figure 7–9) or in vein arrays parallel and oblique to bedding may indicate excess fluid pressure during deformation (Cosgrove, 1993). In many areas, pressure solution is the dominant mechanism that produces slaty cleavage (Chapter 18). Irregular dissolution surfaces develop into discrete cleavage planes at increased pressure (20–40 MPa) and temperature (300–400° C) as deformation progresses. These surfaces form the well-developed slaty cleavage common in zones of low metamorphic grade. Direct evidence of pressure solution may be observed in thin sections as mica or quartz “beards” on larger grains (Figures 8–19b, 8–20, and 8–21), on partial grains (Figure 18–22), and as zones of insoluble residues developed subparallel to each other (Figure 18–20c). Material dissolved in zones of high stress is frequently precipitated in veins that fill fractures in zones of extension in the same rock mass (Figure 8–20c). Fractures are commonly the sites for deposition of dissolved constituents, forming veins—particularly where fractures formed by extension remain open, or are forced to form under the influence of high-pressure fluids. Direct correlation generally exists between the composition of veins and the t emperature—metamorphic grade—of the enclosing rocks during deformation, except in rock masses uniformly affected by hydrothermal alteration and ore mineralization. Calcite and zeolite (± calcite) veins (frequently with prehnite) occur at the lowest temperatures. Calcite-quartz, then quartz-epidote and quartz-feldspar veins occur at progressively higher temperatures. At the upper end of the temperature range, deformation by diffusion processes (to be discussed) dominates in the rock mass, but water still moves and transports materials in solution that may be precipitated in zones of low pressure (Figure 8–20c). Composite veins containing fibrous crystals and multiple mineral assemblages may document a history of repeated extension (Chapter 6) and a range of precipitation temperatures (although veins may also be the product of simple shear deformation). GRAIN-BOUNDARY DIFFUSION CREEP (COBLE CREEP) This process involves thermally driven diffusion mass transport along dry grain boundaries. Coble creep occurs at low to moderate temperatures, but below 400° C is Microstructures and Deformation Mechanisms | 193 (b) (a) (c) FIGURE 8–20 (a) Stylolites subparallel to bedding in Tymochtee Dolomite, northwestern Ohio. Smaller stylolites are oblique to bedding. (b) Styolites parallel to bedding in Massanutten Sandstone, northwestern Virginia. Width of photograph in both (a) and (b) is approximately 7 mm. Plane light. (Charles M. Onasch, Bowling Green State University.) (c) Negative print in plane light of a thin section of a folded oölitic limestone in the Nolichucky Shale (Upper Cambrian) from Melton Valley near Oak Ridge National Laboratory. Tectonic stylolites (white) are developed parallel to the axial surface of the fold (perpendicular to maximum compression), and calcitefilled tension veins (dark gray to black) formed mostly perpendicular to the stylolites. Veins that formed subparallel to the stylolites are later veins. Note the development of fine stylolites around the edges of oöids with minimal dissolution and thicker better-developed stylolites that have dissolved major parts of oöids. Width of field is approximately 2 cm. 194 | Mechanics: How Rocks Deform FIGURE 8–21 Mica beards formed parallel to slaty cleavage on an ankerite grain in fine-grained W ilhite Formation siltstone near Tellico Plains, Tennessee. Note the faint spiral p attern in the interior of the ankerite c rystal. Width of ankerite porphyroblast is approximately 1 mm. Crossed polars. FIGURE 8–22 Annealed mineral assemblage in a thin section of recrystallized Mt. Athos Quartzite from the Central Virginia Piedmont. Most grains are quartz with a few grains of plagioclase. Note that many quartz grain boundaries meet at 120° angles. Width of photograph is approximately 3 mm. Crossed polars with gypsum plate inserted. overwhelmed by pressure solution. Above 400° C, Coble creep becomes dominant where the diminished amount of water makes pressure solution less efficient and the additional heat energy accelerates the diffusion creep process. A flow law that describes Coble creep is where ε̇ is strain rate, δ is grain-boundary thickness, τ is shear stress, Ω is atomic volume, d is spacing of edge dislocations, k is creep rate, and T is absolute temperature (Poirier, 1985). DISLOCATION CREEP εε̇ = 141D gb δδτΩ τΩ d 3kT (8–3) Dislocations are a manifestation of strain through a combination of glide and climb motion of the dislocations through Microstructures and Deformation Mechanisms the crystal, driven by heat and pressure. This process occurs at moderate to high temperatures as dislocation creep, beginning at temperatures where calcite and quartz will undergo recrystallization: 200–350° C. Dislocation creep is a two-step process that includes both strain and accommodation of the lattice to strain; the glide of dislocations (strain) is accommodated by either recrystallization or dislocation climb (recovery). A flow law for dislocation creep is  Q  −  nn  RT  εε̇ = εε̇0 τ e (8–4) where ε̇ is the initial strain rate for the crystal being deformed, n is the stress exponent defined as (d ln ε̇/d ln τ), Q is the apparent activation energy for the process, and R is the universal gas constant (1.987 cal deg-1 mol-1) (Poirier, 1985). Dislocations are constantly produced and migrate through a grain as the rock is strained, causing each grain to change shape as it deforms and as chemical bonds are rearranged. Dislocation glide does not require creep to occur, nor does climb of dislocations necessarily accompany glide. Minerals may be deformed by glide only, leading to formation of tangles of dislocations, deformation lamellae, and undulatory, patchy, or sweeping extinction under the microscope. Climb involves the reorganization of dislocations and may decrease dislocation density by formation of low-angle (subgrain) boundaries (see later in the chapter). Climb of dislocations is thermally driven and thus is more efficient at higher temperatures. Dislocation creep produces grains that either contain fewer dislocations or have a time-invariant (on average) dislocation density, which is related to the magnitude of the applied stress. At the low-temperature end of the process, because dislocation creep is temperature dependent, dislocations may become pinned at grain boundaries. As a result, the rock mass becomes strain hardened (Chapter 7), and greater stress is required to increase the amount of strain. Strain hardening may also be produced by interference of dislocations. In contrast, cataclastic flow may be accompanied by pressure solution that enhances sliding along irregular grain boundaries at low temperature, and, because it produces finer grains, it is a strain-softening process. At higher temperatures (greater than half the absolute melting temperature), thermal energy permits dislocations to bypass obstacles by climbing to a parallel lattice plane. Dislocations may be annihilated by the same process, thereby reducing the number of dislocations and internal strain in the crystal, with recrystallization being the result. This is the most common plastic-flow process that leads to recrystallization in rocks at moderate to high temperatures (Kerrich and Allison, 1978) (Figure 8–22). VOLUME-DIFFUSION (NABARRO-HERRING) CREEP Another process involving diffusion of lattice defects is volume-diffusion or Nabarro-Herring creep, which | 195 involves diffusion of point defects (vacancies) through crystals toward points of high stress and occurs at high temperature and low differential stress. It is a very slow process, even at high temperature, and is not considered an important deformation mechanism in crustal rocks. A flow law describing Nabarro-Herring creep is ε̇ε = α Dsd ττΩ Ω d 2 kT (8–5) where α is a factor determined by grain shape and the boundary conditions of deformation, and Dsd is the coefficient of self-diffusion of the crystal (Poirier, 1985). GRAIN-BOUNDARY MIGRATION AND SLIDING Movement of grain boundaries can occur either in the plane where they reside (sliding) or perpendicular to the plane (migrating). The slip of grains past one another, analogous to the frictional process of sand grains or ball bearings moving aside when a stick is pushed into them, is an important deformation mechanism in rocks. It is a sliding process that implies no cohesion on grain boundaries. It is accompanied by other processes, such as Coble creep and grain-boundary migration at moderate to high temperatures, and is restricted to high-angle boundaries. This nonfrictional mechanism is called grain-boundary sliding. A single grain in a rock being deformed by a creep mechanism will behave like the entire mass of grains; if the mechanism is grain-boundary sliding, a single grain will maintain its initial shape even though the shape of the aggregate changes significantly. Cataclastic flow at low temperatures is an analogous (but not identical) frictional mechanism occurring in fault zones where grains move past one another under simple shear. Grain boundary migration is a fundamental kind of dynamic recrystallization in rocks. It leaves behind grains containing few (or no) dislocations. Grains are consumed that contain many dislocations and thus have higher free energy—the energy available to do work—that lie in the path of a migrating boundary. This describes the process of straininduced grain-boundary migration. Other processes may produce stress-induced grain-boundary migration by an excess of elastic strain energy being stored in a crystal, or a diffusioninduced grain-boundary migration by differences in chemical potential between individual grains (Poirier, 1985). Superplastic Flow Superplasticity is a term used to describe a macroscopic behavior that results from sliding along grain boundaries and probably involves both Coble creep and grain-boundary sliding (Nicolas, 1987). It was first observed as a phenomenon of extreme ductility in certain fine-grained alloys undergoing deformation in high-temperature uniaxial tension experiments. Elongation strains of 1,000 to 2,000 percent have 196 | Mechanics: How Rocks Deform been observed in some alloys. Superplastic flow in metals is thought to occur by a combination of grain-boundary sliding (to provide the large strains) locally accommodated by diffusion creep (to provide a shorter diffusion path), because other slower processes would not permit the phenomenon to occur at finite rates (Poirier, 1985). Superplastic flow is thought to occur at temperatures greater than half the absolute melting point in coarsegrained rocks (Boullier and Gueguen, 1975). In contrast, the mechanism has also been reported in fine-grained rocks (average grain diameter 10 mm or less) at low temperatures under a strong component of inhomogeneous simple shear, as occurs in fault zones (White and White, 1980). As indicated by the diversity of ideas just cited, superplastic flow of geologic materials may occur under a variety of conditions involving a combination of deformation mechanisms. Deformation producing a decrease in grain size at low temperature to the critical 10-mm size may enable strain rate to increase dramatically as grain- boundary sliding is initiated with no change in temperature. At high temperatures (> 0.5 Tm), grain-boundary sliding and dislocation creep, or grain-boundary diffusion, may produce superplasticity (Kerrich and Allison, 1978). Geochemical Processes The vast majority of crustal rocks are composed of eight elements: O, Si, Al, Fe, Ca, Na, K, and Mg. Understanding the chemical behavior of these elements in rocks and fluids FIGURE 8–23 Highly deformed garnet (dark red) with muscovite and quartz pressure shadows developed on both ends. Sample from the eastern Blue Ridge, North Carolina. Crossed polars with gypsum plate inserted. during deformation and metamorphism is important for structural geologists. Oxygen and silicon are the most common elements and bond together to form the ubiquitous silica tetrahedron, which collectively bonds with the other six cations to form the wide variety of silicate minerals. Chemical processes are frequently coupled to deformation and have a direct influence on the kinds and shapes of structures that form in a rock mass. Conversely, deformation and deformation rate can affect the rates of chemical reactions. Mass-Transfer Processes Mass transfer involves the movement of material— elements, ions, minerals, or mineral aggregates—in a rock mass. Material may be added or removed locally by several processes that may become more efficient during deformation. PRESSURE DISSOLUTION Pressure dissolution, formerly called pressure solution (discussed earlier), involves dissolution of minerals at points of contact under compressional stress, and is accompanied by either complete removal of the dissolved material from a rock mass or re-precipitation into nearby veins or even more locally as pressure shadows adjacent to hard objects like pebbles, or garnet and magnetite crystals (Figure 8–23). In addition, insoluble constituents accumulate along surfaces where dissolution has occurred. Stylolites (Figure 8–24) are irregular surfaces coated with Microstructures and Deformation Mechanisms | 197 FIGURE 8–24 Stylolites in coarsegrained limestone (“Tennessee Marble”) composed of calcite— cemented fossil fragments. These stylolites formed during diagenesis. Sample from near Lenoir City, Tennessee. (RDH photo.) insoluble or residual minerals, and these structures provide tangible evidence of dissolution. The dissolution reaction of minerals such as calcite and quartz in the presence of an aqueous fluid is given by 2CaCO3 + H2O + CO2 ↔ Ca+2 + 2HCO3− calcite water dissolved calcium carbon dioxide ion SiO2 + quartz 2H2O ↔ water bicarbonate ion H4SiO4 silicic acid. Pore space σ1 Dissolution occurs here (8–6) (8–7) The left side of equations 8–6 and 8–7 describes the solid minerals, calcite and quartz, and the reactants, water and/or CO2, whereas the right side depicts the dissolved phases. Pressure dissolution at points of contact (Figure 8–25) forces the reaction to the right; decrease in pressure forces the reaction to the left and calcite or quartz precipitates again. These reactions proceed slowly at room temperature, but rates are more rapid at elevated temperatures (200–300° C). At higher temperatures (> 300° C) other processes, such as recrystallization, become more efficient than pressure dissolution in affecting changes in a rock mass. There is also less water available at elevated temperatures. Pressure dissolution is a very important geologic process that occurs under conditions that range from those accompanying diagenesis in depositional environments to the temperatures where rock masses are being metamorphosed and recrystallization becomes dominant. Precipitation occurs here FIGURE 8–25 Pressure dissolution and precipitation in millimeter-size sand grains. Factors like grain size and mineral composition of a rock also affect the rate and efficiency of the pressure dissolution process. Finer-grained rocks, particularly those containing appreciable quantities of fine- to clay-size calcite or quartz and clay minerals, have greater surface area and will dissolve more readily than a coarser, purer rock mass. Marshak and Engelder (1985) showed that impure marls in the Hudson River fold belt in New York are more susceptible to pressure dissolution than coarser-grained limestones in the same area that contain fewer impurities. 198 | Mechanics: How Rocks Deform than the feldspar and thus deformation is facilitated by the change in mineralogy. This behavior is an example of strain softening (see Chapter 7). m af af VOLUME LOSS q Other pressure dissolution reactions are more complex; for instance, under greenschist facies conditions Kfeldspar reacts with water to form muscovite and quartz (Figure 8–26) and K+ ions are removed from the system If mobile elements are removed from the rock system via pressure dissolution or other chemical mass transfer processes, the rock mass undergoes a loss of volume. One way to evaluate volume loss in a rock system is to compare the mineralogy and chemistry of an undeformed (or weakly deformed) protolith with its deformed equivalent. As soluble minerals and elements are removed via pressure dissolution, the concentration of insoluble minerals and elements increases in the deformed rock (Figure 8–27a). In carbonate rocks, clay minerals and iron oxides are conserved while calcite and dolomite are preferentially removed. Volume loss can even occur in granitic rocks deformed in shear zones. Volume loss can be quantitatively evaluated by comparing the concentrations of immobile elements, such as Al, Ti, P, Mn, Zr, and Y in the deformed rock (A) with those in the protolith (B) via the following relationship: 3KAlSi3O8 + H2O ↔ KAl2(AlSi3O10)(OH)2 + 6SiO2 + 2K+. (8–8) A/B = 1/(1 + Δ),(8–9) This reaction occurs along the surface of the K-feldspar that, under greenschist facies conditions, behaves as a brittle material. But as deformation progresses and the Kfeldspar fractures, commonly along cleavage planes, more surfaces are exposed to fluid and fine-grained muscovite and quartz are precipitated. These minerals are weaker where Δ represents bulk-rock volume change (if Δ = 0 there is no volume change and if Δ < 0 there is volume loss). A graphical means of evaluation is given by plotting the concentration of conserved elements for the deformed rock versus its protolith (an isocon diagram of Grant, 1986) and using the slope of best-fit line as (A/B) and then solving for Δ (Figure 8–27b). m FIGURE 8–26 Muscovite (m) and quartz (q) formed from the breakdown of K-feldspar (af) in a greenschist facies mylonite from the Blue Ridge province, Virginia. (CMB photo.) K-feldspar water muscovite quartz 20 Undeformed limestone Deformed limestone 90% calcite (50% volume loss) 80% calcite 4% clays 4% quartz 2% Fe-oxide (a) 8% clays 8% quartz 4% Fe-oxide e= op 15 Sl Deformed rock (A) 1.4 1 (no volume loss) 20MnO 50ZrO2 10 A/B = 1/(1 + ∆) ∆ = (1/(A/B)) – 1 5TiO2 5 ∆ = (1/1.41) – 1 ∆ = –0.29 3P2O5 0 (b) 2Al2O3 0 5 10 15 20 Protolith (B) FIGURE 8–27 (a) Schematic illustration of soluble minerals and insoluble minerals in undeformed limestone and after 50 percent volume loss in deformed limestone. Note that with a 50 percent volume loss the percentage of the insoluble minerals doubles in the deformed limestone. (b) Isocon diagram comparing amount of insoluble elements in the protolith (B) versus the deformed rock (A). The slope of the best-fit line is used to determine the volume loss (∆). Microstructures and Deformation Mechanisms KAl2(AlSi3O10)(OH)2 + DEHYDRATION Dehydration involves expulsion of water from a rock mass, which can happen during deposition and compaction of sediment and continue during cementation as pore spaces between grains are filled with minerals. Additional water is expelled as pore space decreases during compressive deformation. As burial depth increases, pore space continues to decrease and clay minerals with open structures, such as the montmorillonite group (e.g., smectite), which contains loosely bonded water between the layers in the crystal lattice, begin to expel water. This slowly changes the crystal structure with increased burial and deformation first to a more ordered clay mineral, illite, and then with increasing temperature to a more stable crystal structure forming muscovite. All of this occurs at temperatures ranging from those at the Earth’s surface to temperatures approaching 300° C. | 199 SiO2 → muscovitequartz Al2SiO5 + KAlSi3O8 + H2O sillimanite K-feldsparwater (8–11) METASOMATISM Water continues to be expelled from hydrous minerals, such as chlorite, in regional metamorphic rocks as temperature and deformation increase through the greenschist and into the amphbolite facies. Most hydrous minerals, including muscovite, break down under the highest temperature-pressure conditions of the amphibolite facies, with the only hydrous mineral that survives into the granulite facies being biotite. Rocks that have undergone a chemical transformation so that the original rock mass (paleosome) is partially or completely replaced by new material (neosome) underwent metasomatism. Metasomatism related to high temperature deformation processes in the presence of water and the formation of migmatite (mixed rocks formed by partial melting) is important in the study of the interior parts of most mountain chains where middle to lower crustal rocks are exposed (Figure 8–28). Rocks that have been metasomatized under high-grade regional metamorphic conditions commonly contain increased amounts of feldspar and decreased amounts of biotite and hornblende. Replacement that occurs with metasomatism involves grain-boundary migration as one phase replaces another. The mechanisms by which this process takes place have been debated for decades, and are still not well understood. Presence of trace amounts of fluids along grain boundaries and heat help drive the process as well, but there is an inverse relationship between available heat and fluids like water. This is demonstrated by the fact that, under higher temperature metamorphic conditions, fewer and fewer hydrous phases are stable. Many of the rocks present in high temperature regional metamorphic assemblages are described as being residues (restites) from former more water-rich assemblages. (a) (b) (Al,Mg)8(AlSi3O10)3(OH)10· 12H2O → smectite KAl2(AlSi4O10)(OH)2 + H2O illite (clay mineral) KAl2(AlSi3O10)(OH)2 + H2O muscovite → (8–10) FIGURE 8–28 Biotite gneiss migmatite in Bear Creek, near Jackson, Georgia. (a) Light layers are granitic, probably derived from melting of the biotite gneiss (originally a graywacke) during deformation and metamorphism. (b) Marker pen lines drawn on the rock surface in (a) identify some of the granitoid melt in the more biotite-rich components. (RDH photos.) 200 | Mechanics: How Rocks Deform Movement of material during metasomatism and migmatite formation aids the deformation process by enhancing the plasticity of the rock mass and providing lubrication of grain surfaces during folding and formation of foliations. Melt composition of at least 7 percent is a threshold for fluid (viscous) behavior in a rock mass at high temperature (Rosenberg and Handy, 2005). In rocks of granitic composition, the first vestiges of melt may form under saturated conditions at temperatures as low as ~650° C; under anhydrous conditions, minimum melts form at higher temperatures. Factors That Influence the Rates of Chemical Reactions Rates of chemical reactions in rocks range from almost instantaneous to incredibly slow. Think about chemical precipitation of calcite between sand grains to form a cement in sediment buried beneath the sea floor and the chemical precipitation of quartz and feldspar in veins at high temperatures. Temperature is the most obvious influence on reaction rate, but presence of fluids can greatly accelerate reaction rates to precipitate or alter one mineral to another at the same temperature. Pressure or stress can also influence reaction rates. A good example is dissolution of quartz or calcite at points of high stress in a rock and deposition in regions of lower stress (Figure 8–25). Grain size is another factor that can have a profound influence on reaction rate. Rocks made of fine-grained minerals recrystallize more readily, but the process is much slower in coarse-grained rocks, even with fluids present. Chemical reactions are facilitated by the presence of water and other fluids. As rates of chemical reactions increase, material is more readily transferred in or out of the rock mass, and deformation is enhanced. At elevated temperatures water is driven out of a rock mass. Processes that depend on abundant water become less efficient at high metamorphic grades, and other processes become more efficient. Higher concentrations of dislocations have been suggested to accelerate reaction rates (Wintsch and Dunning, 1985). Microstructures Inclusion Trails and Deformation Lamellae Deformation of quartz and occasionally other minerals produces several features that may be useful in assessing the deformation history in a rock mass, including temperature and pressure conditions. Fluid inclusions may become aligned at low temperatures and resorbed at higher temperatures, and features called deformation lamellae may occur FIGURE 8–29 Deformation lamellae (“zebra stripes”) crossing the quartz grain from lower right to upper left in low-temperature deformed quartz grains in a calcite-cemented Middle Ordovician sandstone from near White Sand in northeastern T ennessee. The indistinct shades of gray are subgrains, an additional indicator of unrecovered strain. Crossed polars. (RDH photo.) as a product of low-temperature deformation (Figure 8–29). Deformation lamellae consist of subparallel thin, optically distinct bands that may have slightly different refractive indicies than the quartz grain in which they occur, so they appear as alternating lighter and darker bands. They may be bound by fluid inclusions, but are commonly associated at a high angle with undulatory extinction. Studies of these features using the transmitted electron microscope reveal that they consist of alternating layers of high and low dislocation density, tangles of dislocations, subgrains that are too thin to be resolved under the petrographic microscope, or walls of dislocations that form subgrains that are outlined by fluid inclusions (Groshong, 1988). Fluid inclusions may be partially or completely filled with liquid, filled with gas, or occasionally contain solid material, along with liquid or gas. They provide useful information about temperature at the time of formation. Deformation lamellae form at low temperatures in quartz. Parallel orientation of these features in a thin section would suggest they formed at the same time; nonparallel orientation in a thin section of sandstone would suggest that the quartz may have been derived from the same source and contained the lamellae before being eroded and transported. Unrecovered Strain, Recovery, and Recrystallization We have examined deformation mechanisms and how they affect a rock mass; the remaining task is to clearly Microstructures and Deformation Mechanisms distinguish between a strained crystal and the processes of recovery and recrystallization that restore the crystal to a lower energy condition made up of less strained to unstrained crystals. On the microscopic scale, deformation of a crystal is indicated by unrecovered strain. Undulatory extinction in quartz grains (Figure 8–30) is caused by a difference in optical-extinction properties, caused by dislocations or microcracks distorting the lattice. Subgrains are small parts of crystals with different lattice orientation in adjacent parts of the same crystal. They begin to form through the mechanism of dislocation glide as additional strain accumulates in the crystal. Although the accumulation of dislocations in a crystal is a strain-hardening process, subgrain formation, once dislocations are no longer being produced, is a strain-softening process that represents the first visible stage of reorganization of the crystal to an internally less-strained or lower-energy state (Figure 8–31a). Subgrain boundaries consist of low-angle boundaries in which the lattice has a misorientation of less than 10° with respect to the nearest boundary of the crystal. This causes a change in optical properties so they are readily observed using crossed polars in a petrographic microscope. As the crystal is deformed at higher thermal or straininduced energy states, it will form sites for nucleation of entirely new unstrained crystals. In a crystal being deformed by dislocation glide and climb, steady-state flow may be accommodated by one of two thermally activated (a) | 201 FIGURE 8–30 Highly strained quartz grains in a matrix of calcite in Sandsuck Formation limestone from Springtown in southeastern Tennessee. Some of the unrecovered strain is inherited from the source of the quartz eroded and transported into the Sandsuck depositional site, probably from a metamorphic terrane, but much of the strain, identifiable as undulatory extinction, consists of low-angle boundaries, deformation lamellae, and some fluid inclusion trails. Note that numerous subgrains appear to radiate from grain boundaries, and that the boundaries where the three large quartz grains join are much straighter than the remainder of the grains. This suggests that parts of the quartz grains were dissolved by pressure solution after they were deposited in the limestone. Width of photograph is approximately 1 mm. Crossed polars. (RDH photo.) (b) FIGURE 8–31 (a) Plastically deformed quartz grains in Lower Cambrian Weverton Quartzite from South Mountain near Harpers Ferry, West Virginia. Some grains have been strongly flattened into the foliation; a few maintain vestiges of originally round shape. All have very small, unstrained grains formed at the edges of original sand grains with subgrain structure here recognized by undulatory extinction. Field is approximately 2 mm wide. (b) Partially recrystallized fabric in Setters Quartzite, Baltimore, Maryland. The rock fabric consists of a mosaic of relict larger quartz grains that still preserve some subgrains, but there are also abundant unstrained fully recrystallized quartz polyhedra; note 120° grain-boundary intersections and absence of subgrains in the new polyhedra. A few grains formed by bulging are also present at grain boundaries. This is the subgrain rotation recrystallization stage of Stipp et al. (2002). Width of field is approximately 3 mm. Both (a) and (b) were photographed under crossed polars. (Both photos courtesy of Charles M. Onasch, Bowling Green State University.) 202 | Mechanics: How Rocks Deform mechanisms—dynamic recovery or dynamic recrystallization. The term recovery is used to generally describe processes that reduce dislocation density and dislocation interaction, and also increase the rate of dislocation glide and climb in crystals being deformed by dislocation creep (Nicolas, 1987). Recrystallization is a thermal- and stress-driven process that results in a decrease in dislocation density and creation of new grain boundaries through grain-boundary migration, and other deformation mechanisms discussed earlier. The net result is a decrease in strain in a crystal. A major difference between the two processes is that dynamic recrystallization involves strain softening, and dynamic recovery does not (Tullis and Yund, 1985). Recovery, which commonly produces low-angle boundaries, is the first stage in decreasing the amount of strain in deformed crystals; recrystallization, which may be initiated independent of recovery, completes the process of decrease in strain energy of a deformed crystal and produces high-angle grain boundaries (Figure 8–31b). The newly formed grains contain lattices oriented at a high angle (> 10°) to the lattice in the parent crystal, thereby producing high-angle boundaries. Recrystallization may occur as dynamic or syntectonic recrystallization while stress is being applied to the rock mass, or it may occur as static recrystallization after stress has been removed (Sibson, 1977). Dynamic recrystallization is accompanied by a decrease in elastic strain energy and an increase in grain-boundary (surface) energy. Dynamic rotational recrystallization produces a “core-andmantle texture” (Figure 8–31a) when dislocation climb continues to insert dislocations into subgrain boundaries at the perimeter of the grain. This continued insertion increases the magnitude of the angular mismatch of the lattice across the boundary until the lattice ruptures, converting the boundary from a low-angle subgrain boundary to a high-angle grain boundary. Core-and-mantle structure may also be produced by dynamic recrystallization where the concentration of dislocations or strain at the host grain boundary triggers the migration of a new grain boundary, forming small grains on the boundary of the larger host crystal. The original strained lattice may have formed subgrains to attain a lower energy state and then later recrystallized to form small new crystals with high-angle boundaries. The newly crystallized quartz or feldspar grains meet at angles near 120°, a low-energy state arrangement that therefore provides the greatest stability in an unstrained crystal (Figure 8–31b). As unstrained crystals form by dynamic recrystallization, they immediately are strained and again begin to form low-angle boundaries and subgrains that also eventually recrystallize initially by bulging. Static recrystallization is driven by reduction in both strain energy and surface energy (Figure 8–32). If enough heat is available, recrystallization may thus be favored over high strain rate during continued deformation, even if the rock fabric is recycled several times during multiple episodes of recrystallization and progressive deformation. The end product of a texture dominated by strained crystals would not provide enough clues that the crystals are not original and are in fact the last of several generations of crystals. Strain removed by recovery and recrystallization is the elastic strain of individual dislocations and defects. We have examined intracrystalline deformation mechanisms that function under different conditions, produce dislocations, and lead to recrystallization of individual grains. Most rocks that go through this process contain a fabric consisting of strongly oriented crystals—a foliation (Chapter 18). The question of how this crystallographicpreferred orientation of minerals is produced by deformation and recrystallization in rocks has been debated for many years. Materials scientists and geologists have also long been aware that dislocation glide results in rotation of crystallographic axes during strain. The role of dynamic and static recrystallization in deformation processes has been resolved only recently. Obviously, formation of preferred orientations, cleavage, and foliations in metamorphic rocks, and in many fault rocks as well, depends on strain. Dislocation glide and rotation processes, in addition to recrystallization, are probably the most common mechanisms leading to preferred orientation. Preferred orientation has been produced experimentally without accompanying recrystallization (Tullis, 1971). In Chapter 18, we will return to this problem and examine the mechanisms of cleavage formation and their relationship to recrystallization. Crystallographic Preferred Orientations Consider an undeformed quartz sandstone with its many detrital grains; each quartz grain has a set of crystallographic axes (specifically its a1, a2, a3, and c-axes), and in an undeformed sandstone the orientation of the crystallographic axes would be random (Figure 8–33a). Now, imagine the same rock being sheared at high temperatures and pressures; ductile deformation ensues as individual mineral grains and the rock mass changes shape. Crystal plastic processes, such as dislocation creep in the individual quartz grains, produce a preferred alignment of crystallographic axes (Figure 8–33b). Dislocations move more readily through the crystal along specific slip planes governed by the quartz crystal structure, and in the process the crystallographic axes become aligned. For instance, quartz has four potential slip systems: these include rhomb <a>, basal <a>, prism <a>, and prism <c>, each related to a specific crystal face and a crystallographic axis. Ultimately, the deformed rock has a crystallographic preferred orientation (CPO) or lattice-preferred orientation (LPO). Microstructures and Deformation Mechanisms ion rmat Defo ses cea (b) | 203 Matrix recrystallizes, sample annealed Defo rm cont ation inue s (a) All components continue to deform and recrystallize (c) FIGURE 8–32 Relationships between static and dynamic recrystallization. (a) Deforming rock mass containing flattened original quartz sand grains. (b) Static recrystallization; larger grains and groundmass are recrystallized. (c) Dynamic recrystallization; larger grains and groundmass recrystallize as deformation continues, new grains recrystallize and become deformed, and many grains record strain after deformation. NO crystallographic preferred orientation 0 5 millimeters (a) Undeformed quartz sandstone FIGURE 8–33 (a) Undeformed quartz sandstone with schematic representation of the quartz c-axes for individual grains (red arrows) and stereogram of c-axes with no crystallographic preferred orientation. (b) Deformed quartz sandstoneCrystallographic with schematic preferred representation of orientation preferred orienthe quartz c-axes for individual grains (red arrows) and stereogram of c-axes illustrating a well-developed crystallographic tation with an asymmetric girdle distribution. Z 0 5 millimeters 204 | Mechanics: How Rocks Deform Undeformed quartz sandstone (a) Crystallographic preferred orientation Z Foliation 0 X 5 millimeters Deformed quartz sandstone (b) FIGURE 8–33 (continued) Structural geologists have long quantified the microfabrics of minerals—such as quartz, calcite, olivine, and biotite— in deformed rocks. This subdiscipline of structural geology is sometimes referred to as microtectonics. In certain minerals, for example planar micas and needle-like amphiboles, a grain-shape preferred orientation also means the minerals have a crystallographic preferred orientation (Figure 8–34). In minerals like quartz, olivine, and calcite, however, the 0 shape of individual mineral grains does not necessarily reflect whether or not it has a crystallographic preferred orientation. A qualitative assessment of whether a crystallographic preferred orientation exists can be made for low birefringence minerals (quartz, feldspar, olivine) by inserting a one- wavelength plate (a gypsum plate) under crossed polarizers to see if there is a preferred color pattern that indicates a preferred crystallographic pattern (Figure 8–35). 5 Z millimeters limeters b m Foliation Foliation X b n = 200 m (a) Kamb contours at 2, 6, 12, and 24 σ (b) FIGURE 8–34 (a) Grain shape and crystallographic preferred orientation of biotite, (b), and muscovite, (m), in a granitic gneiss. (b) Stereogram of poles to (001) plane for biotite grains in the granitic gneiss; note how most poles are nearly perpendicular to the foliation. Microstructures and Deformation Mechanisms | 205 FIGURE 8–35 Crystallographic preferred orientation as illustrated with the one-wavelength plate (gypsum plate). Quartz vein in a phyllite from the Semail Ophiolite metamorphic sole in northern Oman. Width of micrograph is 5 mm. (CMB photo.) For decades, the standard tool for microfabric analysis was the universal stage mounted on a petrographic microscope (Figure 8–36), which allowed the orientation of individual crystal axes to be measured in a thin section. Although there are a number of ways to display these data, the most common presentation is a stereogram with orientations plotted relative to the foliation and lineation in the rock (Figure 8–37). Measuring the individual orientation of hundreds of quartz c-axes or calcite twin planes is a time-consuming process, but the results provide much information regarding the sense of shear, type of shear, and the deformation conditions, particularly temperature. The type of crystallographic preferred orientation pattern developed in a deformed rock depends on many factors including the: (1) slip systems active in a mineral during deformation; (2) finite and infinitesimal strain; (3) kinematic vorticity; (4) the three- dimensional strain; and (5) recrystallization rate (Lister and Hobbs, 1980; Schmid, 1994). Ideally, we can use the crystallographic preferred orientation pattern in a rock to learn about these deformation factors. Coaxial deformation Non-coaxial deformation Z Z X FIGURE 8–36 A universal stage mounted on a petrographic microscope. (CMB photo.) FIGURE 8–37 Simplified pole figure diagrams for quartz c-axis fabrics developed during non-coaxial and coaxial deformation. X | Mechanics: How Rocks Deform FIGURE 8–38 (a) Quartz c-axis opening angle versus deformation temperature plot. Dashed lines indicate extents of datasets used to plot the visual best-fit line (green) with ±50 °C temperature range (gray box) shown behind. Schematic examples of crossgirdle (b) and two point maxima (c) c-axis fabrics, showing their opening angles (OA). (Modified from R. D. Law, 2014, Deformation thermometry based on quartz c-axis fabrics and recrystal lization microstructures: A review: Journal of Structural Geology, v. 66, p. 129–161.) Quartz c-axis fabric opening angle 206 OA 120 Lineation 90 (b) 60 OA Lineation 30 (c) 0 0 (a) Foliation 100 200 300 400 500 600 700 800 900 Deformation temperature (°C) Experimental deformation of quartz aggregates by noncoaxial deformation (general or simple shear) produces an asymmetric girdle distribution of quartz c-axes, in which the girdle is oblique to the foliation and illustrates the overall sense-of-shear (Figure 8–38b) (Tullis, 1977; Bouchez et al., 1983). Coaxial deformation produces a symmetric crossed girdle distribution of quartz c-axes (Figure 8–38c). The active slip system within an individual mineral changes depending on the deformation temperature. At greenschist facies conditions, basal and rhomb <a> slip in quartz is predominant, at amphibolite facies conditions prism <a> slip is activated, and at even higher temperatures prism [c] becomes activated. Different slip systems yield different crystallographic preferred orientation patterns (Schmid and Casey, 1986). Crystallographic preferred orientation also changes with increasing strain. Heilbronner and Tullis (2006) sheared undeformed quartzite under simple shear conditions and observed the maxima on the inclined cross-girdle changes with increasing shear strain and the amount of recrystallization. Quartz c-axis fabric opening angles have been employed as a geothermometer. Kruhl (1998) noted that, with increasing metamorphic grade, the c-axis fabric opening angle increases, and the crossed girdle pattern transitions to a two point maxima at high metamorphic grade (Figure 8–38). This technique is grounded on the assumption that deformation temperature controls recrystallization mechanisms and fabric development. As noted by Law (2014), however, fabric opening angles are also sensitive to variables such as strain rate and hydrolytic weakening (presence of water), and therefore quartz c-axis fabric opening angles temperature estimates need to be carefully interpreted. In the past two decades, a powerful new technique has emerged to quantify microfabrics: EBSD (electron backscatter diffraction). The EBSD technique uses a scanning electron microscope (SEM) to determine the orientation of crystallographic axes in polished thin sections. Accelerated electrons in the SEM beam are diffracted by the crystalline structure in minerals, and the diffracted electrons can be utilized to determine crystallographic orientation. EBSD can measure the crystallographic orientation in thousands of individual grains relatively quickly (when compared to the universal stage method), but also provides quantitative information about mineral composition, grain size distribution, and grain boundary geometries. Johanesen and Platt (2015) examined a peridotite shear zone in the Ronda massif of southern Spain and used EBSD analysis to determine crystallographic preferred orientations, and infer differential stress based on grain size distributions (Figure 8–39). With the advent of EBSD (and other technologies) structural geologists are better able to characterize and quantify crystallographic and microstructural properties of deformed rocks than ever before. Laboratory Models of Deformation Processes Many simple geologic materials have been deformed in the laboratory. Mixtures of quartz and feldspar, the common constituents of granitic rocks, and pure mineral aggregates such as quartz sandstone, pure marble (calcite), and dunite (olivine) have been studied extensively. Because of the geologically short timescale of human activities, mylonite and other well-recrystallized and foliated metamorphic rocks can be produced experimentally in pure quartz sandstone only at temperatures in the range of 800° to 1,000° C, which permit high strain rates in the range of 10−5 to 10−7 s−1 (pronounced 10 to the −5 per second) and plastic flow to be achieved (Figure 8–40; Tullis et al., 1973). Both the temperature and strain rate needed to activate these processes in the laboratory greatly exceed the geologic conditions normally encountered by rocks being deformed in the core, toward the flanks of a mountain chain, or in the mantle. Geologic strain rates are on the order of Microstructures and Deformation Mechanisms {100} {010} z x KR41 253 points Max OA = 11.43 KR118 fine 101 points Max OA = 7.70 {001} | 207 FIGURE 8–39 (a) EBSD inverse pole figure map of olivine in peridotite shear zone from southern Spain. (b) Stereogram plots of crystallographic preferred orientation in olivine. One point per grain is plotted for each sample, then contoured by point density. Contours represent two multiples of uniform distribution. Lower hemisphere equal area projection, X is the lineation, and Z is the pole to the foliation. (From K. E. Johanesen and J. P. Platt, 2015, Rheology, microstructure, and fabric in a large scale mantle shear zone, Ronda Peridotite, southern Spain: Journal of Structural Geology, v. 73, p. 1–17.) {010} 0 {001} (a) {100} μm 300 KR118 coarse 151 points Max OA = 5.82 (b) FIGURE 8–40 Thin section of an experimentally produced quartzite mylonite demonstrating that mylonite formed by both pure and simple shear. Curved light area of flattened quartz grains flowed around the sides of the dark obstacle, bulging the container as the ram compressed the sample from above. The deformed quartz resembles the “ribbon” texture observed in mylonite. Recrystallized original quartz grains are present on the ends of the sample immediately adjacent to the obstacle and the ram. This sample was deformed at 800° C at a strain rate of 10−7 s−1, and the sample was shortened by 50 percent. Maximum width of the bulged part of the sample is ~6 mm. Crossed polars. (From J. Tullis, J. M. Christie, and D. T. Griggs, 1973, Geological Society of America Bulletin.) 208 | Mechanics: How Rocks Deform 10−10 to 10−16 sec−1. Such accelerated laboratory conditions are necessary, however, to create and study these materials during the investigator’s lifetime. Mixtures of quartz and feldspar in various proportions are useful analogs because they permit study of two materials of markedly different mechanical properties in geologically realistic compositions (close to granite). Quartz deforms by dislocation creep at a much lower temperature than does feldspar, particularly in the presence of a small quantity of water. Feldspar generally remains brittle in laboratory experiments until temperature and pressure are very high (900–1,100° C, 1,500 MPa), even with water present. Consequently, coexisting quartz and feldspars, as in granitic rocks, deform differently in the deforming rock mass. Experimental and field studies indicate that feldspar does recrystallize at higher temperatures around the edges of large grains with the appearance of small and unstrained polygons, leaving the original large grains largely unstrained (Tullis and Yund, 1985). As recrystallization progresses, the size of the old grains decreases and new and smaller grains are replaced by recrystallized grains. Presence of micas in a quartz-feldspar aggregate also increases the rate of deformation under the same temperature and pressure. Water, even in small quantities, increases the deformation rate and lowers the temperature threshold for most deformation mechanisms. In order to better understand deformation and recrystallization processes in rocks, Hirth and Tullis (1992) conducted a number of experiments at different temperatures and pressures using quartz aggregates (quartz arenite and novaculite). These experiments were conducted at temperatures above those commonly observed in the formation of these textures in natural quartz, because the experiments would otherwise take too long to run. As a result, they recognized three regimes of dislocation creep. Regime 1 involves low-temperature deformation at rapid strain rates wherein dislocation climb is hindered, and recrystallization occurs by strain-induced grain-boundary migration. Quartz arenite (coarse-grained) samples undergo strain softening, but the very fine-grained novaculite samples do not. Quartz grains acquire a patchy undulatory extinction in thin section, and recrystallization begins at grain boundaries. Following nucleation of new unstrained grains, additional growth of new grains occurs by strain-induced grain-boundary migration. Regime 2 occurs at higher temperatures or lower strain rates. The rate of dislocation climb in Regime 2 becomes sufficiently rapid to involve recovery; steady-state flow is achieved at relatively low strain rates, and sweeping undulatory extinction outlining subgrains occurs in quartz grains. The low-angle boundaries continue to accumulate dislocations and thus evolve into high-angle boundaries—recrystallization. Recrystallized grains commonly form along grain boundaries. At still higher temperatures or still slower strain rates, Regime 3 is characterized by sufficiently rapid dislocation climb to accommodate recovery, but with greatly increased grainboundary migration and initiation of steady-state flow. Recrystallization occurs here by both grain-boundary migration and subgrain rotation. Regime 1 is the only one where strain weakening was noted. The addition of small amounts of water to the samples catalyzes the transition from Regime 1 to 2 and from Regime 2 to 3, permitting the transitions to occur at lower temperatures. A drawback with the Hirth and Tullis scheme is that it characterizes quartz deformation and recrystallization in nature at greenschist facies or lower temperatures. It does tell us, however, that quartz recrystallization processes can be complete, producing unstrained quartz at temperatures of 300° C. Stipp et al. (2002) studied quartz recrystallization in natural quartz veins in rocks along the Tonale fault in northern Italy. Temperature conditions there ranged from 250° to 700° C during deformation, and they employed mineral assemblages in the enclosing metasedimentary rocks to calibrate the temperatures. They observed different kinds of recrystallization behavior in quartz across this range of temperatures. They determined that the transition from cataclasite to mylonite occurs around 280° C. They identified “bulging” recrystallization that occured between 280° and 400° C, subgrain rotation recrystallization occurred in the temperature range from 400° to 500° C, and the transition to grain-boundary migration occurred at approximately 500° C (Figures 8–31 and 8–41). They also were able to map these (a) (b) FIGURE 8–41 Three dynamic recrystallization realms recognized by Stipp et al. (2002). (a) Bulging recrystallization occurs at relatively low temperature (~280° C) along grain boundaries and possibly along microcracks in quartz grains. (b) Subgrain rotation recrystallization occurs at medium temperature in relict quartz grains and in quartz ribbons. These relict structures can be completely consumed by formation of polygonal (unstrained) quartz grains. (c) | Microstructures and Deformation Mechanisms 209 (b) (c) 0 FIGURE 8–41 (continued) (c) Grain-boundary migration 200 μm recrystallization of quartz occurs at high temperature producing unstrained quartz in irregularly sized and shaped grains. The three textures are illustrated at the same relative scale. (From Stipp et al., 2002, Journal of Structural Geology, v. 24, p. 1861–1884.) FIGURE 8–42 Chessboard pattern in quartz from the west flank of the Toxaway dome, eastern Blue Ridge, South Carolina. (Photo courtesy of Nicholas E. Powell and Jamie S. Levine, Appalachian State University, Boone, North Carolina.) three recrystallization mechanisms in quartz veins nearby in the contact aureole of the Adamello pluton in southern Switzerland. In the laboratory they determined that quartz deformation took place via different crystallographic mechanisms (slip systems) at different temperatures. Recognition of a unique quartz texture—chessboard pattern (Figure 8–42)—can be used as an indicator of deformation at high temperature and pressure (> 630° C and 1 GPa) (Stipp et al., 2002; Law, 2014). This pattern is generated by formation and glide of prism-[c] edge dislocations as they climb into tilt-dominated subregion boundaries in quartz (Wallis et al., 2018), or as an interference pattern between prism-[c] slip and basal <a> slip (Law, 2014) (Figure 8–43). slip Z Pris m [c ip a> Y ] sl Bas al < X (a) (b) Foliation Basal slip plane (green) and prism tilt wall (red) Lineation X Y Prism slip plane (red) and basal tilt wall (green) [c] s lip Bas al < a> Pris m X slip Z (c) FIGURE 8–43 Origin of chessboard extinction pattern in quartz. This pattern can be observed only if the thin section is cut close to the XZ plane of the strain ellipse, as indicated in the end of the block diagram facing the reader in (c). (a) Quartz c-axis maximum fabric in the XZ plane at a low angle to the mineral lineation. (b) Chessboard extinction pattern created by combined prism-[c] and basal <a> slip. (c) Relationships between the dominant foliation and lineation in a metamorphic rock and the slip patterns in an oriented quartz crystal. (Courtesy of Prof. R. D. Law, Virginia Tech.) 210 | Mechanics: How Rocks Deform A series of experiments designed by Means (1986, 1990) involved organic compounds with low melting points, such as monoclinic biphenyl, hexagonal octachloropropane, and triclinic paradichlorobenzene. These compounds strain and recrystallize under low stress at room temperature, because of their low melting points, and so their behavior can be observed directly under a petrographic microscope (Figure 8–44)—something impossible with most rocks, metals, and ceramics. A number of intriguing surprises have arisen from this work. Means and his students recognized a number of ways that subgrain boundaries can form and textures that appear to be the products of grain-boundary sliding from grain-boundary migration (and the converse). These experiments permit direct observation of both static and dynamic recrystallization, as well as direct correlations of strain fields with sequences of deformation mechanisms. These experiments have provided structural geologists with a greater appreciation of the complexity of deformation processes. Experiments help us to better understand various deformation processes that produce microstructures that we see in natural materials, but experiments that attempt to duplicate processes operating deep in the Earth cannot be carried our at similar rates in a laboratory. The work of Stipp et al. (2002) enhances our understanding of quartz deformation and recovery-recrystallization by directly comparing experimental results with calibrated field studies, thus providing great insight into the T-P conditions of formation of different quartz recovery-recrystallization fabrics. These results permit us to more accurately estimate the deformation temperatures of quartz-bearing rocks in a thin section. (a) (b) (c) FIGURE 8–44 Low-melting-point organic compounds that deform under controlled conditions on the stage of a petrographic microscope and exhibit various recrystallization and deformation processes. (a) Deformation-induced twin lamellae (narrow lines) in crystals of paradichlorobenzene. Width of field is 0.7 mm. Crossed polars. (W. D. Means, 1986, Journal of Geological Education, v. 34.) (b) Undeformed (or annealed) mass of interlocking octachloropropane crystals. Note that junctions of most crystals make ~120° angles. Width of field is 0.5 mm. Crossed polars. (c) Abundant subgrains developed in crystals of (b) by horizontal, dextral shear of about 0.3 mm. Also, note more irregular grain boundaries due to grain-boundary migration. Field width is 0.5 mm. Crossed polars. (Unpublished photos courtesy of Winthrop D. Means, SUNY Albany.) Final Thoughts Understanding of the nature and kinds of microstructures should be an integral part of any investigation of geologic structure. We have now explored the different kinds of microstructures and deformation mechanisms and have gained some idea about the physical conditions under which they form. Deformed rocks reveal a broad array of structures on all scales. Means (1993) raised the questions, what Microstructures and Deformation Mechanisms kinds of deformation processes yield features that will have a memory of movement history, and do distinct deformation processes necessarily have distinct struc tural signatures? We know from our discussions in Chapter 8 that dislocations can be annihilated and the dislocation density reduced by recovery and recrystallization. This process thus decreases the memory of part of the movement history within the rock mass, so few or no indicators frequently remain of the earlier history of the rock mass. For rocks that have not undergone recovery and recrystallization, an array of microtextures ESSAY | 211 provide abundant useful information about the deformational history of a rock. Moreover, in quartz and the micas, some grains may undergo recrystallization and annihilate the accumulated strain in crystal lattices, whereas others, such as the feldspars, may not recrystallize until much higher temperatures have been reached, providing an opportunity to bracket the T-P conditions of deformation. We now turn our attention from rock mechanics to a study of fractures and faults. Fault Rocks—A Fourth Class of Rocks Mylonites and cataclasites—fault rocks—do not fit the usual grouping of rocks into igneous, sedimentary, and metamorphic rocks, nor are they easily related to the rock cycle (Figure 1–18). They form in unique environments, in fault zones where deformation commonly includes high shear strain. The resulting fabrics (textures plus structures) in these rocks are quite varied and are controlled by the depth in the Earth where they form, the temperature, pressure, and availability of fluids at these depths, from a few meters below the surface to the depths reaching the base of the lithosphere (Figure 1–9). Add the variable of movement rate of an active fault: strain rate, and we can understand why fault rocks do not fall into the usual three classes of rocks. While mylonite was first definied by Lapworth (1885) in his studies of the Moine thrust in Scotland, until recently many geologists thought of faults only in terms of brittle behavior, although the ductile character of mylonite was part of Lapworth’s original definition. If a rock mass is being deformed at temperatures high enough for dynamic recrystallization to occur, the recovery and recrystallization processes in the crystals that attempt to remove strain will compete with the renewed accumulation of strain in the crystals. If this process is occurring in a fault zone within the ductile-brittle transition, brittle and ductile processes may compete as a function of how rapidly the rock mass accumulates the new strain—the strain rate. High strain rate may force the observed deformation from an otherwise ductile mode into brittle deformation, whereas low strain rates will favor producing mylonite. Competition also exists between strain rate and recovery or recrystallization rate within the rock mass. The competing processes and the resulting products differ in subtle ways (Hatcher and Hooper, 1981). On one hand, rocks are being deformed very rapidly but may not recover and recrystallize very rapidly—or not at all. If deformation occurs at low temperature and low confining pressure, the deformation mechanism will be brittle fracture and frictional sliding, and cataclasite will be produced (Figure 8E–1). On the other hand, if the temperature is elevated, fluid is available, and the strain rate is low enough (as along some fault zones), the rock will probably become a mylonite. Mylonites are strongly foliated metamorphic rocks that exhibit high ductile strain and incomplete recrystallization or recovery. Larger grains are flattened into the foliation, and ribbon quartz (which may be internally recrystallized) is common. Reduced grain size characterizes mylonitization (Bell and Etheridge, 1973; Hatcher, 1978). Factors that determine whether mylonites form that preserve a strongly deformed fabric, or if a metamorphic dynamically or statically recrystallized microfabric forms, depend on strain rate, the duration of strain, and temperature, as well as other factors such as the amount of fluid available and magnitude of shear stress. Sometimes, dynamic recrystallization takes place in a rock mass, where the rock mass cannot recover rapidly enough to keep up with the shear strain rate. If the mylonitic texture is to be preserved on the microscopic scale, it must be frozen in by cooling and rapid cessation of strain; otherwise, static recrystallization may coarsen the grains and eliminate high dislocation densities characteristic of non annealed mylonite (Figure 8E–2a). Note the crosscutting veins indicate the rock was broken, the fractures were filled with quartz, and the rock again broken and sealed. Finally, at moderate to high temperature and low strain rate, intracrystalline elastic strain is recovered or recrystallized faster than the strain rate can increase it by multiplication of dislocations (Wise et al., 1984). Enough thermal energy may remain after the stress is relieved so that the remaining strain is removed by static recrystallization, resulting in the 212 ESSAY | Mechanics: How Rocks Deform continued (a) (1) (2) (b) (1) (2) FIGURE 8E–1 (a) (1) Siliceous cataclasite from the Towaliga fault zone, Georgia, formed at low temperature and pressure and containing highly fractured constituents. We do not know how many cycles of breaking and sealing affected this and similar cataclasite bodies throughout the eastern U.S. that formed ~200 Ma just prior to the opening of the Atlantic Ocean. (a) (2) Thin section of cataclasite from the same rock illustrating the crosscutting relationships that are present on a micro-scale similar to those visible in the hand specimen. Width of field is approximately 3 mm. (b) (1) Quartz mylonite hand specimen also from along the Towaliga fault in central Georgia. The specimen is composed predominantly of quartz ribbons, but the white minerals are feldspar. (b) (2) Thin section of the same specimen reveals a fabric of overlapping quartz ribbons with large amounts of unrecovered strain. This quartz has not begun the bulging stage of Stipp et al. (2002) (see Figures 8–31 and 8–41). Width of field is approximately 3 mm. Plane light. U.S. quarter for scale in (a)(1) and (b)(1). (RDH photos.) microfabric of a “normal” metamorphic rock (Figure 8E–3) or an annealed mylonite. In the latter case, hand specimens preserve the mylonitic texture, but microscopically, it is entirely recrystallized (Figure 8E–2b). Recall our earlier discussion of the recrystallization processes that occur at different temperatures and the resulting textures in deformed rocks that enable us to estimate the temperature range in which deformation occurred (Fig. 8–28; Stipp et al., 2002). Mylonite and cataclasite commonly occur along faults. In nature, the competing processes (just described) overlap to a great degree, and mylonites should not result from every occurrence of high strain rate. Mylonitic texture may develop in ordinary metamorphic rocks in areas where there are no faults, because of extremely localized development of high shear strain. Rocks in highly strained and thinned fold limbs that are undergoing ductile flow might contain mylonitic texture, because a large amount of strain can be concentrated there. On the other hand, faults that form before the metamorphic-thermal peak in a rock mass will produce mylonite, but the mylonite will probably be overprinted by metamorphism. Mylonite in the fault zone will exhibit recrystallized microtextures common to metamorphic rocks, rather than a Microstructures and Deformation Mechanisms (a) (1) (2) (b) (1) (2) | 213 FIGURE 8E–2 (a) (1) Dynamically deformed (nonannealed) mylonite from the Towaliga fault zone near Indian Springs, Georgia. This specimen contains a contact between mylonitized quartzo-feldspathic rock (granite?) and more mica-rich mylonite. Note the cuspate-lobate structure along the contact. This indicates a large viscosity contrast at the contact. (RDH photo.) (a) (2) Photomicrograph in polarized light (with gypsum plate inserted) of a thin section of the same specimen as in (a) (1). The feldspar (light orange and cracked blue crystals) remains brittle, whereas the quartz (bright reds and blues) and biotite (very dark bands) flowed as ribbons and recrystallized. Field is approximately 3 cm wide. Plane light. (Thin section specimen courtesy of Robert J. Hooper, Houston, Texas.) (b) (1) Mylonite from the Rumble shear zone near Forsyth, Georgia, formed dynamically but was statically annealed. The saltand-pepper texture of this rock is a megascopic clue that the microstructure is annealed. Feldspars with tails and filamentous quartz ribbons preserve the original mylonitic texture. (RDH photo.) (b) (2) Thin section of the same specimen as in (b) (1) illustrating the annealed fabric that resembles that of a metamorphic rock. The only microscopic clues that this is a mylonite are the fragmented feldspar porphyroclast and a finer-grained texture of the quartz and biotite in the V-shaped area immediately to the right of the large porphyroclast. Quartz ribbons are totally internally recrystallized, but the original shape of the ribbons is preserved. Width of field is approximately 1 mm. Crossed polars with a gypsum plate inserted. (RDH photo.) mylonitic texture, but will preserve some of the megascopic textures of mylonite (Figure 8E–2b). This relationship is important because few clues remain concerning the origin and nature of these early formed fault rocks in the internal parts of mountain chains. As a consequence, other criteria such as stratigraphic data (Chapter 10) must be used to distinguish between stratigraphic and fault contacts separating rock bodies. To summarize, products of strain—including strain recovery and recrystallization—and the competing processes that form cataclasites, mylonites, and normal metamorphic rocks are all gradational. They involve a delicate balance between the thermal regime of the rock mass, pressures and fluids within the rock body, the strain rate, and the timing relative to the thermal peak. continued Temperature A B “Normal” (retrograde) mylonite Transition (mixed) Cataclasite 0.01 500 Kyanite Transition 1.0 0.1 Sillimanite 425 Almandine 400 (garnet) Biotite T°C 10 600 Deformation Annealed mylonite and “normal” metamorphic rocks (PT = 4 kb) FIGURE 8E–3 Relationships between recrystallization-recovery rate, strain rate, temperature, and total strain and the products of deformation. Point A represents a rock that was deformed under increasing temperature. Mylonitic texture would probably be annealed following cessation of deformation, unless the rock mass was cooled without increasing temperature so that the existing textures would be preserved. Point B represents a rock deformed following the thermal peak. Mylonitic (or metamorphic) texture would be preserved, and much of the strain in the rock may not be annealed. Brittle-ductile transition ESSAY Mechanics: How Rocks Deform Strain rate | Recovery rate 214 300 Chlorite 200 t(Ma) References Cited Stipp, M., Stünotz, H., Heilbronner, R., and Schmid, S. M., 2002, The eastern Bell, T. H., and Etheridge, M. A., 1973, Microstructure of mylonites and their Tonale Line: A “natural laboratory” for crystal-plastic deformation of quartz descriptive terminology: Lithos, v. 6, p. 337–348. over a temperature range from 250 to 700° C: Journal of Structural Geology, Hatcher, R. D., Jr., 1978, Eastern Piedmont fault system: Reply: Geology, v. 6, v. 24, p. 1861–1884. p. 580–582. Wise, D. U., Dunn, D. E., Engelder, J. T., Geiser, P. A., Hatcher, R. D., Jr., Kish, Hatcher, R. D., Jr., and Hooper, R. J., 1981, Controls of mylonitization pro- S. A., Odom, A. L., and Schamel, S., 1984, Fault-related rocks: Suggestions for cesses: Relationships to orogenic thermal/metamorphic peaks: Geological terminology: Geology, v. 12, p. 391–394. Society of America Abstracts with Programs, v. 13, p. 469. Lapworth, C., 1885, The Highland controversy in British geology: Its causes, course, and consequences: Nature, v. 32, p.558–559. Chapter Highlights • Minerals change their shape via the movement of point defects and dislocations through the crystal lattice. • The nature of deformation, or the deformation mechanism, at the micro-scale is primarily determined by temperature, differential stress, and strain rate. • Cataclasis occurs at low-temperature and high-strain rates. • Pressure solution occurs at low temperatures when water is present that facilitates dissolution of minerals at high stress locations. • Crystal-plastic deformation occurs at medium to high temperature over a range of strain rates. • Specific microstructures in deformed rocks provide evidence of the active deformation mechanisms and physical conditions occurring during deformation. • Crystal plastic deformation commonly produces a crystallographic preferred orientation in minerals. • Deformation experiments on both rocks and analogue materials provide key insights into deformation mechanisms and microstructures that occur in naturally deformed rock. Microstructures and Deformation Mechanisms | 215 Questions 1. Why are deformation processes in metals not good models for rock deformation? 2. Of all factors that control the rates and thresholds of deformation processes, which single factor do you think is most important? Why? 3. How could you tell a cataclasite from a mylonite in the field? With the aid of a petrographic microscope in the laboratory? 4. How would you determine whether a rock has been deformed by pressure solution or by volume-diffusion creep? 5. What are the most important factors influencing the rate of chemical reactions? 6. A limestone contains several stylolites that formed at a high angle to the bedding in the limestone, and it also contains a set of calcite-filled fractures that formed perpendicular to and cut the stylolites. Explain how this happened. 7. Use modal mineralogical data from an undeformed limestone and its deformed equivalent to estimate the amount of volume change the rock underwent during deformation. MINERAL UNDEFORMED LIMESTONE DEFORMED LIMESTONE Calcite 80% 78% Dolomite 14% 13% Clay 4% 6% Fe-Al oxide 2% 3% 8. What is the difference between subgrain formation and formation of recrystallized grains in a strained rock? 9. Describe the sequence of deformation mechanisms that would occur with increasing temperature in an impure sandstone under stress from 100° to 450° C in the presence of water. 10. What is bulging recovery (Figure 8–41a), and under what temperatures does it occur? 11. What microstructures are evident in the quartz (q), feldspar (f), and hornblende (h)? Why do the different minerals have different microstructures? Width of micrograph is 2 mm, cross-polarized light. Sample from mylonite in the Hylas zone, east-central Virginia. q f q q h 12. What microstructures are evident in the quartz that makes up most of this rock? What can be inferred about the conditions under which this rock was deformed? Width of micrograph is 2 mm, cross-polarized light. Sample from a quartzite in west-central Virginia. 13. Describe the texture of this rock. What can be inferred about the conditions under which this rock was deformed? Width of micrograph is 6 mm, cross-polarized light. Sample from a cataclasite in the coast shear zone, British Columbia. 216 | Mechanics: How Rocks Deform Further Reading Groshong, R. H., Jr., 1988, Low-temperature deformation mechanisms and their interpretation: Geological Society of America Bulletin, v. 100, p. 1329–1360. Reviews pressure solution and other low-temperature deformation mechanisms, and discusses how these are recognized in natural rocks. Suggests that rocks “enjoy” rather than “suffer” deformation. Heilbronner, R., and Tullis, J., 2006, Evolution of c-axis pole figures and grain size during dynamic recrystallization: Results from experimentally sheared quartzite: Journal of Geophysical Research, v. 111, issue B10. 19 p. doi:10.1029/2005JB004194. This experiment study illustrates how crystallographic preferred orientations change with increasing strain, and how slip systems evolve during deformation. Hirth, G., and Tullis, J., 1992, Dislocation creep regimes in quartz aggregates: Journal of Structural Geology, v. 14, p. 145–159. Discusses results of experimental deformation of orthoquartzite and novaculite samples under varied temperatures and strain rates. They recognized three regimes in which dislocation creep and recrystallization processes are affected, presenting wellillustrated understandable examples of each. Hull, D., and Bacon, D. J., 2001, Introduction to dislocations, 4th ed.: Oxford, England, Butterworth-Heinemann, 242 p. Defects and dislocations in crystals are explained clearly with good illustrations and without a great deal of mathematics. Karato, S.-I., 2008, Deformation of Earth materials: An introduction to the rheology of the solid Earth: Cambridge, Cambridge University Press. 482 p. An upper level treatment of the material science of deformation. Kerrich, R., and Allison, I., 1978, Flow mechanisms in rocks: Microscopic and mesoscopic structures, and their relation to physical conditions of deformation in the crust: Geoscience Canada, v. 5, p. 109–119. A concise summary of rock-deformation processes with good examples. Lloyd, G. E., and Knipe, R. J., 1992, Deformation mechanisms accommodating faulting of quartzite under upper crustal conditions: Journal of Structural Geology, v. 14, p. 127–143. Discusses, with well-illustrated examples, the deformation mechanisms that accompany faulting and low-temperature deformation of pure quartzite. Means, W. D., 1990, Review paper: Kinematics, stress, deformation, and material behavior: Journal of Structural Geology, v. 12, p. 953–971. Reviews basic continuum mechanics and discusses applications to deformation processes and material behavior. Mathematics is used, but at a level understandable to junior-senior geology students. Nicolas, A., and Poirier, J. P., 1976, Crystalline plasticity and solidstate flow in metamorphic rocks: London, John Wiley & Sons, 444 p. A rigorous book providing a comprehensive survey of plastic deformation processes affecting rocks. Passchier, C. W., and Trouw, R. A. J., 2005, Microtectonics, 2nd edition: Berlin Heidelberg, Springer, Inc. 366 p. A lavishly illustrated textbook that discusses deformation mechanisms and microstructures. Schedl, A., and van der Pluijm, B. A., 1988, A review of deformation microstructures: Journal of Geological Education, v. 36, p. 111–120. Reviews the different grain-scale deformation processes, subgrain formation, recovery and recrystallization processes, and some shear zone terminology. Schmid, S., 1983, Microfabric studies as indicators of deformation mechanisms and flow laws operative in mountain building, in Hsü, K. J., ed., Mountain building processes: New York, Academic Press, p. 95–110. Discusses deformation processes that can be observed on a microscopic scale and how they are related to larger-scale structural features commonly observed in mountain chains. Stipp, M., Stünotz, H., Heilbronner, R., and Schmid, S. M., 2002, The eastern Tonale Line: A “natural laboratory” for crystal-plastic deformation of quartz over a temperature range from 250 to 700° C: Journal of Structural Geology, v. 24, p. 1861–1884. This paper provides calibration of quartz behavior in nature over a significant range of temperature—through much of the temperature range of observation of quartz deformation in rocks from the external to the internal parts of mountain chains, and from the upper to the lower middle crust. Tullis, J., and Yund, R. A., 1985, Dynamic recrystallization of feldspar: A mechanism for ductile shear zone formation: Geology, v. 13, p. 238–241. Tullis, J., and Yund, R. A., 1987, Transition from cataclastic flow to dislocation creep of feldspar: Mechanisms and microstructures: Geology, v. 15, p. 606–609. These papers clearly distinguish between dynamic recrystallization and recovery processes and the deformation mechanisms that occur in feldspar under various physical conditions. PART 3 Fractures and Faults OUTLINE 9 Joints and Shear Fractures 10 Faults and Shear Zones 11 Fault Mechanics 12 Thrust Faults 13 Strike-Slip Faults 14 Normal Faults 269 283 315 331 218 247 9 Joints and Shear Fractures Joints are the most ubiquitous structure in the Earth’s crust. . . . They control the physiography of many spectacular landforms and play an important role in the transport of fluids. D. D. POLLARD AND ATILLA AYDIN, 1988, Geological Society of America Bulletin FIGURE 9–1 Several orientations— sets—of near-vertical joints produced this irregular topography in flat-lying sandstone, Canyonlands National Park, Utah. (Photo by Jesse Varner, accessed through Wikipedia.) 218 Fractures along which there has been no appreciable displacement parallel to the fracture and only slight movement perpendicular to the fracture plane are joints (Figure 9–1). This kind of fracture is extensional, with the fracture plane oriented parallel to σ1 and σ2 and perpendicular to σ3. As such, joints do not form on shear planes. Joints are the most common of all structures, present in all settings in all kinds of rocks as well as in poorly consolidated to unconsolidated sediment. For example, joints occur in unconsolidated glacial sediments in New England and in unconsolidated sediments of the Gulf and Atlantic Coastal Plains. Fractures also form associated with faults and other shear zones. Many of these are extensional, and therefore are joints, but some are shear fractures (Figure 9–2). The kind of fracture that forms depends on the orientation and magnitudes of the principal stresses at the instant the fracture forms and on the mechanical properties of the rock (coefficient of internal friction, anisotropy, etc.). Joints and Shear Fractures Mode I—opening Mode II—sliding Mode III—tearing (a) Mode II here (analogous to edge dislocation) Mode III here (analogous to a screw dislocation) Mixed-mode here (analogous to mixed dislocation) Mode II here Slipped region (b) Mode III here Mixed-mode here FIGURE 9–2 (a) Three modes of fracture formation. (b) Mode II and III behavior may occur during formation on different parts of the same shear fracture. | 219 Three types of fractures have been identified, each type formed by a separate kind of motion (Figure 9–2a). Mode I fractures are joints formed by opening the fracture—extension; Mode II fractures form by sliding; and Mode III fractures form by a tearing motion. Mode II and III fractures are shear fractures, but may propagate into Mode I fractures that form off of the ends of the shear fractures (Scholz, 2002), and not into faults. They may be closer analogues, albeit at a markedly different scale, of edge and screw dislocations (Chapter 8): the same fracture can exhibit both Mode II and III, as well as Mode I— mixed-mode—behavior in different parts of the same fracture (Figure 9–2b). Study of joints and shear fractures is useful in both pure and applied science. Studying the sequence of fracturing and fracture filling in rocks to understand structures bracketed by fracturing events is applied directly in documenting the antiquity of deformation that produced fracturing (or lack of it) in the rocks beneath dams, bridges, and power plants (Figure 9–3). Fracture sequences help to explain the nature of brittle deformation and the timing and mechanical relationships of joints to faults and folds. That valuable minerals may be found in joints and shear fractures has been known for centuries. Joints serve as the plumbing system for ground-water flow in most areas. They provide the only routes by which ground water can move through igneous and metamorphic rocks at an appreciable rate, and they dominate as conduits in well-indurated sedimentary FIGURE 9–3 Near-vertical view of intersecting fracture sets exposed in the excavation for the foundation of a nuclear power plant in South Carolina. Before the foundation could be constructed, all fractures had to be demonstrated to have been inactive for the most recent 500,000 years and to be incapable of tectonic movement during the future life of the plant. Many of the fractures are filled with minerals that have not been deformed. Note construction workers on floor of pit (white hard hats). (Malcolm F. Schaeffer, Duke Power Company.) 0 5 meters 220 | Fractures and Faults and volcanic rocks. Consequently, fracture porosity (and permeability) produced by joints is important for water supplies, notable exceptions being the classic regional aquifer systems of the Gulf and Atlantic Coastal Plains and the Great Plains in North America. Joint orientations in road cuts greatly affect both road construction and maintenance. Those oriented parallel to or that dip toward a highway become hazardous during and after construction because they provide potential movement surfaces. Intersections of joints with each other or joints with bedding or cleavage may form wedge-shaped blocks, which, if they are oriented downward into a highway or railroad cut, may produce rock slides—wedge failures—that pose hazards during construction or later as these blocks loosen with age. Undercutting and oversteepening of slopes during construction may lead to sliding and increased maintenance costs. Rock bolts are frequently employed to stabilize large blocks that cannot be removed; cement grout, rock bolts, or both may be used if the rock is weak or the fracture density high. In mines, subhorizontal joints in the roof must be rock-bolted to prevent collapse. A technique in wide use today for enhancing recovery of natural gas and oil from organic-rich shales involves forcing water or water-based fluids, or nitrogen, into horizontal drill holes that open existing fractures or form new fractures by hydraulic fracturing or “fracking” (see the first Essay in this chapter). This creates porosity in the rock mass around the drill hole and permits natural gas or oil to flow into the hole for recovery. This has become a controversial technique in which claims have been made that it contaminates ground water—the deep disposal of fluids used in this process have been demonstrated to cause earthquakes (Chapter 11 Essay). Joints are planar or irregular surfaces that are said to be systematic or nonsystematic. Systematic joints have a subparallel orientation and regular spacing. Joints that share a similar orientation in the same area are referred to as a joint set. Two or more joint sets in the same area make up a joint system. Most systematic joints are planar surfaces. Joints that do not share a common orientation and those with highly curved and irregular fracture surfaces are nonsystematic joints. They occur in most areas but are not easily related to a recognizable stress field. Occasionally, it can be shown that systematic and nonsystematic joints formed at the same time, but nonsystematic joints commonly terminate at systematic joints (Figure 9–4). FIGURE 9–4 (a) Systematic (red lines) and nonsystematic (brown lines) joints in Middle Cambrian Conasauga Shale, Oak Ridge, Tennessee. Note that systematic joints are linear and form parallel sets; nonsystematic joints are irregular. (RDH photo.) (b) Line drawing showing relationships in (a). (a) (a) Systematic joints Nonsystematic joints Nonsystematic joints Systematic joints (b) Joints and Shear Fractures ESSAY | 221 Fracking Hydraulic fracturing is a technique that has been used for many years for increasing the porosity of oil and gas wells by opening existing fractures or by creating artificial fractures, or for measuring stress in the Earth (see Essay, Chapter 5). Coupled with the recent advances in horizontal drilling technology (invented in the 1970s and improved during the 1980s and 1990s), the technique now referred to simply as “fracking” has made it possible to access the huge, untapped reserves of natural gas and oil where no technology existed before to produce them economically (Figure 9E1–1). These natural gas- and oil-bearing formations—long known to petroleum engineers and geoscientists to contain these valuable hydrocarbons—are concentrated primarily in black, organic-rich shale deep below the surface (Figure 9E1–2a). Since 2010 fracking technology has become the primary method to extract these hydrocarbons, but its use has been met with much controversy in spite of its productivity. The United States has become a major producer of natural gas from shale in Pennsylvania, West Virginia, and several other eastern states, as well as Texas and Louisiana. The Bakken black shale in North Dakota that was known to contain billions of barrels of “tight” oil is now producing major quantities of Colorado Co C o olllo olo orad rado ra ad do do Group oil, enough to decrease the amount of oil the United States has to import each year. So, why is fracking such a controversial technology? Residents in regions where water-based fluids are employed to make hydraulic fractures have claimed that their ground water has been contaminated by the fluids used for fracking. These fluids may contain a combination of inorganic and organic compounds that reduce surface tension and tiny beads called “propants” that are forced under pressure into the newly opened fractures to keep the fractures open and permit the gas or oil to flow into the horizontal well. Part of the problem was created with the enormous volume of fluid required to make this technology work, and some companies permitted their containment facilities to leak. In addition, during the early stages of drilling the vertical part of the hole, drillers commonly insert steel pipe called casing and cement it into place (Figure 9E1–2b). There may be more than one stage of casing and each has to be cemented. If there are remaining voids not filled with cement or cracks form in the cement, these can provide conduits for escape of fluids into the local ground water. There have been videos of residents igniting the water coming out of a faucet, raising WILLISTON ST TON BASIN SN Niobrara MONTANA M THRUST T BELT BE E BASIN n Bakken Utica Heath Frederick Book Cody BIGHORN BASIN Mowry Hilliard Baxter MancosNiobrara GREATER GREEN RIVER BASIN Mancos SAN JOAQUIN BASIN yMontereyTemblorr SANTA MARIA BASIN VENTURA TURA BASIN SN Monterey LOS ANGELES BASIN BA AS N Basins Shale plays: Current Prospective Shale depth: Shallowest Intermediate Deepest Manning Mann anning ing in Cany Canyon C yon on POWDER RIVER BASIN Utica Gamm ammon amm mon o Gammon MICHIGAN BASIN NiobraraMowry NORTH PARK BASIN Niobrara Marcellus FOREST CITY BASIN DENVER ER R BASIN N Antrim ILLINOIS BASIN UINTAPICEANCE BASIN Devonian (Ohio) New Albany Hermosa PARADOX BASIN L Lew ew ew Lewis APPALACHIAN BASIN ExcelloCHEROKEE RATON Mulky PLATFORM BASIN BASIN Pierre Woodford SAN S SA A JUAN AN -Niobrara ANADARK AN Chattanooga VALLEY AND Fayetteville BASIN BASIN BLACK RIDGE WARRIOR PALO DURO BASIN BASIN Bend MARIETTA ARKOMA BASIN Avalon-Bone BASIN Conasauga FloydSpring FORT ARDMORE Neal WORTH BASIN Barnett-Woodford FloydPERMIAN TX-LA-MS BASIN Chattanooga BASIN SALT BASIN Barnett HaynesvilleMARFA Bossier BASIN Tuscaloosa BarnettWoodford WESTERN W ST R RN N GULF Pearsall BASIN Eagle Ford 0 100 0 200 0 300 0 400 00 miles 0 200 400 600 00 0 0 kilometers FIGURE 9E1–1 Simplified tectonic map indicating the locations of basins (lavender) containing organic-rich black shales that have potential or known natural gas and oil reserves. Source: U.S. Energy Information Administration. 222 ESSAY | Fractures and Faults continued Horizontal well (Nitrogen fracking, gas) Conventional well (oil and gas) Coal beds Conventional well (oil and gas) Horizontal well (Nitrogen fracking, oil) Sandstone, shale, and coal 3,000–5,000 ft Shale and limestone Limestone (oil and gas) Limestone reefs (oil) Silty dolomite and shale Siltstone and limestone Organic-rich black shale (gas) Shaly limestone Limestone (oil and gas) Sandy-shaly limestone Limestone Not to scale (a) Kelly bushing Drill platform Artificial fractures Surface casing Concrete around intermediate casing Production tubing Organicrich black shale Concrete around surface casing Horizontal drillhole drill hole Intermediate casing Production casing Not to scale (b) (1) Natural fractures (b) (2) FIGURE 9E1–2 (a) Hypothetical cross section through a region illustrating options for conventional (vertical) or combined vertical-horizontal drilling into different formations. (b) (1) Schematic diagram of a hypothetical drilling operation into a black shale at depth, with enlargements of surface casings and platform and (2) cross section through the horizontal drill hole viewed end-on showing the development of fractures. Note that many existing natural fractures are opened and some new fractures are produced. Joints and Shear Fractures | 223 Time (d) 11:57:48 8 12:13:37 7 12:29:29 9 12:45:20 0 13:01:12 2 13:17:04 4 13:32:55 5 13:48:47 7 14:04:38 8 14:20:30 0 14:36:22 2 (c) (c) FIGURE 9E1–2 ( continued) (c) 3D visualization of operational fracking wells. Spheres represent fracture hypocenters with color representing the time of formation. Note that the cloud of hypocenters around each bore expands with time indicating fracture propagation. Diagram by Yunhui Tan and Terry Engelder (Pennsylvania State University) based on proprietary industry microseismic data from the Marcellus gas shale. additional suspicion about fractures being generated at many thousands of meters (feet) depth that propagated to the surface. In many cases, however, stable isotope analyses of the carbon in methane samples collected from faucet water revealed that the carbon had a near-surface origin (Jackson et al., 2013), such as a barnyard, and not an ancient deep-Earth source. Liquid-based fracking technology must be used where the rocks that are to be fracked are at depths greater than ~1,500 m (~5,000 ft). If the formation of interest is at a depth of < 1,500 m, however, fracking can be accomplished using compressed or liquid nitrogen, because the thinner overburden permits the rocks to be fractured using a gas rather than a liquid. This alternative is much more environmentally compatible because there are not huge volumes of liquids that have to be contained and later disposed of, and the size of the drilling and fracking operation on the surface is much smaller—another environmental gain. This modification of the fracking technology has been applied in parts of Kentucky, Tennessee, and other places where the depth to the formation of interest is relatively shallow. What is the shallow limit to applying the hydraulic fracturing technique? Fracking can be used at any depth, but if the technique is being used to recover economic quantities of hydrocarbons, the overburden thickness of rocks above the formation that contains the gas or oil is a deciding factor in determining whether the hydrocarbons contained in the formation might have already leaked away. A few hundred meters of rock above the formation of interest might be too little overburden to hold in the hydrocarbons for millions of years. These depths are commonly below the depth of today’s ground water—a minimum of ~1,000 m. Another direct effect of the fracking process is earthquakes of magnitude 5 to 6 (magnitude 5 is the threshold of significant damage). The generation of earthquakes by deep, high-pressure fluid disposal has been known since at the least the 1960s (discussed in greater detail in the Chapter 11 Essay). Nevertheless, with increased fracking in the United States to produce natural gas and oil, small earthquakes have become more frequent in areas where fracking is going on, particularly in Oklahoma, Texas, and Ohio. Most of these earthquakes have been produced by deep disposal of fluids (Hand, 2014). Many earthquakes are large enough to be felt by nearby residents, and enough public pressure has emerged that several state legislatures have gotten involved. A few states—such as Vermont and North Carolina—have outlawed the use of fracking technology. Ironically, both of these states have little black shale and thus little to no potential for producing economic quantities of hydro carbons. Germany declared a seven-year moratorium on fracking in 2014, citing concerns about the potential for ground water contamination. Hydraulic fracturing is a viable technology where is it used responsibly. Experiments have been performed to hydraulically fracture a suitable rock mass and then mine out the fractured volume to determine how far these artificially opened fractures actually propagate. They have demonstrated that fractures propagate only a limited distance into the rock mass (Fisher and Warpinski, 2011). There also is a parallel technology in common use where an array of seismometers is deployed in the area around a well that is being fracked. The seismometers locate and track fractures as they form and similarly have demonstrated that the fractures propagate 224 | Fractures and Faults ESSAY continued ‒4,900 ‒5,000 Depth below sea level (ft) ‒5,100 ‒5,200 ‒5,300 5 4 5 8 1 7 8 12 19 14 18 25 43 49 Stress-induced slip on natural fractures 153 277 527 ‒5,400 ‒5,500 ‒5,600 ‒5,700 35 25 12 15 10 1 5 112 204 322 497 629 700 2111 Water injection Stress-induced slip on natural fractures Sand Distribution N = 5853 FIGURE 9E1–3 Graph of the depth frequency distribution of microseismic events (fractures) recorded near a fracked well. Modified from diagram by Yunhui Tan and Terry Engelder (Pennsylvania State University) based on proprietary industry microseismic data from the Marcellus gas shale. Ninety-five percent of fractures occur in the blue-shaded area. only limited distances (50–100 m) from the horizontal borehole (Figures 9E1–2c and 9E1–3). Hand, E., 2014, Injection wells blamed in Oklahoma earthquakes: Science, v. 345, p. 13–14. Jackson, R. B., Vengosh, A., Darrah, T. H., Warner, N. R., Down, A., Poreda, References Cited R. J., Osborn, S. G., Zhao, K., and Karr, J. D., 2013, Increased stray gas Fisher, K., and Warpinski, N., 2011, Hydraulic fracture-height growth: Real data: abundance in a subset of drinking water wells near Marcellus shale gas Society of Petroleum Engineers Annual Technical Conference, SPE 145949, extraction: Proceedings of the National Academy of Sciences, v. 110, p. 8–19. no. 28, p. 11250–11255. Systematic joints may be unfilled; that is, the fractures may be open and devoid of minerals. Generally, these are the most recently formed fractures. Some joint surfaces are highly irregular; others are marked by low concentric ridges, and those with a feathered texture are termed plumose joints (Figure 9–5). Veins are filled joints (and shear fractures; Figure 9–6), and the fillings range from feldspar and quartz (hightemperature pegmatite and aplite veins) to quartz, calcite and dolomite, chlorite, and epidote (and combinations) as well as ore minerals like pyrite. Fractures may also be filled with combinations of zeolites, calcite, and other low-temperature minerals such as prehnite and iron oxides-hydroxides. Unraveling a sequence of crosscutting relationships as well as the compositions of fillings, or lack thereof, and the orientations of fractures may lead to resolution of the chronology of brittle deformation and the thermal history of a rock mass. Both filled and unfilled fractures may occur in conjugate (paired) systems. For paired sets to be conjugates, they must form at nearly the same time. Conjugate joint sets may be produced by tension or shear. Many intersect at an acute angle and are thus shear fractures, but some conjugate joints that meet at 90° may also form by simple shear. It is difficult to prove the conjugate nature of shear fractures unless intersections at outcrop scale emphasize their relationships to each other and to associated structures such as folds or faults (Figure 9–7). Many intersecting fracture sets are first taken to be conjugates, but detailed analysis of their movement histories shows that they formed at different times as joints. If conjugate shears can be proved, the Joints and Shear Fractures | 225 FIGURE 9–5 Plumose joints in Devonian siltstone near Watkins Glen, New York. Note the plumose structure on both layers in the center of the photo that indicates the fracture propagated right to left. (W. H. Bradley, U.S. Geological Survey.) FIGURE 9–6 Several crossing sets of veins—four joint sets later filled with calcite—in limestone at Highgate Springs, Vermont, probably formed at different times. The S-shaped veins may have had a component of shear, along with tension. (C. D. Walcott, U.S. Geological Survey.) 226 | Fractures and Faults FIGURE 9–7 Possible joint orientations related to principal stress axes and larger structures. Note that joints form perpendicular to σ3, which is tensile. Red arrows identify the most important stress axis. (From D. U. Wise, R. Funiciello, P. Maurizio, and F. Salvini, 1985, Geological Society of America Bulletin, v. 96.) σ2 σ2 σ3 σ3 σ3 σ11 (b) Simple vertical uplift and lateral spreading (c) Compressional arching with extension above a neutral surface σ2 σ2 σ1 σ1 (a) Subsiding basin σ2 σ2 σ3 σ3 σ1 σ3 (d) Gravity extension along a coast or mountain front (e) Stretching along a zone of differential uplift or subsidence (f) Hinge line of a subsiding continental margin or basin σ2 σ1 σ1 σ3 (g) Classic E. M. Anderson stress system for graben formation acute angle will be bisected by σ1 (and the Z-axis of the strain ellipsoid) at the time they formed. Curved fractures are common and may be caused by textural or compositional differences within a thick bed or larger rock mass (Kulander et al., 1979) or by changes in stress direction or stress intensity. Many systematic joints may be curved on the mesoscopic scale, but most are planar regionally, although they, too, may have some regional curvature. Fracture Analysis Study of joints in an area reveals the sequence and timing of formation—information with both pure and applied scientific value. Fracture studies in the field provide information on the timing and geometry of brittle deformation of the crust and the way fractures propagate through rocks. Laboratory study of fractures in rocks, artificial materials, and glacial ice enables comparison with natural fractures and leads to an understanding of the mechanics of brittle failure. σ1 (h) Rhine graben stylolitebased stress system σ3 σ11 σ3 (i) Stretching of brittle surface rocks above a semiductile basement undergoing regional compression Significance of Orientation Study of orientations of systematic fractures provides information about the orientation of one (or more) principal stress directions involved in brittle deformation. Regional joint-orientation patterns may be determined by measuring strike and dip (Appendix 2) of mesoscopicscale joints over a wide area. A good estimate of regional joint orientation is sometimes obtained by measuring the strike of linear stream segments on satellite imagery, topographic maps, or aerial photos (Figure 9–8). Data gathered either on the ground or from maps and photos related to orientation and spacing of lineaments may be analyzed to help us to understand the relationships between joints and their influence on drainage development and development of other topographic features. Data may be plotted using an equal-area net (Appendix 2) or rose diagrams (Figure 9–9), although the latter show only the strike and frequency of orientations. Rose diagrams are as useful as equal-area plots for study of joints because most joint sets dip steeply. Shallow-dipping sets are better shown on equal-area plots. Joint sets may also be analyzed statistically. Joints and Shear Fractures | 227 FIGURE 9–8 Aerial photograph of a highly fractured rock mass showing a joint system consisting of several crossing joint sets in Precambrian granitic rocks east of Jeffrey City, Wyoming. (LANDSAT/Copernicus image retrieved from Google Earth.) 0 500 1,000 1,,000 1,0 1 00 meters Studies of joint and fracture orientations from LANDSAT and other satellite imagery and photography have a variety of structural, geomorphic, and engineering applications. As one example, Wise et al. (1985) have used LANDSAT data to interpret relationships between fractures and the Alpine tectonics of Italy (Figures 9–7 and 9–10). They were able to improve delineation of the boundaries of widely known structural features and, because the region is tectonically active, to draw N +++ + ++ ++ ++ + + + + ++ ++ + + ++ + ++ +++ + ++ ++ + + + ++ + + + + ++ + + + + + + + + + + + ++ + + + ++++++ + + ++ + ++ + + +++ + + + + + ++ ++++ + +++++ ++ + + + ++ +++ ++++ + + + + + + + +++ + + + +++ + + + + + + + + ++++ + + ++ + +++ +++ + + + + + + + + ++ +++ ++ + +++ + ++++ ++ + ++ ++ + + +++ + + ++ + ++ + + + ++++ ++ + + (a) conclusions about the orientation of the present-day stress field and the interrelationships of major structural features. Geometric analysis of joints may help determine crustal extension directions, keeping in mind that joints form in the prevailing stress field. The fractures must be shown independently to be joints by finding evidence of extension across one or more sets, and the joint sets can be related to the YZ extension plane (Figure 9–11). N (b) N (c) N (d) FIGURE 9–9 Lower-hemisphere, equal-area plots and rose diagrams of orientations of joints in the Blue Ridge Foothills near Pigeon Forge, Tennessee. (a) Point diagram of 256 poles to joints. (b) Rose diagram of strikes of the same joints. The circle diameter represents 10 percent of the population. (c) Percent per 1 percent area contour diagram of (a). (d) Kamb contour diagram of (a). Contour interval 2 sigma. (See Appendix 1 for plotting and contouring techniques.) 228 | Fractures and Faults N65W 1 n = 633 2 N21E N34W Po N30W N77W N43W N71E N64E N66E is ax N67W n = 550 N53E axis tic N66W 3 N68E n = 588 ria Ad FIGURE 9–10 Fracture and lineament orientations in Italy. Frame 1 is oldest; 9 is youngest. (From D. U. Wise, R. Funiciello, P. Maurizio, and F. Salvini, 1985, Geological Society of America Bulletin, v. 96.) N64E N31W N60W N28W N73W Po Valley Southern Alpine Adriatic N67W N48E N32W N34E N65E N38W 4 N8W n = 547 N70E N67E 5 6 N81E N14W n = 482 (373 + 109) n = 376 N85E N66W N77E N51E N14W N7E N33E N38E Elba N41E Northern Tyrrhenian N10W N7W N87E N23W Southern Tyrrhenian N83E N13W 7 N21E N87E 8 n = 351 n = 257 N79W 9 n = 114 N45W N13E N55W N25E N79W N18E Ligurian N22E N26E Extension direction Shear direction Z Y Shear direction FIGURE 9–11 Jointing related to the strain ellipsoid. N52W Residuals N79W Fracture Formation in the Present-Day Stress Field X Compression direction Italian Peninsular Joint Some have suggested that joint orientation in the sedimentary cover may be controlled by stress in the crystalline basement beneath. Joints may propagate from older crystalline basement rocks into overlying, previously unfractured sedimentary rocks (Hodgson, 1961). The mechanism is poorly understood, but propagation into cover rocks may occur during reactivation of basement fractures—provided the basement fractures and stresses are suitably oriented. Engelder (1982), however, hypothesized that some regional joint sets in eastern North America are a product of the present-day stress field—not inherited patterns from older crust. The joint sets thought to have formed in the contemporary stress field are those not related to any older stress regime. After considering their orientations, surface markings (such as smooth or plumose), and information about stress orientation derived from hydraulic-fracturing measurements and earthquake Joints and Shear Fractures focal-mechanism solutions, Engelder concluded that joints form perpendicular to present-day σ3 (Figure 5–20). Hancock and Engelder (1989) investigated neotectonic joints in a variety of settings, including relatively young rocks. They concluded that neotectonic joints form in the upper 0.5 km of the crust where the stress difference is low, but where effective σ3 is tensile and horizontal, and that these late-formed joints can in turn influence the orientation of the contemporary stress field in an area. The suggestion that joints form in the present-day stress field is borne out of the fact that partially consolidated fine-grained sediments, glacial deposits, and even Quaternary stream deposits frequently contain joints. These fractures frequently exhibit no relationships to fractures in the underlying bedrock. Fold- and Fault-Related Joints Joints frequently form during brittle folding. They may form normal, parallel, and oblique to fold axes and axial surfaces, depending on stress conditions. In one practical application, Nickelsen (1979) made a detailed study of a well-exposed series of deformed Pennsylvanian sandstone, | 229 coal, and shale layers at the Bear Valley strip mine in Pennsylvania (Figure 9–12). He was able to separate early jointing events from later faulting, cleavage formation, folding, later folding that produced new joint sets, and finally, more faulting, which also produced new joints. Joints frequently form adjacent to brittle faults. Movement along faults commonly produces a series of systematic fractures in which spacing decreases closer to the fault zone, and the number of sets also increases. Most are probably joints, but some form as shear fractures. Fracture Mechanics: Griffith Theory Joints and faults are easily observed ruptures in the Earth’s crust. Many faults (Chapter 10) are traceable for hundreds of kilometers; some joint sets are easily traced for tens of kilometers using a combination of field measurements of joint orientations and lineament analysis. For years, geologists have debated the origin of joints and other fractures in FIGURE 9–12 Radiating joints parallel to white lines visible around the hinge of a syncline preserving light-colored sandstone above darker shale and siltstone exposed in the Bear Valley, Pennsylvania, strip mine. Lines indicate fracture orientations. (RDH photo.) 230 | Fractures and Faults rocks. Much of the evidence favors origin of joints perpendicular to σ3, because many joints display no offset, except a few millimeters to a few centimeters perpendicular to the fracture, and thus should be related to a tensional stress field. Jointing and formation of shear fractures may be mechanically related by resolution of the same stresses (and brittle deformation) into normal and shear components, particularly in some folds and close to brittle fault surfaces. This indicates that tensional stress may be present in rock masses undergoing simultaneous compression and shear. We will see this relationship again when we discuss fault mechanics and the interrelationships between all fault types (Chapter 11). What is the ultimate source of these fractures? How are they initiated? Griffith (1920) suggested that ellipticalshaped submicroscopic cracks exist in glass (Figure 9–13) and hypothesized that stress is concentrated and magnified by several orders of magnitude at crack tips. This hypothesis may be originally attributable to Inglis (1913), with Griffith building on these ideas and deriving the energy balance relationships that determine whether or not a crack propagates. The following is summarized from a more detailed treatment of Griffith’s theory in Scholz (2002). If an elliptical crack with semiaxes b and c (with c >> b, and the c-axis of the elliptical hole perpendicular to one of the principal stress directions) occurs in a homogeneous solid, such as glass, the stress concentrations at the ends of the crack increase in direct proportion to c/b as   c  σ ≈ σ∞ 1 + 2     b  (9–1) σ∞ b c or 1 1   c 12  c 12   1 + 2  c 2  ≈ 2σ∞  c 2 , σ (9–2) σ≈ ≈σ σ∞ 1 + 2  ρ   ≈ 2σ∞  ρ  ∞   ρ    ρ     where ρ is the radius of curvature of the crack and σ∞ is the remote principal stress that acts perpendicular to the c-axis of the ellipse. Griffith (1920) employed an energy-balance approach for crack propagation and assumed that the body containing the crack is perfectly elastic, the crack length is 2c, and the crack is loaded by external forces. If the crack length exceeds 2c by an increment dc, the work, W, will be done by external forces and will result in a change in internal strain energy, Ue. Energy will be expended by creating the new crack surface, Us. The total energy, U, for a static crack will be U = (−W + Ue) + Us. (9–3) If the effects of the cohesive strength between extension surfaces dc are removed, crack propagation will proceed—using up energy—until a lower energy state closer to equilibrium is reached. Surface energy increases as the crack grows because work must be done against cohesive forces to increase surface area. This results in lengthening (propagation) of the crack until this energy is used up. Most fracture-forming environments occur below the water table, and so an increment attributable to fluid pressure should also be considered rather than thinking of the fracture-forming process as taking place in totally dry rock. Secor (1969) showed that work is also done on the walls of a crack by fluid pressure. If the dominant source of energy to drive crack propagation is the work done as a result of increased fluid pressure (hydraulic fracturing) during crack inflation, elastic strain energy will be stored around the inflating crack. When the crack propagates, energy is thus available for creation of a new crack surface from both the stored elastic energy and the work done on the walls of the crack by the pressurized fluid as the crack opens incrementally during propagation. The available energy is usually a small fraction of the total surface energy of the crack, and so the crack must also propagate in small increments between times when the crack is being inflated (elastically) by flow of more fluid into it. At equilibrium, an expression for critical stress for crack propagation σf is 1 FIGURE 9–13 Stress distribution around an elliptical hole in a plate composed of a homogeneous material. The elliptical hole has semi-minor and semi-major axes b and c, respectively. Arrows and length of arrows indicate orientation and local magnitudes of uniform stress, σ∞ , located far from the hole. (Modified from Figure 1.2(b) in C. H. Scholz, 1990, The Mechanics of Earthquakes and Faulting, Cambridge University Press.) σ f = (2Eγ/π γ /πc ) 2, (9–4) where E is Young’s modulus and γ is the specific surface energy of the crack. If we consider the process of crack generation as one producing a set of multiple regularly spaced cracks, the theoretical tensile strength, σt , of a Joints and Shear Fractures crack (actually is the strength of rock, because a crack cannot have any strength) can be expressed as σt = Eλ 2 πa (9–5) The theoretical tensile strength will exist at the ends of a crack of length 2c when the following relationship to critical stress exists: 1  c 2 σt = 2σ f   . a and 2γ = Eλσ1 π (9–6) , where λ is the wavelength of the sine wave stress (atomic forces) variation with separation of atoms by the crack, and a is the equilibrium crack spacing (λ ≈ a). Combining equations 9–5 and 9–6, 1  Eγ 2 σt =   .  a  (9–7) (9–8) This equation relates theoretical crack strength to critical stress at equilibrium σf . Griffith’s equations describe behavior of the material under conditions of uniaxial tension, whereas Coulomb’s equation for the Mohr envelope (equation 5–23) describes behavior more exactly for compression (Figure 9–14; Secor, 1965). Griffith’s criterion does not apply to all failure conditions because cracks are closed by compression, increasing rather than decreasing rock strength. Moreover, b) Griffith curve extended τ 4K 2K Shear Stress Coulomb curve extended 231 | c 4 τ= / √3 1 K+ /√ 3σ or τs = τo + σn ϕ tan m ulo o (C 30° Mohr circle (G riffi th ) K K 2K τ 2 − 4K σ− 4K 2 =0 2 √3 K ̶2K Normal Stress (tensile) 0 K 2K 3K 4K 5K Normal Stress (compressive) FIGURE 9–14 Mohr envelope combining both the Griffith and Coulomb failure criteria. Griffith’s equation works better in the parabolic, mostly tensional region; Coulomb’s equation works better in the straight-line part of the envelope. This Mohr diagram is plotted in units of tensile strength. The dashed lines are the projections of lines for the Coulomb and Griffith equations beyond the intersection point c (marked with a circled x). Mohr circle is added for reference. K—stress intensity factor. (After D. T. Secor, 1963, Geology of the central Spring Mountains, Nevada [unpublished Ph.D. dissertation]: Stanford, California, Stanford University.) σn 232 | Fractures and Faults the stresses developed at the crack tips appear independent of crack size and are determined by the shape of the crack, although some have maintained that larger stress concentrations are a function of only crack length (Suppe, 1985). They also predict the orientation of the cracks (Jaeger et al., 2007). Griffith cracks in glass have since been confirmed with the aid of the electron microscope and have dimensions on the order of 100 μm wide by 1,000 μm long. Their existence in other brittle materials, and the applicability of Griffith theory to predict propagation of fractures through rocks, have been debated for many years. Griffith cracks are generally accepted for convenience as a feature of rocks to better understand the process of fracture formation on the submicroscopic scale, despite the anisotropic nature of rocks and the other kinds of fractures that may be present (such as along bedding, cleavage, textural variations, and grain-boundary segments). The size of Griffith cracks in rocks that nucleate joints must be on the order of the maximum grain diameter. A homogeneous stress state exists in a rock mass if no Griffith cracks or discontinuities are present (granted, there may be other conditions that result in a homogeneous stress state). Griffith cracks concentrate stress at crack tips and edges, raising it by several orders of magnitude. The amount of increase depends on the orientation and dimensions of each crack. Larger and suitably oriented cracks will undergo greater stress magnification than smaller and less suitably oriented cracks. Cracks with greater stress magnification will propagate into larger fractures; those with less will remain microcracks. Those suitably oriented would propagate parallel to σ1 and perpendicular to σ3; least favorably oriented for propagation are cracks oriented perpendicular to σ1 and parallel to σ3. The tensile stress, σt , at the tip of an elliptical crack (elliptical in the plane of the crack) in a brittle material under tension σ∞ , perpendicular to the crack, is σt ≅ 2 (2c )2 , σ∞ 3 2b (9–9) where 2c is the length of the crack and 2b is the width (Suppe, 1985). Solving this equation predicts that crack propagation may occur at low stress, because stress amplification results from the relationship between length and width. For example, if the ratio of length to width of the crack is 10 to 1, stress amplification is about 66. If the ratio is 40 to 1, stress amplification is about 1,067. Griffith theory predicts that, for principal stresses σ1 and σ3 , failure will occur under extension in one direction if (σ1 − σ3)2 = 8K0 (σ1 + σ3) and (σ1 − σ3)2 − 8K0 (σ1 + σ3) = 0 (9–10) or, alternatively solving equation 9–10 for the points of intersection of the straight line (Coulomb behavior) and the parabola (Griffith behavior) (Figure 9–14) yields τ 02 = 4Kσn − 4K2 , or τ 02 − 4Kσn + 4K2 = 0, (9–10a) where K is uniaxial tensile strength and τ0 is cohesive strength. If σ1 + 3σ3 > 0 in equation 9–10, the principal stresses required for failure are given by equation 9–10. If σ1 + 3σ3 < 0, failure is independent of the value of σ1 and occurs when σ3 equals the uniaxial tensile strength K. Equations 9–10 and 9–10a, along with the qualifiers, make up the Griffith criterion for failure. Griffith theory works well to predict the behavior of homogeneous materials under tensional stresses and will predict the shape of the parabolic part of the fracture envelope in the tensional field of the Mohr diagram (Figure 9–14), but, because there must be no cohesion between surfaces, it does not work well under compression. A modified Griffith theory has been devised that permits fractures to form under compression with the necessity that they overcome friction by reaching a “critical stress” for crack propagation (Jaeger et al., 2007). The importance of Griffith theory is that it predicts that the compressive strength (at zero confining pressure) of most materials will be eight times the tensile strength. Measured ratios of seven rock samples range from 9 to 17, with an average near 14 (Jaeger et al., 2007, their Table 6.15.1). An important conclusion to be drawn from this discussion is that the stress difference (σ1 − σ3) must be eight times the compressive strength before the Coulomb-Griffith failure envelope in the Mohr diagram is reached in compression, and < 4 times the tensile strength before it is reached in tension. This again confirms that most rocks have lower tensile than compressive strengths. Joints and Fracture Mechanics Development of the following concepts of fracture toughness and fracture energy are summarized from Scholz (1990, 2002). If a crack is planar, well defined, and there is no cohesion between the crack walls, a relationship exists between the stress σij at a crack tip and the resulting displacement 1 σij = K n (2π πr ) 2 fij (θ ) (9–11) and 1  K  r  2 U i =  n   fi (θ ),  2E  2π π (9–12) where r is the distance from the crack tip, θ is the angle measured from the crack plane to the point where the Joints and Shear Fractures stress is σij , and Kn is called the stress intensity factor and is specific for each fracture mode (Figure 9–2a), with the designations K I for Mode I, K II for Mode II, and K III for Mode III. f i(θ) expresses θ as a function of Ui , the energy term defined in equation 9–3. The notation σij is tensor notation indicating the stress σij is a second-rank tensor, and Ui , total energy, is a first-rank tensor; i and j can independently have values of 1, 2, 3. . . . Values for K I , K II , and K III depend on the geometry and magnitude of the applied stress and the determined intensity of the cracktip stress field (Scholz, 1990, 2002). The stress intensity factor may be related to the Griffith energy-balance relationships by d (−W + U c ) , G=− dc (9–13) K2 , G= E (9–14) | 233 σyy τyx τyz where G is the energy release rate, or crack extension force, and Uc is elastic strain energy. Two different equations are needed, one for plane stress, and another for plane strain K 2 (1 − vν 2 ) , G= E (9–15) where ν is Poisson’s ratio. For Mode III, the right side of equations 9–14 and 9–15 have to be multiplied by (1 + ν) for plane stress, and divided by (1 − ν) for plane strain. From equation 9–3 and the equilibrium condition dU/dc = 0 (recall c is equilibrium crack length), cracks will propagate when 2 Kc = 2γγ , G= E (9–16) where G is fracture energy when uniform stresses, σij , are applied remotely (far field) from the crack, and Kc is the criticalstress intensity factor (also called fracture toughness). Kc and E are both material properties that provide general failure criteria, because they can be determined and related experimentally for individual rock types (Scholz, 1990, 2002). The relationships for the three fracture modes (Figure 9–15) are 1 K I = σ yy (π πc )2 1 πc )2 K II = σ xy (π 1 K III = σzy (π πc )2 , FIGURE 9–15 Resolution of normal (σyy) and shear (τyx and τyz) stress components around an elliptical crack in a plate subjected to a uniform stress field. (Modified from Figure 1.7(b) in C. H. Scholz, 1990, The Mechanics of Earthquakes and Faulting, Cambridge University Press.) (9–17) and, from equation 9–15, the crack extension forces for each corresponding mode are π πc G I = (σ yy )2 E 2 πc G II = (σ xy ) E π πc (1 + v ) . G III = (σzy )2 E (9–18) For plane strain, it is necessary to replace E with [E / (1 – ν2)] for both Modes I and II. Stress intensity factors permit useful inferences to be made about the propagation and behavior of joints. Using the expression for K I in equation 9–17 for a Mode I fracture, when K I reaches a critical value, (9–19) K I = K Ic where K Ic is fracture toughness, a natural property, the joint will propagate. The most useful attribute of the stress intensity factor is that it is based on a heterogeneous stress field at a crack tip. This property predicts, for example, that if two joints of unequal length exist in the same stress field, the longest will meet the criterion in equation 9–19 first. This property also predicts that an existing joint subjected to the greatest stress among a set of joints of equal length will propagate first in a stress field that varies with position in a rock mass (Pollard and Aydin, 1988). Experiments can produce joints by forcing fluid into microscopic rock pores to lower the effective normal stress 234 | Fractures and Faults (normal stress minus pore pressure, equation 9–20) until the tensile strength of the rock is exceeded. Theoretical and field studies indicate that fluid probably plays an important role in formation of many joints. Studies by Secor (1965), Pollard and Holzhausen (1979), and Segall and Pollard (1983) revealed that joints form more readily in the presence of fluid, generating fractures by hydraulic fracturing. Secor (1965) considered effective normal stress (σn − P, where P is fluid pressure) and concluded that joints can form in a compressive environment if fluid pressure is high. Fluid under pressure (compression) is forced into the fracture and promotes continued fracture propagation. This process occurs in the upper crust where water is abundant and, interestingly, may also be the mechanism for forcible dike emplacement, with magma serving as the fluid (Odé, 1957; Pollard and Muller, 1976; see Chapter 20). Fractures in rock may begin as Griffith cracks (microcracks in grains) and then coalesce into more continuous oriented fractures to ultimately form joints. One consequence of Griffith theory is the prediction that stress difference for jointing must be less than four times the tensile strength of the rock (Jaeger and Cook, 1976), although fracturing may occur whenever σ3 is tensile and equal to the uniaxial tensile strength of the rock. Terzaghi (1923) suggested that shear resistance of soils (or rock) may be calculated by a modified version of the Coulomb criterion, |τc| = τ 0 + (σn − Pw ) tan ϕ, (9–20) where τc is critical shear stress, τ 0 is cohesive strength, σn is normal stress, Pw is pore pressure—pressure exerted by a fluid against the walls of a microscopic opening in a rock, ϕ is the internal friction angle, and tan ϕ is the coefficient τ of internal friction (μ) in equation 5–23. This idea has been applied extensively to shear fractures and faults formed in rocks that are saturated with fluid (Hubbert and Rubey, 1959) (Figures 9–14 and 9–16). This also must be taken into account in determinations of stress intensity factor. Equation 9–17 for a Mode I fracture should thus be modified to accommodate fluid pressure as 1 K I = (σ yy − P )(π πc ) 2 . (9–21) Estimates of fracture toughness should be modified as well, but the nature of predictability and usefulness of the stress intensity factor remain unchanged. While the simple Terzaghi modification of the Coulomb equation can be readily verified under controlled laboratory conditions, in natural systems fluid pressure must be resolved into both vertical and horizontal components. This produces a net decrease in the diameter of the Mohr circle for effective normal stress. Nevertheless, the circle is still shifted toward the tensile field so that an additional increase in pore pressure may lead to failure at values of zero or negative (tensile) effective normal stress (Mandl, 1988). Fracture Surface Morphology Most joints form by extensional fracturing of rock in the upper few kilometers of the Earth’s crust. The limiting depth for formation of extension fractures ideally should be the ductile-brittle transition (Chapter 6), which is influenced by rock type, fluid pressure, strain rate, Compression failure occurs Mohr envelope Tension failure occurs Mohr circles in stable field σn σn − P Effect of fluid pressure σn − P FIGURE 916 Mohr circles for stress, showing the effect of a fluid and pore pressure on effective normal stress. A dry material (dashed circles) remains in the stable field in contrast to the same material after adding fluid pressure. Failure would occur whenever the circles became tangent to the envelope. The envelope relative to the fluid-saturated material indicates failure because of decreased strength and effective normal stress. Joints and Shear Fractures geothermal gradient, and the stress difference. Under appropriate conditions such as high strain rate, however, high-temperature veins (e.g., pegmatites) form below the ductile-brittle transition, and extension fractures commonly form during ductile deformation in ductile shear zones (Hudleston, 1989; Chapter 11). Features on joint surfaces, such as plumose structure (Figure 9–5), provide clues to the direction of joint propagation. Other features provide details of the mechanics of formation of extension fractures and information on the rate and direction of propagation of individual joint planes. In Figure 9–17, hackle marks indicate zones where the joint propagated rapidly, while the arrest line is perpendicular to the direction of propagation and forms parallel to the advancing edge of the propagating fracture (Hodgson, 1961; Kulander et al., 1979). Propagation of a joint always begins at a preexisting flaw in the rock mass, a grain of atypical FIGURE 9–17 (a) Detail of plumose joint surface showing primary surface structures: 1. Main joint face. 2. Twisthackle fringe. 3. Origin. 4. Hackle plume. 5. Inclusion hackle. 6. Plume axis. 7. Twist-hackle face. 8. Twist-hackle step. 9. Arrest lines. 10. Constructed fracture-front lines. (From B. R. Kulander and S. L. Dean, 1985, Proceedings of the International Symposium on Fundamentals of Rock Joints.) (b) Detail showing other features associated with propagation of the joint. (From Kulander, Barton, and Dean, 1979, The application of fractography to core and outcrop fracture investigations, U.S. Department of Energy METC/SP-79/3.) | 235 size or hardness, a fossil, a concretion, a pore space, an irregularity in bedding, or other mechanical discontinuity. The joint may propagate from the flaw under ideal extensional conditions and form a symmetrical plumose surface with symmetrical twist hackle and arrest lines. Asymmetric plumose structure, twist hackle, and other features require stress orientation to change as the joint propagates (Figure 9–18) (Kulander et al., 1979). The explanation is reasonable if the asymmetric plume occurs on a fracture through a single bed and if the beds above and below have symmetrical plumes, but if the same sense of asymmetry occurs on plumes in successive layers, the fracture is likely to be a hybrid shear (mixed-mode fracture) and not a joint (Hancock and Engelder, 1989). Such observations are important to understand the mechanisms of fracture formation and determine whether a series of fractures consists of joints, shear fractures, or hybrid shears. Bedding plane 8 2a 9 4 1 5 6 3 10 2b 7 Bedding plane 8 (a) re S o ati ag tu rac n tio ec ir nd p pro twist hackle rder o d econ le ck ha t is Tw F St t line rig Streak in P rin ci (b) pa l se ar Co Arres or irr M sion n te ist M ace ef l k ac ep h st istkle Tw ac h istTw le ck k rea O p ste ha 236 | Fractures and Faults FIGURE 9–18 (a) Subhorizontal plumose joint in Middle Proterozoic Killarney Granite on Georgian Bay near Killarney, Ontario. The plumose pattern here indicates that the fracture propagated from top to bottom of the photo. The irregular pattern at the edge of the smooth fracture is twist hackle. This joint was created as a Pleistocene glacier moved over the rock surface and plucked a mass of bedrock. (RDH photo.) (b) Glacially produced joint surface in Killarney Granite at the same locality as (a) with arrest lines that are concentric with the origin of the fracture. The joint therefore propagated right to left. Faint plumose structure is also visible on the joint surface. (RDH photo.) (a) (b) Joints and Shear Fractures (c) | 237 (d) FIGURE 9–18 (continued) (c) Twist hackle at the edge of a joint in Jurassic Aztec Sandstone, southeastern Nevada. (d) Irregular plumose structure on a joint surface in Devonian Genesee siltstone near Watkins Glen, New York, indicating that either a change of propagation direction during fracturing or a component of simple shear was present. [Parts (c) and (d) courtesy of Atilla Aydin, Stanford University.] Bedding and foliation planes in coarser-grained rocks constitute barriers to joint propagation. Bedding in uniformly fine-grained rocks, such as shales and volcaniclastic rocks, appears to be less of a barrier or none at all. Joints frequently propagate through a sandstone bed and are slightly offset from those in the next layer above or below. Variation in bed thickness also affects propagation direction as well as spacing between joints. Thin beds (e.g. in shale) produce more closely spaced joints, while thick beds (e.g., massive sandstone or limestone) produce widely spaced joints. This relationship is not quite as simple as just stated, because rock type and texture may also influence joint spacing (Ladeira and Price, 1981). Differences in stress magnitude between layers produce a barrier to joint propagation through a section of alternating sedimentary rock types. For example, assuming horizontal layering, joints will not propagate from sandstone into shale if the least principal horizontal stress in the shale is greater than that in the sandstone: fractures will terminate at the contact between the two rock types (Engelder, 1985). Engelder (1985) characterized both the environment and mechanisms of joint formation and described four categories of joints as end-member paths for increase of stress (Figure 9–19): tectonic, hydraulic, unloading, and release joints. All categories embody the assumption (based on many observations) that the failure mechanism is tensile. Tectonic and hydraulic joints form at depth in response to high fluid pressure and involve hydrofracturing. Hydraulic joints form during burial and vertical compaction of sediment at depths greater than 5 km where escape of fluid is hindered by low permeability, which creates locally abnormally high pore pressure. This process is static, whereas tectonic joints form by essentially the same mechanism, but the stresses are tectonic and horizontal compaction occurs. Unloading and release joints form near the surface as erosion removes overburden, and thermal-elastic contraction occurs. Unloading joints typically form when more than half the original overburden has been removed from a rock mass. Contemporary tectonic or remaining ancient stresses may serve to orient these joints. This is thought to occur during cooling and elastic contraction of a rock mass as it is exhumed by erosion and may occur at depths of 200 to 500 m. The most common unloading joints are subhorizontal. Decrease in horizontal stress provides a similar opportunity for release joints to form. Orientation of release joints is controlled by the existing rock fabric, in contrast with the three other types recognized by Engelder (1985, 1993), which are stress controlled. Release joints form late in the history of an area and are ultimately oriented perpendicular to the original tectonic compression that formed the dominant fabric in the rock, which could be bedding or a foliation. Tectonic stress may further increase the stress perpendicular to future joint planes as burial depth and degree of lithification increase. After erosion begins, and the rock mass begins to cool and contract, these joints begin to propagate parallel to bedding or an existing tectonic fabric, such as a prominent cleavage. In that way, release joints may also develop parallel to fold axial surfaces. | Fractures and Faults to Tec nic Release joint uda tion compression Tectonic joint Den l Depth co m pa Unloading joint cto nic Hydraulic joint Te Dewatering re Po De ompaction e ur s es pr nu da C cti on ria Bu tio n Effective stress perpendicular to joint 238 Hydrostatic gradient Tensile strength of rock Lithostatic gradient Joints in Plutons Fractures form in plutons in response to cooling and later tectonic stress (Figure 9–20) (also see the next section and Chapter 20). Orientations of joints that form in a cooling pluton may be influenced by the boundary of the pluton or by its general shape and internal structure. Some large stocks contain joints that are more or less concentric with the internal structure of the pluton and may also be related to the shape of the contact with the country rock. Fracture density and orientation may vary with changes in rock texture or fabric as well as proximity to the contact of the pluton with the enclosing rocks. Columnar joints (discussed later) form in flows and shallow plutons as a response to cooling and crystallization of magma. Balk (1937) studied fractures in igneous bodies and recognized that fracturing occurs both as a result of flow related to emplacement of semi-solid magma and as a product of later regional stresses. Early joints form in plutons during the final stages of magma crystallization. He FIGURE 9–19 Loading paths for Engelder’s tectonic, hydraulic, unloading, and release joints as a function of three variables: (1) pore pressure, (2) depth, and (3) effective stress perpendicular to the joint. Arrows indicate expected directions of movement along pathways. (From Journal of Structural Geology, v. 7, Terry Engelder, p. 459–476, © 1985, with kind permission from Elsevier Sciences, Ltd., Kidlington, United Kingdom.) recognized that many early fractures form in relation to flow banding in the pluton, either across, parallel, or diagonal to banding. Many joints are filled with hydrothermal minerals or crystallization products from late-stage volatile-rich magmas that crystallize pegmatite, aplite, and quartz veins. Balk concluded that the cross fractures are joints and that the diagonal fractures, which form as conjugate sets, are shear fractures. Parallel or longitudinal fractures are more difficult to relate to extensional or shear stresses. Balk also found that joints are more common and more closely spaced near the margins of a pluton. He suggested that processes related to magma emplacement and cooling of the margins may fracture both the early cooled parts of the magma and the country rock (Figure 9–20), forming both joints and faults. Many joints in plutons, as in most other rock masses, form by tectonic and unloading forces superposed long after the pluton has cooled. Balk’s analysis of fractures in plutons is useful where early formed fractures related to emplacement can be separated from later tectonic and unloading joints. One way to accomplish this is to study Joints and Shear Fractures Dike | 239 Dikes Dike Dikes FIGURE 9–20 Joint patterns developed in a pluton. Note the greater joint density near the pluton margins (edge of block). The curved surface on top is the present erosion surface. Short, brown, discontinuous lines are joints that form parallel to flow directions. Longer green lines parallel to the shorter are sheeting (unloading) joints. Near-vertical joints (orange lines) form by regional bending of the crust, possibly related to intrusion of the pluton. Small faults (blue lines) displace the margin of the pluton, along with older joints, and dikes (red lines) inside it. (Modified from Robert Balk, 1937, “Structural behavior of igneous rocks”, Geological Society of America Memoir 5, modified from a drawing by Hans Cloos of structures in a pluton in the Strehlen massif, eastern Germany.) the properties of joints present both inside and outside the pluton, taking into account differences in rock type. Nontectonic and Quasitectonic Fractures Sheeting A kind of joint that forms subparallel to surface topography, generally in massive rocks and corresponds to the unloading joints of Engelder (1985), is called sheeting. Most often, these fractures may be observed in igneous rocks, but they also form in metamorphic rocks. The spacing between sheeting fractures increases downward into the crust (Figure 9–21). Quarrymen have used sheeting fractures for centuries in quarrying dimension (building) stone to minimize the amount of blasting necessary to remove large blocks. Sheeting is thought to form by unloading over long periods of time as erosion removes large quantities of overburden from a rock mass. The mass expands perpendicular to the Earth’s surface (σ3 vertical) so that extension fractures form perpendicular to the expansion direction and parallel to the surface (Johnson, 1970). Many sheeting joints appear to form perpendicular to a small compressive σ3 , an unexplained phenomenon that is not supposed to happen according to the Griffith failure criterion, although Griffith recognized that tensile stress can still occur at a crack tip even if the far-field stress is all compressive (Price and Cosgrove, 1990). This appears to be a fundamental problem that warrants further investigation. Columnar Joints and Mud Cracks Columnar joints form in flows, dikes, sills, and (occasionally) in volcanic necks in larger plutons in response to cooling and shrinkage of congealing magma (Figure 9–22) and are thus nontectonic structures. Thermal gradients and contraction processes in the magma control the orientation of columnar joints. The orientation of columns is generally perpendicular to the sides of a pluton. They may become curved if the thermal gradients and contraction processes are nonuniform or if the magma is still moving slightly as the joints form. Columnar joints commonly have five or six planar sides. Ideally, the most efficient geometric resolution of fractures in a uniaxial contraction 240 | Fractures and Faults FIGURE 9–21 Subhorizontal sheeting joints in a granite quarry in Massachusetts. Note that the joints are sub-parallel to the surface and that spacing increases with increased depth to a maximum of 6 m at the lower left. (L. C. Currier, U.S. Geological Survey.) FIGURE 9–22 (a) Columnar joints in Quaternary basalt near Whistler, British Columbia. (a) Joints and Shear Fractures | 241 FIGURE 9–22 (continued) (b) Closeup of columnar basalt in (a). Columns are about 1 m across. Note Mode I fractures perpendicular to the long axes of the columns. (RDH photos.) (b) stress field is a set of hexagonal prisms if the stresses, cooling rate, and thermal gradient were perfectly uniform throughout the cooling magma body (Figure 9–23). A highly symmetrical cylindrical stress field will form in which joints begin to form as the magma contracts. This forms hexagonal extension fractures in the congealing magma. Mud cracks (Chapter 2) form on the Earth’s surface by a similar mechanism—shrinkage and evaporation of water in unconsolidated sediment (Figure 2–10); they appear as four-, five-, six-, or seven-sided polygons, which frequently curl up at the edges. We now leave our discussion of joints and shear fractures and begin an exploration of faults and faulting processes. ESSAY FIGURE 9–23 Formation of hexagonal fractures that form around uniformly distributed centers (axes) of contraction. Arrows indicate orientations of tensile stresses. esozoic Fracturing of Eastern North M American Crust—Product of Extension or Shear? The present-day Atlantic Ocean probably opened along the coast of eastern North America ~200 Ma following initial strike-slip faulting and then a period of rifting of the continental crust that produced block-faulted basins that formed the Triassic–Jurassic basins along the axis of the Paleozoic Appalachian orogen (Withjack et al., 2012). The basins and the adjacent Piedmont were intruded by diabase dikes (Figure 9E2–1) throughout the Appalachians from Alabama to southern New England. The dikes from Virginia southward mostly trend northwest-southeast and contain olivine; from Virginia northward, they trend more northerly to northeasterly and contain quartz (Ragland et al., 1983). 242 ESSAY | Fractures and Faults continued A similar pattern occurs on both sides of the Atlantic, interpreted by May (1971) to indicate extension along the line where early Mesozoic separation of the continents began. An alternative explanation by de Boer and Snider (1979) is that Mesozoic dikes in eastern North America formed as a product of doming over a mantle hotspot in the Carolinas. The dikes examined by May and by de Boer and Snider have since been shown to be crosscut by a younger set of north– south-trending Mesozoic diabase dikes in the Carolinas and Virginia; this set converges toward a point near Charleston, South Carolina (Ragland et al., 1983; Figure 9E2–1). Both dike sets appear to be extensional. Fracture zones filled with quartz and then broken by reactivation several times and each time healed by quartz to form siliceous cataclasite (coarse-grained breccia and finegrained gouge) occur in the same region (Figure 9E2–1). In the central and southern Appalachians, they are oriented approximately north–south and east–west (Conley and Drummond, 1965; Birkhead, 1973; Garihan et al., 1988, 1993; Huebner and Hatcher, 2013); in some places, they appear to offset diabase dikes (e.g., Huebner and Hatcher, 2013, their Figure 4D), but in others, the siliceous cataclasites are cut by the dikes (Garihan et al., 1988, 1993). Thus, the diabase dikes and siliceous cataclasite fracture zones may have formed about the same time ~200 Ma. If so, several extension directions may have existed at the same time, but that is mechanically unlikely. Note that the siliceous cataclasite zones are filled with remobilized quartz (with or without feldspar and prehnite). Many contain open spaces, boxwork structure, and vugs into which quartz crystals have grown, further indicating their extensional nature. They also contain abundant evidence of reactivation, with ground-up and fragmented early quartz recemented by later vein quartz. These zones rarely exhibit evidence of offset parallel to their lengths: rock-unit boundaries between bodies that trend into them are only minimally offset. One area in the southern Piedmont of Georgia contains siliceous cataclasite dikes that have a left-lateral displacement of a few kilometers (Hooper, 1989). Swanson (1982, 1986) suggested that the crust of eastern North America was subjected to largescale left-lateral deformation as North America and Africa were attempting to separate, but this deformation was short lived as the two continents began to pull apart, the Atlantic Ocean began to open, and extension dominated. Evidence supporting left-lateral deformation is present in both the central and southern Appalachians (Swanson, 1982; Huebner and Hatcher, 2013). In addition to left-lateral offset of diabase dikes along cataclasite zones, there are TN PA AL VA M MD NJ DE GA N SC NC Charleston 0 100 200 300 kilometers FIGURE 9E2–1 Distribution and orientations of Triassic–Jurassic diabase (red and purple lines) and some siliceous cataclasite f racture zones (dark green areas) in the southeastern United States. Triassic–Jurassic basins are represented by shaded areas. (Modified from P. C. Ragland, R. D. Hatcher, Jr., and D. Whittington, 1983, Geology, v. 11.) Joints and Shear Fractures | 243 (a) (b) FIGURE 9E2–2 (a) Photomicrograph of siliceous cataclasite from near Westminster, South Carolina. Note the abundant angular fragments and crosscutting veins. (b) Quartz mylonite specimen from central Georgia. The quartz was ductilely deformed at temperatures just above the threshold for plastic flow. This deformed individual quartz grains into a series of elongate, overlapping “ribbons.” Specimen is 22 cm long. (Specimen courtesy of Matthew T. Huebner, Tennessee Valley Authority, Chattanooga, TN.). 244 | ESSAY Fractures and Faults continued Siliceous cataclasite dikes Z Shear planes Y Z Z X N X X Siliceous cataclasite dikes and quartz mylonite Diabase dikes (a) t1 (Triassic) (b) t2 (Early Jurassic) (c) FIGURE 9E2–3 Possible strain-ellipsoid orientations for siliceous cataclasite and diabase dikes in the eastern United States. (a) Model 1—Diabase dikes with a N 45° W orientation form by extension; siliceous cataclasite dikes form at the same time by shear, N–S diabases formed later by reorientation of the extensional stress field of the strain ellipse. Against the model: Because cataclasites contain open-boxwork quartz, extension is required for at least part of their history. They also have little or no displacement. (b) Model 2—All diabases and siliceous cataclasites formed by extension, produced by multiple orientations of the strain ellipsoid at about the same time. The N–S diabases formed later. Against the model: It requires nearly simultaneous and mechanically unlikely multiple extension directions, also unlikely over short periods of geologic time. (c) Model 3—N 45° W diabases formed by extension; siliceous cataclasites were initiated by shear without much accompanying displacement. Siliceous cataclasites were reactivated by later extension and filled with hydrothermal quartz. N–S diabases formed by later extension involving a strain ellipsoid with a different orientation. quartz mylonite bodies that appear to be associated with the cataclasites (Figure 9E2–2). These were either formed at greater depths during an earlier period of movement as the two continents were in the early stages of trying to separate, or are totally unrelated to the cataclasite. The fact that both cataclasite and mylonites are composed of quartz may indicate some commonality of origin. Is it possible that the early diabase dikes are purely extensional features and that the siliceous cataclasite zones are conjugate shears (Figure 9E2–3)? If so, the siliceous cataclasite bodies are shear fractures with no displacement parallel to the shear zone, and after they were formed, were followed by repeated opening normal to the shears and filled with quartz. If not, simultaneous or alternating crustal extension in several directions would be required. geology with a focus on the Columbus Promontory: Carolina Geological Society Annual Field Trip November 6–7, 1993, Field Guide, p. 55–65. Garihan, J. M., Ransom, W. A., Preddy, M., and Hallman, T. D., 1988, Brittle faults, lineaments and cataclastic rocks in the Slater, Zirconia, and part of the Saluda 7.5-minute quadrangles, northern Greenville County, SC, and adjacent Henderson and Polk Counties, NC, in Secor, D. T., Jr., ed., Southeastern geological excursions: Columbia, South Carolina, Southeastern Section Geological Society of America, p. 266–312. Hooper, R. J., 1989, Tectonic implications of a regionally extensive brittle fault system in the Piedmont: Evidence from central Georgia: Geological Society of America Abstracts with Programs, v. 21, p. 22. Huebner, M. T., and Hatcher, R. D., Jr., 2013, Polyphase reactivation history of the Towaliga fault, central Georgia: Implications regarding the amalgamation and breakup of Pangea: Journal of Geology, v. 121, p. 75–90. May, P. R., 1971, Pattern of Triassic–Jurassic diabase dikes around the North Atlantic in the context of predrift position of the continents: Geological Soci- References Cited ety of America Bulletin, v. 82, p. 1285–1291. Birkhead, P. K., 1973, Some flinty crush rock exposures in northwest South Ragland, P. C., Hatcher, R. D., Jr., and Whittington, D., 1983, Juxtaposed Mes- Carolina and adjoining areas of North Carolina: South Carolina Geologic ozoic diabase dike sets from the Carolinas: A preliminary assessment: Geol- Notes, v. 17, p. 19–25. ogy, v. 11, p. 394–399. Conley, J. F., and Drummond, K. M., 1965, Ultramylonite zones in the western Swanson, M. T., 1982, Preliminary model for an early transform history in cen- Carolinas: Southeastern Geology, v. 6, p. 201–211. tral Atlantic rifting: Geology, v. 10, p. 317–320. de Boer, J., and Snider, F. G., 1979, Magnetic and chemical variations of Meso- Swanson, M. T., 1986, Preexisting fault control for Mesozoic basin formation zoic diabase dikes from eastern North America: Evidence for a hotspot in the in eastern North America: Geology, v. 14, p. 419–422. Carolinas?: Geological Society of America Bulletin, v. 90, p. 185–198. Withjack, M. O., Schlische, R. W., and Olsen, P. E., 2012, Development of the Garihan, J. M., Preddy, M. S., and Ranson, W. A., 1993, Summary of mid-Mesozoic passive margin of eastern North America: Mesozoic rifting, igneous activity, brittle faulting in the Inner Piedmont and nearby Charlotte Belt of the and breakup, in Roberts, D. G., and Bally A. W., Phanerozoic rift systems and Carolinas, in Hatcher, R. D., Jr., and Davis, T. L., eds., Studies of Inner Piedmont sedimentary basins: New York, Elsevier Publishing, p. 301–335. Joints and Shear Fractures | 245 Chapter Highlights • Joints are the most common structures in rocks. • Joints are extension fractures in which movement occurs perpendicular to the fracture. • Joints can form by tectonic processes, hydraulic fracturing, and mechanical unloading. • Increased pore fluid pressure, lowers the effective stress and can produce fractures in tension. • Shear fractures form by movement parallel to the fracture plane. Questions 1. How can we distinguish between systematic and nonsystematic joints? 2. What does an asymmetric twist-hackle structure on a joint surface tell you about the way the joint formed? 3. How would systematic orientation of joints be established by a hydraulic-fracturing mechanism? 4. How could filled joints and unfilled joints form at the same time with different orientations? 5. What is the best evidence that most joints form by extension? 6. How do columnar joints form? 7. Explain the role of water and its effect on fracture formation using Terzaghi’s modification of the Coulomb-Mohr equation (equation 9–20). 8. What evidence tells us that some regional joints in eastern North America may have formed in the present-day stress field? 9. Suppose joints formed at a locality where the earliest set was filled with quartz-feldspar (pegmatite), then cut by a set containing quartz-epidote, which was in turn crossed by a quartz-calcite-prehnite set, then by a set of calcite- and laumontite-filled joints, and finally by an unfilled joint set. (Each set has a different orientation.) What can you conclude from the temperature conditions in which these minerals form about the conditions under which these different joint sets formed? 10. Are sheeting joints and Engelder’s release joints related? 11. How can tectonic stresses tens or hundreds of millions of years ago influence orientations of joints that formed in the past five million years? 12. Why are the tensile strengths of rocks almost always less by a large amount than their compressive strengths? 13. If the brecciation and formation of each of the veins in Figure 9E2–2b represents a separate event, how many events are represented in this photomicrograph? Further Reading Engelder, T., 1985, Loading paths to joint propagation during a tectonic cycle: An example from the Appalachian Plateau, USA: Journal of Structural Geology, v. 7, p. 459–476. Classifies joints and relates them to variables of effective stress normal to the joint, depth, pore pressure, tensile strength of the rock, and hydrostatic/lithostatic gradients through time. Engelder, T., 1993, Stress regimes in the lithosphere: Princeton, New Jersey, Princeton Press, 457 p. Outlines basic rock and fracture mechanics, microfractures, stress measurement, hydraulic fracturing, and earthquakes. Gale, J. F. W., Laubach, S. E., Olson, J. E., Eichhubl, P., and Fall, A., 2014, Natural fractures in shale: A review and new observations: American Association of Petroleum Geologists Bulletin, v. 98, pp. 2165–2216. Discusses formation of joints and other fractures in shale but most of the discussion is applicable to fracture formation in other rock types. They also discuss the use of fracking to open old fractures and create some new ones. Hancock, P. L., 1985, Brittle microtectonics: Principles and practice: Journal of Structural Geology, v. 7, p. 437–457. Analyzes brittle structures as a way to solve tectonic problems. Joints are assumed to result from either extension or shear. Pollard, D. D., and Aydin, A., 1988, Progress in understanding joints over the past century: Geological Society of America Bulletin, v. 100, p. 1181–1204. Reviews development of ideas on joint formation, including tectonic and nontectonic joints. 246 | Fractures and Faults Scholz, C. H., 2002, The mechanics of earthquakes and faulting, 2nd edition: Cambridge, England, Cambridge University Press, 471 p. Secor, D. T., 1965, Role of fluid pressure in jointing: American Journal of Science, v. 263, p. 633–646. Formation of joints under influence of pore fluids under pressure is a model that follows directly from Hubbert and Rubey’s model for thrust faults (Chapters 10 and 11). Wise, D. U., 1982, Linesmanship and the practice of linear geoart: Geological Society of America Bulletin, v. 93, p. 886–888. A tongue-in-cheek look at the ways lineaments are misinterpreted. Wise listed 32 rules derived from “logic” used in interpreting and misinterpreting lineaments. Wise, D. U., Funiciello, R., Maurizio, P., and Salvini, F., 1985, Topographic lineament swarms: Clues to their origin from domain analysis of Italy: Geological Society of America Bulletin, v. 96, p. 952–967. Lineaments in Italy from LANDSAT and other data were analyzed in an attempt to relate them to systematic joints in a tectonically active region. 10 Faults and Shear Zones Faults generate seismic activity, so our interest in them is practical as well as scientific and aesthetic. Understanding faults is necessary for the design and long-term stability of dams, bridges, buildings, and power plants, especially because of the devastating effects active faulting has on populations that live near them. The study of faults also helps us understand deformation and mountain-building processes. Faults are responsible for some of the Earth’s most spectacular scenery (Figure 10–1), including the Alps in Europe, the Grand Tetons in Wyoming, and the Canadian and Montana Rockies. Faults are largely responsible for uplifting blocks in the great mountain chains on Earth. A fault is a fracture having appreciable displacement parallel to the fracture surface. Sometimes it is difficult to specify what “appreciable” displacement is, and what we may or may not choose to call a fault is a somewhat scale-dependent judgment. We have no difficulty identifying a very large The occurrence of faults and dykes must have been known from the earliest days of mining. It was only gradually, however, that they became an object of scientific study. ERNEST M. ANDERSON, 1942, The Dynamics of Faulting FIGURE 10–1 McConnell thrust on the Trans–Canada Highway west of Calgary, Alberta. The light-gray rocks with prominent layering that produce the rugged topography are Cambrian–Devonian limestones; the dark-gray rocks to the lower right below the boundary are Cretaceous shale. The white buildings at the base of the cliff belong to a cement plant; there is greater than 1,600 m of relief from the top to the base of the highest point, Mt. Yamnuska. (RDH photo.) 247 248 | Fractures and Faults fault that has moved many kilometers; on the other hand, a fault having a few centimeters of offset may be important in one study, but in another may be considered only a large fracture or a joint with slight offset, because of the different scales of each study. Even small offsets become significant, however, when we weigh the impact of an active fault with small displacement on nearby buildings or dams. Faults occur in many forms and dimensions. They may be hundreds of kilometers or only a few centimeters long. Their outcrop traces may be straight or sinuous. They may occur as razor-sharp boundaries or as fault or shear zones, millimeters to several kilometers wide (Figure 10–1). Fault or shear zones may consist of a series of anastomosing brittle faults and fractured rock (cataclasite) formed mostly in the upper crust near the surface, or of ductile shear zones composed of mylonite produced by faulting at great depth. Movement on ductile faults is distributed over a zone that may be several kilometers wide, in contrast with brittle faults, where movement may be confined to a single plane but also distributed within a damage zone along the fault. Our discussion in this chapter deals with the properties of brittle faults, as well as structures associated with ductile shear zones and determination of shear sense in fault rocks. FIGURE 10–2 (a) Anatomy of faults. Arrows indicate relative sense of movement. (b) Oblique-slip fault showing the components of net slip and the rake of net slip measured in the fault plane. Fault Anatomy We need to understand the basic anatomy of faults (Figure 10–2) before discussing details of fault behavior. The most obvious feature related to faulting is the displacement of some marker, commonly bedding in sedimentary rocks, but all linear and planar features (fold axes, foliation, dikes, etc.) may be displaced across a fault. Displacement occurs along the actual movement surface—the fault “plane”— commonly non-planar over appreciable distances. For nonvertical faults, the rock mass resting on the fault plane is the hanging wall, and the rock mass beneath the fault plane is the footwall—terms that originated in mining. The orientation of a fault plane is described by its strike and dip (Appendix 1); linear features (such as slickenlines, discussed later) may also occur along the fault plane. Fault surfaces are frequently curved into a concave-up shape; we call this a listric geometry (Figure 10–3). Both thrust and normal faults exhibit this behavior. Slip along a fault can be dip slip (Figure 10–2a) where movement is down or up parallel to the dip direction of the fault, strike slip where movement is parallel to the strike of Strike line Fault plane Slip vector Angle of dip (α) Marker unit Hanging wall Footwall (a) Marker unit Slip vector p sli t e- en rt ik pon co Di S m m p-s po lip co ne Rake n Net slip t (b) Faults and Shear Zones High-angle; steep dip | 249 H T Li st ric su rf ace Concave-up Low-angle; shallow dip FIGURE 10–3 Concave-up listric surface that can form with either normal or thrust faults. B A C A' FIGURE 10–4 Oblique-slip fault showing the net separation (A–A’) of a marker layer and its components, strike separation (AB), and dip separation (BC), measured in the fault plane. These could also be termed the components of “true displacement.” Movve M Mo veme ment me nt direc dir irec ectition ec tit on o the fault plane, or oblique slip that combines both dip-slip and strike-slip movement (Figure 10–2b). The net slip, or displacement, is the total amount of displacement measured parallel to the direction of slip. We cannot actually determine the absolute motion sense on a fault without some primary criterion, such as establishing benchmarks FIGURE 10–5 Components of dip separation—heave (H), the horizontal component, and throw (T), the vertical component. before an earthquake and surveying them afterward, but the rake of net slip, measured in the fault plane, is commonly a useful measurement (Figure 10–2b). Another term is separation—the amount of apparent offset of a faulted surface, such as a bed or a dike, measured in a specified direction (Figure 10–4). We can speak of strike separation, dip separation, and the total or net separation of a fault. The terms heave and throw are used to describe the horizontal and vertical components of dip separation, respectively (Figure 10–5). Common features on fault surfaces are grooves and fibrous minerals, both aligned parallel to the slip direction. These features may be arranged in a series of steps that face in the movement direction of the opposing fault block. Polished fault surfaces are called slickensides, and the striations on them are slickenlines (Figure 10–6). Slickenfibers—aligned fibrous minerals on a movement surface—indicate the trend of relative movement (such as north–south or northeast–southwest) on a fault. The small steps may also be used to determine movement direction. Hanging wall (missing) movement Step down Slickenfibers Fault zone FIGURE 10–6 (a) Calcite slickenfibers on a movement surface in the Lower Devonian Kalkberg Formation, Hudson Valley, New York. Note the stepping down of the fibers toward the top of the photo, indicating the hanging wall (missing) moved toward the top. Field book for scale. (Photo by Stephen Marshak, University of Illinois.) (b) 3D block illustrating the relationships shown in (a). 250 | Fractures and Faults The direction of down-stepping is commonly the movement direction of the opposing block. Slickenlines must be cautiously interpreted as they most commonly record only the last movement on the fault. Slickensides and slickenlines do not necessarily prove significant displacement occurred along a fault, because they may be produced on bedding surfaces during flexural-slip folding (Chapter 15) or form on joints that have a small shear displacement. Anderson’s Classification The fault classification devised by Anderson (1942), a British geologist, defined three basic fault categories: normal faults, thrust (reverse) faults, and wrench (strike-slip) faults (Figure 10–7). Elements of his classification probably were in use long before Anderson’s work, but the history is difficult to trace. (a) (b) Normal faults (”normal” movement to miners) are dip-slip faults in which the hanging wall has moved down relative to the footwall (Figure 10–7a). Thrust (and reverse— ”reverse” movement to miners) faults are dip-slip faults in which the hanging wall has moved up relative to the footwall. The distinction between thrust (reverse) faults is thrusts have a low angle of dip (30° or less), and reverse faults have a moderate to steep dip (45° or more), but the same motion sense (Figure 10–7b). Both high- and low-angle segments occur on many thrust faults; low-angle segments may likewise be found along many reverse faults—hence our treatment here of thrusts being essentially the same as reverse faults, with only a difference in dip. Anderson described two categories of strike-slip (wrench) faults, based on the direction of relative motion as seen by an observer looking across the fault (Figure 10–8). Strike-slip faults, where the side opposite the observer moves to the right, are dextral or right-lateral strike-slip faults. Those in which the opposite side moves to the left are sinistral or left-lateral strike-slip faults. Note that if the observer moves to the opposite side of a fault block from the side of first observation (and turns to face across the fault again), the same sense of relative motion will again be observed. Strike-slip faults commonly have steep dips, although moderate and shallow-dipping segments occur, as along the Alpine fault in New Zealand, and the San Andreas in California. Transform faults are strike-slip faults, originally predicted by Wilson (1965), that form to compensate differences in motion between segments of lithospheric plates (Figure 10–9a). Unlike most faults, these are (a) (c) (b) FIGURE 10–7 Anderson’s fault classification. (a) Normal. (b) Thrust. (c) Strike-slip. Arrows indicate relative movement sense. FIGURE 10–8 Sinistral (left-lateral) (a) and dextral (right-lateral) (b) strike-slip faults. Faults and Shear Zones Motion on transform in short unconnected segments that may overlap; radial faults, which converge toward a single point; and concentric faults, which are concentric to a point (Figure 10–10; see also Figure 2–37). Bedding faults or bedding–plane faults occur parallel to bedding planes (Figure 10–11). Many thrust and normal faults are bedding-plane faults for part of their length, because the fault propagated along a weak layer parallel to bedding (Chapters 12 and 14). U D U D U U U D D D U D D U D 10 km (a) U D U D U D U U D (b) D U 10 km Spreading direction D U D U D D U D U D Transform fault (c) Ridge axis Ridge axis so named because they were first recognized in the oceans, linking segments of mid-ocean ridges where ridge segments are spreading at different rates. Wilson’s prediction was confirmed by first-motion studies of earthquakes along the Mid-Atlantic Ridge (Sykes, 1967). Several kinds of transforms occur, because they connect segments of plates where motion is being compensated within a plate or across a plate boundary, or are themselves plate boundaries. They include ridge-ridge, ridge-arc, and arc-arc transform faults (Figure 10–9b). The San Andreas fault, in addition to being a major dextral strike-slip fault, is also considered a ridge-ridge transform located in continental crust, because it connects the northern end of the East Pacific Ridge in the Gulf of California with a segment that occurs off the coast of northern California. Other useful terms that describe faults are en echelon faults, which approximately parallel one another, but occur 251 | 2 km FIGURE 10–10 (a) En echelon faults with dextral steps, (b) radial, and (c) concentric faults in map view. U—upthrown block; D— downthrown block. (a) Ridge-ridge (a) Ridge-arc Arc-arc (b) (b) FIGURE 10–9 (a) Motion on transform faults. (b) Several kinds of transform faults. Fault teeth indicate upthrown block. Dashed lines in (a) are oceanic fracture zones, not extensions of the fault. FIGURE 10–11 Bedding (-plane) fault in cross-section view. (a) Before movement, showing the future path of the fault (dashed line) that will propagate parallel to weaker beds (brown layers) and climb more steeply across stronger beds. (b) Fault formed by dip-slip motion of the hanging wall up relative to the footwall, producing a thrust. 252 | Fractures and Faults Recognizing Faults thereby providing a primary criterion that can be observed on the surface as an indication of offset along a fault. Fault scarps form where a topographic surface is offset by dipslip motion along a fault and directly indicate movement (Figure 10–12a; Figure 10–13). A fault scarp may evolve through time into a fault-line scarp by differential erosion. This will lower the level of the topographic surface and may remove a resistant layer in the hanging wall (Figure 10–12b). As long as erosion preserves the original motion sense of the fault, the fault-line scarp is a resequent fault-line scarp. The resistant layer may later be etched into relief in the footwall, however, producing a false opposite apparent motion sense on the fault without subsequent movement, and is called an obsequent fault-line scarp (Figure 10–12b). The real sense of motion on faults must be determined by using other primary criteria. Repetition or omission of stratigraphic units, or displacement (offset) of a recognizable marker (Figure 10–14), is key to recognizing faults. Repetition of a rock unit or Recognizing or demonstrating the existence of a fault requires the observation of particular features and diagnostic characteristics. If all faults were active, producing earthquakes or aseismic creep, the associated ground breakage would be sufficient for recognition, but most faults are inactive, so we must use other means to recognize them. To add further complication, in many regions we cannot directly observe a fault surface, because it is covered by younger deposits, soil, or vegetation. In regions of active faulting, the topography is commonly strongly influenced by fault geometry and the legacy of faulting may affect the topography long after cessation of activity. Drainage patterns are frequently controlled by faults (Figure 10–12). If active faulting is present, drainage may be successively offset over a few thousand—or a few hundred thousand—years by recurrent movement, Fault-line scarp Fault scarp Upthrown side of fault topographically high (a) Erosionally resistant layer Downthrown side of fault topographically high (b) Erosionally resistant layer FIGURE 10–12 (a) Fault scarp. Note that the upthrown side of the fault is topographically high here. (b) Obsequent fault-line scarp with the downthrown side of the fault topographically high, because of the erosionally resistant layer. FIGURE 10–13 Normal fault scarp in the Cordillera Blanca, Peruvian Andes. White arrow toward the top-center of the photo identifies the very planar major fault surface. White arrows in the foreground mark subsidiary faults. Solifluction lobes in the foreground (labeled) are the product of slow downslope ductile movement of a mixture of watersaturated thawed soil and loose rock above a frozen substratum. These are the kind of features Hansen (1971) used to develop his method for slipline determination (Chapter 15). Photo courtesy of Micah J. Jessup, University of Tennessee–Knoxville. Faults and Shear Zones Area 1 (Undeformed) 253 | K K J C I B D C H D G D F C C E B B D A A C (b) B A Area 2 (Deformed) D G F H D C B A D E F G I B A D E A B C C C B (c) C D D (a) D E K J I H J B D C D E C F D F D C E C C E B D A B A (d) B E C B A (e) FIGURE 10–14 (a) Omission of a unit by faulting in one area that can be shown to be present in a continuous sequence elsewhere. (b) Repetition or omission of stratigraphic units. (c) Offset of stratigraphic markers. (d) Truncation of structures. (e) Repetition by folding. Note the symmetry in the outcrop pattern. sequence generally proves the existence of a fault, if it can be demonstrated that repetition is not related to folding. Repetition by faulting commonly produces asymmetric repetition (Figure 10–14b), whereas repetition by folding commonly produces symmetric repetition (Figure 10–14e). Likewise, units may be omitted from a sequence by faulting. The truncation of structures, beds, or rock units against some feature is another criterion for recognizing faults (Figure 10–14d), although truncation of structures does occur against unconformities and intrusions (Chapter 2). Truncation of structures on both sides of a discontinuity most likely indicates that the boundary is a fault. Fault rocks such as mylonite or cataclasite (or both) (Chapter 8) commonly occur along the trace of faults and in fault zones and shear zones. Those rocks may be used in conjunction with repetition or omission of stratigraphic units and truncation of structures to show that faulting has taken place. While either indicates that faulting has occurred, it is generally best to use a displaced marker to 254 | ESSAY Fractures and Faults Seismic Risk Associated with Tectonic Structures The Code of Federal Regulations (actually 10CFR, Part 100, Appendix A) was used for many years to specify that documentation of the antiquity of geologic structures in the foundations of critical buildings (such as dams and nuclear power plants) must be provided to show they have not moved during the past 500,000 years. Today this regulation has been superceded by 10CFR Part 100.23, which discusses geologic, seismological, and engineering characteristics, along with geologic and seismic siting factors based on probabalistic risk criteria. It also addresses the importance of determining the potential for surface tectonic (and non tectonic) deformation to help engineers design these structures for the largest possible earthquake that could occur in the region. As a result, faults discovered near or within excavations must be carefully studied to show whether or not they have moved during the Holocene and if they are capable of moving during the projected useful life of the planned buildings. To some, it has been a very costly and difficult regulation, for it requires a level of study and documentation never before achieved. To many geologists, however, it has provided a wealth of new and useful information on the structural history of areas where these projects have been undertaken. Faults have been exposed that would not have been known otherwise, and details of their movement history have been brought to light. The techniques used in resolving these details have ranged from the applications of the classic geologic laws of superposition and crosscutting relationships to modern isotopic and strain-analysis techniques. In tectonically active areas such as the West Coast of the United States, documentation of antiquity of structures involves careful study of crosscutting and overprinting relationships and age determinations using Holocene to Recent fossils, 14C dating of organic material preserved in the fault zones, OSL dating of quartz in recent sediments (Chapter 3), and dating undeformed sediments that truncate these zones. One such study was carried out by Sieh (1984) as part of his doctoral research at the California Institute of Technology. He studied the Holocene history of an excavation 50 m long by 15 m wide by 5 m deep located 55 km northeast of Los Angeles along a segment of the San Andreas fault. The excavation revealed evidence of repeated faulting in sediments deposited along the fault, indicating that 12 earthquakes occurred between A.D. 260 and 1857, with an average recurrence interval of 145 years. Of the 12 earthquakes he documented, 5 prehistoric earthquakes produced displacements comparable to the large-magnitude earthquake of 1857. Careful study of displacement sense and displacement amounts of faults, the overlap (superposition) of younger sediments (Figure 10E1–1), and 14C age dates of wood SW 0 N34E NE 0 1 2 2 Depth (m) 1 0 3 Trench #11 1 meters No vertical exaggeration FIGURE 10E1–1 Section in part of a trench along Pallett Creek on the San Andreas fault studied by Sieh (1984). It shows several overlapping sequences of sediment deposited during the Holocene and disrupted by recurrent movement along the fault. Most disruption events that produced crosscutting faults were overlapped by deposition of younger sediments. Yellows and tan are fine- and medium-grain sands, orange is silt, reddish-brown is clay, green is peat, and gray is recent gravel fill. (Modified from K. E. Sieh, Journal of Geophysical Research, v. 89, no. B9, Plate 4b, © 1984 by the American Geophysical Union.) 3 Faults and Shear Zones fragments in sediments enabled reconstruction of the recent history of faulting here. Sieh used fundamental techniques to work out a very important interval of geologic history—the most recent prehistoric past—in one of the most populous areas in the United States, pointing out a major environmental hazard. Similar studies were carried out earlier in the region of the three major 1811–12 New Madrid earthquakes in southeastern Missouri and northwestern Tennessee by Russ (1979) and later near Charleston, South Carolina, site of the large 1886 earthquake, by Obermeier et al. (1985) and Talwani and Cox (1985). In both areas, it was possible to document earlier large earthquakes, but with much longer recurrence intervals—on the order of 600 years or more. confirm the displacement. Presence of S–C structures, rotated porphyroclasts, and other ductile shear structures (see later) indicates the presence of a ductile shear zone, and will also yield the displacement sense. Abundant veins, silicification, or other mineralization along a fracture zone may be indicative of faulting, but mineralization alone is a poor criterion, because it also occurs in extension fractures and in settings not related to deformation. It must therefore be used carefully and in conjunction with other evidence to demonstrate the existence of a fault. Drag is produced as rock units are differentially displaced across any type of fault or fault zone during movement. The movement sense may be determined, because drag folds exhibit asymmetry in the direction of movement. Drag may occur on thrust faults, so that the layers appear to have been pulled down-dip in the hanging wall, or up-dip in the footwall, toward the fault plane (Figure 10–15a), opposite the sense of relative motion. The opposite effect with drag folds occurs on normal faults (Chapter 14). Reverse drag occurs along some listric normal faults (Figure 10–15b), where the layering appears to have been dragged parallel to movement along the fault. Reverse drag is produced by down-dip folding of sediment along the fault as it moves and the dip decreases, creating more of a rotational displacement on the more steeply dipping segment of the fault, and apparent drag up-dip. Shear Zones Shear zones (also referred to as high-strain zones) are related to faults in that rocks on either side of the zone are displaced relative to each other (Figure 10–16a). Displacement across a shear zone is distributed such that continuity is typically maintained from one side of the zone to another. Shear zones are commonly the result of ductile | 255 References Cited Obermeier, S. F., Gohn, G. S., Weems, R. S., and Gelinas, R. L., 1985, Geologic evidence for recurrent moderate to large earthquakes near Charleston, South Carolina: Science, v. 227, p. 408–410. Russ, D. P., 1979, Late Holocene faulting and earthquake recurrence in the Reelfoot Lake area, northwestern Tennessee: Geological Society of America Bulletin, v. 90, p. 1013–1018. Sieh, K. E., 1984, Lateral offsets and revised dates of large prehistoric earthquakes at Pallett Creek, southern California: Journal of Geophysical Research, v. 89, no. B9, p. 7641–7670. Talwani, P., and Cox, J., 1985, Paleoseismic evidence for recurrence of earthquakes near Charleston, South Carolina: Science, v. 229, p. 379–381. Drag fold Drag fold (a) Reverse drag in the sense of movement Rollover anticline (b) FIGURE 10–15 (a) Drag on thrust and normal faults. (b) Reverse drag on a normal fault. Both (a) and (b) are cross-section view. behavior, but fault zones in which brittle behavior dominates can also have shear zone-like geometries. Ramsay (1980) recognized brittle, brittle-ductile, and ductile shear zones (Figure 10–16b). Ideally, ductile shear zones are tabular (dike-like) in shape with subparallel boundaries separating the more highly strained rock within the zone from the less deformed rock adjacent to the zone. Many real shear zones approximate these features, but others, particularly kilometer or more-wide shear zones, may contain rocks of different type and material properties that prevent generalization about properties. Ductile deformation related to large shear zones may also propagate hundreds of meters to a kilometer or more into the adjacent rocks. Early workers interpreted deformation within shear 256 | Fractures and Faults FIGURE 10–16 (a) Near-horizontal, subparallel ductile shear zones in augen gneiss near Vålån, Swedish Caledonides. Two well-defined ductile shear zones are visible just below the coin. Note how the porphyroclasts are rotated dextrally (clockwise) in the shear zones. (RDH photo.) (b) Shear-zone development in part of the crust in a state of compression. Note the brittle shear zone in the cover undergoes a transformation at depth as it becomes more ductile and affects a larger part of the crust, then becomes a wide zone of ductile deformation deep in the basement where the crust is at a higher temperature. (Modified from Journal of Structural Geology, v. 2, J. G. Ramsay, p. 83–99, 1980, with kind permission from Elsevier Science, Ltd. Kidlington, United Kingdom.) (a) Brittle-ductile shear zone Brittle shear zone (or fault) Sedimentary cover Basement (b) zones to have occurred by: (1) heterogeneous simple shear; (2) heterogeneous volume change accomplished largely by pressure solution; and (3) combinations of the first two. Simple-shear deformation results in no strain incompatibilities between the shear zone and wall rock (see later). In recent years, numerous studies have demonstrated that general shear deformation (Chapter 6) is common in shear zones, and that compatibility is maintained by three-dimensional strain or that discrete slip occurs at the shear zone boundary. Shear-Sense Indicators Determination of shear sense—the movement direction across a ductile shear zone—is important for under standing kinematics and resolving the tectonic history. Brittle faults Ductile shear zone Consider the shear zone in Figure 10–17: this steeply dipping zone of mylonitic rock cuts the granitic host, but what about its kinematics? Did this zone undergo dipslip or strike-slip movement, was there shortening across the zone, and how much slip occurred? In the absence of displaced marker layers and piercing points, we must rely on mesoscopic and microscopic shear-sense indicators to resolve the kinematics. Structural geologists have developed numerous criteria for determining shear sense in deformed rocks. These methods have been summarized by Simpson and Schmid (1983), Lister and Snoke (1984), Passchier and Simpson (1986), Simpson (1986), Hanmer and Passchier (1991), and Passchier and Trouw (2005). As a result, shear-sense determination has become a routine and powerful component of structural analysis. We must be cautious, however, as the observed shear sense is commonly produced by the last ductile event, although relicts of earlier events may be preserved. Faults and Shear Zones A T T Dextral strike-slip ? Reverse dip-slip A Sinistral strike-slip Normal dip-slip FIGURE 10–17 Schematic illustration of a steeply dipping shear zone cutting a granite body. There are no markers with which to determine the displacement sense, so the geologist must examine meso- to micro-scale shear-sense indicators to determine the shear zone kinematics. In essence, we look for asymmetric structures in shear zones that reveal the direction (or sense) in which the rocks have been sheared. Mylonitic rocks are generally well foliated, and many contain a lineation. The first step toward shear-sense determination is consideration of what direction/plane to observe. Traditionally, the strain geometry in shear zones has been interpreted to be monoclinic, such that the overall tectonic transport direction is parallel to the lineation (Chapter 18), and asymmetric structures are best developed on lineation-parallel (foliation-normal) faces (Figure 10–18). Transpressional deformation, however, can produce a lineation normal to the tectonic transport direction, and these lineations are called rolling lineations, with fabric asymmetries best Monoclinic general or simple shear Monoclinic dextral transpression | 257 developed on lineation-normal faces (Figure 10–18). Rolling lineations can be visualized by thinking about rolling out a round ball of dough to form an elongate loaf (a baguette, for instance); the rolling or shearing motion occurs at right angles to the elongated dough and with increased strain the loaf becomes ever longer. This type of deformation does not follow a plane strain path. Triclinic deformation is more complex, producing asymmetric structures on both lineation-parallel and lineation-normal faces. The best approach for understanding shear zone kinematics is to determine shear sense using asymmetric structures on both lineation-parallel and lineation-normal faces. Porphyroclasts are relict earlier large grains—hard objects—that have likely undergone some size reduction, but have survived ductile deformation. Porphyroblasts are large grains that have grown in the rock mass during deformation and metamorphism. Porphyroclasts and porphyroblasts are commonly objects (e.g., feldspars, garnets) that are stronger than the matrix in which they reside, and so they behave much like ball bearings that allow the softer matrix to flow past. If they are rotated in a more ductile matrix, the rotation produces structures that provide clear indicators of shear sense (Figure 10–19). Large porphyroclasts (cm-scale) wrapped by the enclosing foliation are known as augen (German for “eye”). Porphyroclasts commonly develop “tails” of finer-grained material derived from mechanical abrasion or recrystallization of the porphyroclast or the matrix. Shear sense is revealed by the asymmetry of the tails (a stair-stepping geometry) with respect to the porphyroclast (Figures 10–19, 10–20a). Asymmetric tails commonly form characteristic σ and δ shapes on the flanks of porphyroclasts (Figure 10–19); σ tails likely develop where the rate of porphyroclast rotation relative to the rate of recrystallization is low, whereas δ shapes form when the rotation rate is high relative to recrystallization rate, and the tail is rotated along with the porphyroclast past the horizontal (Figure 10–19b). Porphyroclasts can develop without tails, and are called θ, or naked, porphyroclasts. These also can be used to Triclinic simple shear L L (a) L (b) (c) FIGURE 10–18 (a) Homogeneous monoclinic general/simple shear, (b) monoclinic transpression, and (c) triclinic shear. In monoclinic general/simple shear the lineation tracks the overall displacement vector, whereas in monoclinic transpression the lineation is a rolling lineation and is normal to the overall displacement vector. L is the elongation lineation. (Modified from Bailey et al., 2007.) 258 | Fractures and Faults determine shear sense based on the asymmetry of the matrix around the grain. Mineral fish are porphyroclasts commonly composed of micas that generally lack welldeveloped tails, but have an asymmetric lens or lozenge shape when viewed in three dimensions. They are very good indicators of shear sense (Figure 10–20). Boudins (Figure 10–20b) are sausage-shaped structures formed by extension of a stronger layer in a more ductile groundmass (Chapter 19). They are sometimes rotated, producing pressure shadows or wrapped foliations that may indicate shear sense. They may also internally preserve an earlier foliation that can be used in concert with the enclosing foliation to determine the rotation sense. Inclusion trails in garnet, staurolite, cordierite, feldspars, and several other metamorphic minerals may have a “snowball,” an S, or a spiral asymmetric pattern that indicates shear sense (Figures 10–19b, 10–20c). These crystals were rotated during crystallization in a more ductile matrix, recording the rotation sense as they grew. Most inclusion trails record prograde rather than retrograde deformation. Care should be exercised in using inclusion Foliation Foliation Foliation P (a) (b) PB P P Fol ia (c) Foliation Foliation tion P P (e) C-surfaces Relict S-surfaces (g) (h) su b Al ig ne d C-surfaces (f) gr ain s (d) (i) FIGURE 10–19 Several types of shear-sense indicators. Winged inclusions: (a) σ–type. (b) δ–type. (c) θ–type, naked inclusion. (d) Rotated inclusions in a porphyroblast, for example, garnet. (e) Pressure shadows formed on the flanks of a porphyroclast. Note that the apparent shear sense is sinistral, but the actual sense is dextral. (f) Displaced segments of a fractured grain (bookshelf faulting). Note the offset of the fragments is opposite to the shear sense. (g) Shear bands showing the orientation of C–surfaces (horizontal) and relict S–surfaces from the original foliation (inclined). (h) Asymmetric microfolds. (i) Inclined subgrains (dimensional preferred orientation, DPO). Fine lines and dashed lines indicate shear (C) foliation. Rotation in each example is dextral (clockwise), as indicated by small arrows in the upper right part of each block. P—Porphyroclast. PB—Porphyroblast. (Modified from Tectonophysics, v. 152, R. J. Hooper and R. D. Hatcher, Jr., p. 1–17, 1988, with kind permission from Elsevier Science, Ltd., Kidlington, United Kingdom; and C. Simpson and S. Schmid, 1983, Geological Society of America Bulletin, v. 94.) Faults and Shear Zones (a) (c) (d) (e) | 259 (b) FIGURE 10–20 (a) δ porphyroclast of K–feldspar in a foliated granodiorite gneiss in the central gneiss belt of the Grenville orogen, southern Ontario. (Photo courtesy of W. M. Schwerdtner, University of Toronto.) (b) Amphibolite boudins in biotite gneiss showing sinistral rotation of original layering in the boudins, Woodall Shoals, South Carolina. (RDH photo.) (c) Dextrally rotated inclusion trails of quartz, micas, and some feldspar in a garnet in sillimanite grade biotite gneiss from south of Franklin, North Carolina. The inclusion-rich core of the garnet contains an earlier foliation that was rotated as new inclusion-free garnet was overgrowing it. This porphyroblast is approximately 9.7 mm wide. X nicols. (RDH photo.) (d) Fractured and rotated feldspar porphyroclast in 1.15 Ga Blowing Rock Gneiss, south of Boone, North Carolina, indicating apparent dextral, but actual sinistral shear. Feldspar grain is approximately 4 cm long (U.S. dime for scale). (RDH photo.) (e) Muscovite “fish” with dextral asymmetry, in phyllonite from the Brevard fault zone in South Carolina. Width of photo is approximately 3 mm. X nicols. (RDH photo.) trails in minerals, such as garnet, which record growth during a long time period, because inclusion trails at a high angle to the enclosing foliation may indicate two shortening directions (Bell, 1985; Vernon, 1988). Asymmetric pressure shadows formed adjacent to grains or crystals (e.g., pyrite, garnet) in a more ductile matrix may be used for shear-sense determination, if the pressure shadows are asymmetric (Figures 8–23 and 10–19e). They function in the same way as asymmetric tails on porphyroclasts, but display an opposite sense of asymmetry. They may have the same asymmetry as winged porphyroclasts, however, so it is best to use more than one shear-sense criterion where there are pressure shadows in a deformed rock. Distorted layering near porphyroclasts produces “drag folds” that indicate shear sense. Paired folds and veins may form together in shear zones, with tension veins (dilational fractures) forming about 45° to the shear zone boundaries. These veins are subsequently rotated into the shear direction, into an axial-planar orientation with respect to drag folds, and are closed as the shear zone evolves. Flanking structures occur where oblique veins, which formed during deformation, distort the foliation such that an asymmetry develops across these structures (Grasemann et al., 2003). 260 | Fractures and Faults Fractured grains of some strong minerals (for example, feldspars, amphiboles, pyroxenes, garnets, and occasionally quartz) continue to deform brittlely, even in a ductilely deforming matrix. This has also been refered to as “bookshelf” faulting when it occurs on the mesoscopic or larger scale. During progressive deformation, they may fracture and become offset (Figure 10–20d). Slip on these fractures may be synthetic or antithetic to the overall shear sense (Figures 10–19f and 10–20d). Composite Foliations Mylonites typically display at least one foliation formed during deformation. The most common foliation (S–foliation, from the French word for foliation, schistosité) is formed in the shear zone and, with progressive strain, rotates toward the shear zone boundary, and as such can be used to determine shear sense. A secondary foliation (C–foliation, from the French word for shear, cisaillement; Berthé et al., 1979) may also form parallel to the shear zone boundary, cutting the S–foliation. The asymmetry between the S– and C–foliations is a shear-sense indicator (Figure 10–21). With increasing strain, the angle between the S– and C–surfaces decreases and at very high strains it may be impossible to distinguish between the two foliations. Alternatively, the S–foliation can be inherited from the enclosing rocks, crosscut by the younger C– foliation, and preserved between the C–surfaces. Indeed, a third foliation (C'–foliation) may form oblique to the shear zone boundary and obliquely cut the C–foliations. C– and C'-foliations are frequently referred to as shear bands. These fabrics are recognizable at both the meso- and microscopic scales (Figure 10–22). In addition to S– and C–structures, shear zones may deform older preexisting foliations. FIGURE 10–21 The dominant, subhorizontal foliation in this augen gneiss is the original S– or an earlier C–foliation in the gneiss. The inclined foliation is the new C–foliation produced by ductile simple shear. The augen are composed of K–feldspar; the dark mineral is biotite; the white mineral is plagioclase feldspar. Shear sense is top-to-the right (dextral). High-temperature mylonite from the Box Ankle fault zone at Higgins Mill on the Towaliga River near Forsyth, Georgia. The C–surfaces parallel the shear zone boundaries. Width of field is approximately 13 cm. Strain in Ductile Shear Zones Consider a parallel-sided, dextral shear zone that undergoes homogeneous simple shear (Figure 10–23). As strain accumulates, several important things happen. Notice that as the strain ratio (Rs) increases, the amount of shear strain (γ) and the displacement of the undeformed area above the shear zone increases as well (Figures 10–23b and 10–23d). Furthermore, the long axis of the strain ellipse progressively rotates clockwise, such that the θ angle becomes less with increasing shear strain. When graphed, the nonlinear relationship between shear strain and the θ angle is evident (Figure 10–23e), and can be expressed by   γ  θ =  tan−1   / 2 .   2  (10–1) After the first increment of deformation, the long axis of the strain ellipse is oriented 45° to the shear zone boundary (at an infinitesimally small shear strain, say 0.0001, with γ near 0, solving equation 10–1 for θ yields 44.999°). There is also a direct relationship between the θ angle, the principal stretches (SX and SZ), and the strain ratio (Rs) such that SX = cot θ SZ = tan θ (10–2) (10–3) cot θ . (10–4) tan θ In simple shear of homogeneous materials, there is no shortening at right angles to the shear zone, and thus the shear zone maintains a constant thickness. It is important to remember that these relationships apply only for simple RS = tion olia C–f S ion iat l o –f Faults and Shear Zones | 261 FIGURE 10–22 (a) Ductilely deformed Carboniferous megacrystic granitoid in the Monte Rosa nappe in the Pennine root zone at Domodossola, Italy. The large fractured microcline porphyroclasts are aligned parallel to the dominant foliation (S or earlier C), and the younger dextral C’–surfaces are inclined approximately 20° to the C–surfaces. This is a Type I S–C mylonite. (Locality courtesy of H. P. Laubscher, University of Basel, Switzerland. RDH photo.) (b) Shear band C–surfaces deforming earlier S–surfaces in a finegrained Cambrian phyllonite from the fault zone at the base of the Seve thrust sheet, west flank of Tronfjellet, south-central Norway. Note the small fold near the bottom of the photo (circled) that has the same shear sense as the S–C fabric. (RDH photo.) (a) (b) shear deformation and, as we shall see, many shear zones underwent general shear. Mylonitic foliation (C–foliation) in ductile shear zones commonly, but not always, forms parallel to the long axis (SX) of the strain ellipse and tracks its orientation with progressive deformation. With knowledge of shear strain (γ) across a homogeneous shear zone, the displacement (D) across the zone is the product of its width (W) times γ: D = γW. (10–5) Now consider a zone of heterogeneous simple shear (Figure 10–24): in this zone, strain increases toward the center of the shear zone and the long axes of the strain ellipses follow a curved trajectory. Shear strain also varies across the zone and the displacement can be estimated by integrating the shear strain across the width of the zone as W D = ∫ γdW. 0 (10–6) In practice, we would attempt to determine the shear strain at many locations across the shear zone, and find the area under the curve of shear strain plotted against width across the zone (Figure 10–24). The shear strain integration technique typically yields a minimum estimate of displacement, because it does not account for any slip on brittle surfaces within the ductilely deforming zone. General shear zones share some similarities with zones of simple shear, but there are significant kinematic 262 | Fractures and Faults γ= 0.18 γ = 0.58 ψ= Width =1 ψ= 10° 30° Rs = θ = 1.77 37° Rs = θ = 1.19 42° (a) (b) (c) b 40 γ = 2.75 c θ= tan-1 (γ/2) 2 Width θ (°) 30 ψ = 70° Rs = 9.46 θ= 18° d 20 10 0 (d) 0 1 2 3 4 Shear Strain (γ) (e) FIGURE 10–23 Homogeneous simple shear zone with a unit width = 1. Black circles and ellipse are the strain ellipse, ψ = shear angle, γ = shear strain, Rs = strain ratio, θ = angle between long axis of strain ellipse and shear zone boundary. (a) Undeformed state. (b–d) Increasing deformation steps; note material outside shear zone remains unstrained, but the top block is displaced to the right. (e) Graph of θ versus γ for (b–d). between θ and the strain ratio can be used to estimate the kinematic vorticity number (Wm, Chapter 6) (Figure 10–25). Additionally, during general shear, material is shortened across the shear zone and elongated parallel to the zone boundary. differences. For general shear with a shortening component, the long axis of the strain ellipse progressively rotates toward parallelism with the shear zone boundary as deformation increases, but for any given strain ratio θ is less than that for simple shear (Figure 10–25). The relationship γ γ 0 D 1 2 0 0.3 0.6 W 1.7 0.6 Width (m) 0.3 D = area under the curve 0 (a) (b) FIGURE 10–24 (a) Heterogeneous simple shear zone. Note the change in trajectory of the strain ellipse from the edge of zone to the center. W = width of zone; D = displacement across zone. (b) Graph of shear strain (γ) vs. width of zone; note γ = 0 at the edges of the shear zone and reaches a maximum in the center. Displacement across the zone is given by the area under the curve. Simple shear (Wm = 1.0) θ= 0.9 7° γ=1 2 30 θ ( °) Rs , =4 Wm curves γ = 0.5 40 General shear (Wm = 0.6) γ=2 20 γ=3 1.0 10 R s = 4, θ 263 | Faults and Shear Zones (a) 0.4 0.2 = 8° 0 1 4 0.6 0.8 0.95 0.9 12 8 γ=4 16 20 Strain ratio (Rs) (b) FIGURE 10–25 (a) Differences between simple and general shear. Note in both cases the strain ratio is the same (Rs = 4), but θ is less for general shear; also material is elongated parallel to the zone boundary and shortened across the zone in general shear. (b) Graph of θ vs. Rs for different kinematic vorticity (Wm) numbers. Simple shear (Wm = 1.0) curve has the largest θ angle for any given strain. Triangle is simple shear example; diamond is general shear (Wm = 0.6) example from (a). Deflection of an aplite dike across a small shear zone in the Pinaleños Mountains in southern Arizona (Figure 10–26) provides a direct measure of displacement (~30 cm). θ ranges between 5° and 12°, which in simple shear would correspond to shear strains of 7–10, and, when integrated across the width of the zone, yields a displacement of 50 to 100 cm (two to three times greater than the actual displacement). Clearly, this is not a simple shear zone; rather, the deformation followed a general shear path. Shear zones are common features in ductilely deformed rocks, and understanding their kinematics is critical for properly deciphering the tectonic history of the middle and ductiley deforming lower crust in exposed mountain belts. my D= 30 cm ap θ = 5–12° ap gd my my gd 0 10 cm FIGURE 10–26 Sketched interpretation of a general shear zone in a subvertical outcrop of granodiorite (gd) in the Pinaleños Mountains in southern Arizona. The deflected aplite dike (ap) provides a direct measure of the displacement (~30 cm). Outcrop foliation is perpendicular, lineation parallel; my—mylonite. Brittle Shear Zones Brittle shear fractures can develop in shear zones; these fractures were first identified by Riedel (1929) in nearsurface fault zones, and have also been produced experimentally in dry clay (Figure 10–27). Riedel shears (R), and the oppositely moving structures called anti-Riedel shears (R'), form initially at very low strain, but movement is immediately transferred to shears that form subparallel to the shear zone boundaries. Interesting comparisons can be made between the throughgoing shears that nearly parallel Riedel and anti-Riedel shears, and C–surfaces that form in ductile shear zones. Now that we have assembled the tools for recognizing and describing faults and shear zones, we can proceed to Chapter 11 on fault mechanics to deal with the problem of how faults form and move. 264 | Fractures and Faults Movement direction Board W R' R Clay slab FIGURE 10–27 Experiment to produce Riedel shears in a clay layer. W—width of shear zone. R—Riedel shear. R'—anti-Riedel shear. (From J. S. Tchalenko, 1970, Geological Society of America Bulletin, v. 81.) ESSAY Board Existence and Displacement Sense of Large Faults Some of the very large inactive faults in ancient mountain chains were discovered by recognition of one or more of the criteria for faulting discussed in this chapter. Yet the sense of motion and displacement on some of these faults has been debated for many decades, because elements of the puzzle remain missing, the history of movement is complex, or both. The Lake Char fault (Char is short for Chargoggagoggmanchauggagoggchaubunagungamaugg) in the southeastern New England Appalachians was described by Dixon and Lundgren (1968) as part of an extensive fault complex. It is a west-dipping low-angle fault in Connecticut that steepens along strike northeastward to join the more steeply dipping Clinton-Newbury and Bloody Bluff fault system in Massachusetts (Figure 10E2–1). The low-angle character of the Lake Char fault had been recognized earlier by the gentle dip along its outcrop trace, before Wintsch (1979) suggested that the fault reappears farther west encircling the core of the Willimantic dome, forming a window (Chapter 12). The Lake Char fault had been assumed to be a thrust that moved rocks from the west in the hanging wall over the more easterly rocks now in the footwall. Unfortunately, there are no easily recognized marker units to help measure the displacement. Existence of the fault was confirmed by Dixon and Lundgren (1968), primarily on the basis of mylonite along the trace that truncates earlier structures in the hanging wall and footwall. The sense of movement, as determined by Goldstein (1982), using several shear-sense indicators, surprisingly turns out to be hanging wall down toward the west, indicating that the last movement on the Lake Char fault was normal and thus may not be a thrust. The amount of displacement beyond that reconstructed from the Willimantic dome window remains undetermined. The Brevard fault zone in the southern Appalachians (Figure 10E2–2) was first described by Keith (1907), who thought it was a syncline of younger rocks preserved within older rocks of high metamorphic grade. The sheared nature of the rocks within the fault zone was first recognized by Jonas (1932), who concluded that the Brevard fault zone is a thrust fault, and suggested it is correlative with a major thrust farther north—in Maryland and Pennsylvania—called the Martic thrust. The Brevard fault, like many others in the cores of mountain chains, does not offset easily recognized markers throughout its more than 700 km known length. Consequently, its displacement sense and magnitude remained obscure. A subsequent study by Reed and Bryant (1964) used the orientations and displacement patterns of linear structures, such as quartz C–axes and mineral lineations along the North Carolina segment (see Chapter 18), and concluded Faults and Shear Zones 74° 43° 73° 72° 71° onic alloc htho ns ury wb DU n Ho Hill ult Willimantic dome ey CT a ob sh Na fau e ran ter t ul fa uff Bl Bl oo dy MA Lake Char fa Hartfo Triassic rd –Jurass ic basin DU Cli nto n Ne Berksh ires Tac 43° lt 42° RI Narragansett basin 50 kilometers 73° 42° fault 0 41° 74° 265 NH VT NY | 72° 71° 41° FIGURE 10E2–1 Relationships of the Lake Char fault in eastern Connecticut to the Honey Hill and Clinton-Newbury and Bloody Bluff faults, as well as to the fault that frames the Willimantic dome window. The Narragansett basin contains Pennsylvanian-Permian rocks (orange). The dark maroon areas represent ~1.1 Ga-old basement rocks of western New England. The green area in southeastern New England is the Avalon terrane, an exotic terrane of volcanic and sedimentary rocks that was accreted to North America during the Late Devonian. (Modified from R. D. Hatcher, Jr., P. H. Osberg, A. A. Drake, Jr., P. Robinson, and W. A. Thomas, 1990, Tectonic Map of the U.S. Appalachians, Plate 1, in Geological Society of America, Geology of North America, v. F–2.) that the Brevard is a dextral strike-slip fault. Reed et al. (1970), however, suggested that the Brevard is a sinistral strike-slip fault with a major thrust (dip-slip) component. Then, after studies in South Carolina and nearby Georgia, Hatcher (1971) reported exotic blocks of footwall rocks and a traceable stratigraphy within and southeast—but unfortunately not northwest—of the Brevard fault zone. These studies (Hatcher, 1971) also suggested that the structure is a thrust, as originally concluded by Jonas. Since then, Bobyarchick (1984) has found that the Brevard had a major dextral strike-slip component, and Edelman et al. (1987) concluded that the Brevard had an early thrust component, followed by later dextral strike-slip, and later still moved again by thrusting. This structure was also interpreted as an Alpine root zone (Burchfiel and Livingston, 1967) and as a transported suture (Rankin, 1975). Hatcher (2001) outlined the polyphase history of the Brevard fault zone, which involved a mid-Paleozoic dextral movement phase as a high temperature shear zone, followed by a late Paleozoic dextral phase as a lower temperature shear zone, and then reactivation as a brittle thrust fault during the latest Paleozoic. Merschat et al. (2005) concluded the high temperature phase involved at least 400 km of dextral displacement, so all the rocks to the southeast of the fault were originally deposited off present-day Pennsylvania or New Jersey. Why so many conflicting interpretations for one fault? Part of the problem lies in the absence of critical marker units on both sides of the fault, while another problem lies in the complexity of the structure. The Brevard fault probably has undergone both dip- and strike-slip movement. Yet another difficulty is that different geologists, like the proverbial six blind men attempting to understand an elephant (see Essay in Chapter 18), have worked on different parts of a structure, exposed well in some areas and poorly in others. The underlying lesson is that large faults such as the Brevard and Lake Char, which bound major structural blocks, commonly undergo a long history of movement involving multiple displacements in different directions. 266 ESSAY | 86° fault lu B e tur su as 86° n Ce Pie l tal SC GA Pla in 0 82° 50 fault a olin Car belt NC e ne ter ra nt o dm tra Co on Milt nt mo d Pie Atlanta 32° Smith River allochthon fa u lt rn Inner ge Rid Ridge Easte ard Roanoke Blue ey B r ev VA Ridge Blue Western Ridge and ll Va AL 82° 80° 36° 80° 34° 100 kilometers 84° 32° FIGURE 10E2–2 Location of the Brevard fault zone relative to other major faults and tectonic units in the internal parts of the southern Appalachians. The Brevard fault zone is located at the boundary between the eastern Blue Ridge and the western Inner Piedmont. In this region (lavender) the same stratigraphic units occur on both sides of the Brevard fault, and so it cannot be a terrane boundary or a suture. The dark red represents ~1.1 Ga-old basement rocks. The tan color represents rocks that were deposited on the basement along the Neoproterozoic-early Paleozoic North American margin. The orange and dark lavender colors represent some of the Paleozoic plutons. (Modified from R. D. Hatcher, Jr., P. H. Osberg, A. A. Drake, Jr., P. Robinson, and W. A. Thomas, 1990, Tectonic Map of the U.S. Appalachians, Plate 1, in Geological Society of America, Geology of North America, v. F–2.) 38° Fractures and Faults TN 34° 38° 84° Knoxville continued 36° Faults and Shear Zones | 267 References Cited The nature and significance of fault zone weakening: Geological Society of Bobyarchick, A. R., 1984, A late Paleozoic component of strike slip in the Bre- London Special Publication 186, p. 255–269. vard zone, southern Appalachians: Geological Society of America Abstracts Jonas, A. I., 1932, Structure of the metamorphic belt of the southern Appala- with Programs, v. 16, p. 126. chians: American Journal of Science, 5th series, v. 24, p. 228–243. Burchfiel, B. C., and Livingston, J. L., 1967, Brevard zone compared to Alpine Keith, A., 1907, Description of the Pisgah quadrangle, North Carolina–South root zones: American Journal of Science, v. 265, p. 241–256. Carolina: U.S. Geological Survey Geologic Atlas Folio 147, 8 p. Dixon, H. R., and Lundgren, L., 1968, The structure of eastern Connecticut, in Merschat, A. J., Hatcher, R. D., Jr., and Davis, T. L., 2005, 3-D deformation, Zen, E-an, White, W. S., Hadley, J. B., and Thompson, J. B., Jr., eds., Studies of kinematics, and crustal flow in the northern Inner Piedmont, southern Appalachian geology: Northern and maritime: New York, Wiley-Interscience, Appalachians, USA: Journal of Structural Geology, v. 27, p. 1252–1281. p. 261–270. Rankin, D. W., 1975, The continental margin of eastern North America in Edelman, S. H., Liu, A., and Hatcher, R. D., Jr., 1987, The Brevard zone in South the southern Appalachians: The opening and closing of the Proto-Atlantic Carolina and adjacent areas: An Alleghanian orogen-scale dextral shear zone Ocean: American Journal of Science, v. 275-A, p. 298–336. reactivated as a thrust fault: Journal of Geology, v. 95, p. 793–806. Reed, J. C., Jr., and Bryant, B., 1964, Evidence for strike-slip faulting along the Goldstein, A., 1982, Geometry and kinematics of ductile faulting in a portion Brevard zone in North Carolina: Geological Society of America Bulletin, v. 75, of the Lake Char mylonite zone, Massachusetts and Connecticut: American p. 1177–1196. Journal of Science, v. 282, p. 378–405. Reed, J. C., Jr., Bryant, B., and Myers, W. B., 1970, The Brevard zone: A Hatcher, R. D., Jr., 1971, Stratigraphic, petrologic, and structural evidence reinterpretation, in Fisher, G. W., Pettijohn, F. J., Reed, J. C., Jr., and Weaver, favoring a thrust solution to the Brevard problem: American Journal of K. N., eds., Studies of Appalachian geology: Central and southern: New York, Science, v. 270, p. 177–202. Wiley Interscience, p. 241–256. Hatcher, R. D., Jr., 2001, Rheological partitioning during multiple reactiva- Winstch, R. P., 1979, The Willimantic fault: A ductile fault in eastern tion of the Paleozoic Brevard Fault Zone, Southern Appalachians, USA, in Connecticut: American Journal of Science, v. 279, p. 367–393. Holdsworth, R. E., Strachan, R. A., Macloughlin, J. F., and Knipe, R. J., eds., Chapter Highlights • Faults are shear fractures that produce measurable displacement of some marker parallel to the fracture surface. Active faults can generate earthquakes when they slip. • The three basic fault categories include normal faults, thrust (reverse) faults, and strike-slip faults. Two of the three fault classes can be described based on the movement of the hanging wall relative to the footwall. Strikeslip faults are classified by the sense of relative movement on each side of the fault. • Faults can be recognized by geomorphic features, repetition or omission of stratigraphic units, truncation of structures, and the presence of fault rocks. • Shear zones are ductile faults zones that range from millimeters to kilometers in thickness. • Shear-sense indicators, such as rotated porphyroclasts and S–C structures, can be utilized to understand the kinematics of deformation in shear zones. Questions 1. What do slickensides tell us? 2. What type of contact is evident in the following image? What evidence would you look for in the field to determine if it is a fault? If the contact is a fault, what type of fault is it? Explain. (Road cut east of Richfield, Utah.) Eocene chalky siltstone Jurassic sandstone and mudstone 268 | Fractures and Faults 3. Is the scarp in the following cross section a fault scarp or a fault-line scarp? Explain. What type of fault is exposed in the cross section? How can you tell? W E Sandstone u Fa Shale lt Shale 4. If you found a limestone-sandstone contact in the field in which the contact and rocks in both units dip 40° in the same direction, how would you determine whether the contact is a fault, a stratigraphic contact, or an unconformity? 5. What actually determines whether a fracture is a fault or a joint? 6. When studied carefully, most faults—regardless of whether they are thrust, normal, or strike-slip faults— turn out to be oblique-slip faults with a dominant thrust, normal, or strike-slip component of motion. Why? 7. Why does drag occur on some faults? Reverse drag? 8. Which criteria are most useful for recognizing faults? Why? 9. From the top to bottom a drill core contains Jurassic basalt, Triassic sandstone, Permian shale, Cretaceous limestone, Jurassic basalt, and Triassic sandstone. Based on this sequence, what type of fault is likely present? 10. How are net slip and stratigraphic separation alike? How are they different? 11. What is the overall shear sense (top-to-the-east or top-tothe-west) evident in this slab of mylonitic rock? Was the strain homogeneous or heterogeneous? Explain. Width of field is approximately 13.5 cm. 12. What two rates control whether a σ porphyroclast or a δ porphyroclast develops in a mylonite? 13. How could you distinguish between a transposed C– (or C’–) surface truncated by younger C–surfaces and an earlier S–surface similarly truncated? 14. Assuming a simple shear deformation, what is the shear strain (γ) and strain ratio (Rs) when the angle between the foliation and the shear zone boundary is 10°? How much elongation occurred parallel to the shear zone boundary? 15. In general shear why is the angle between the foliation and the shear zone boundary less than it is for simple shear? 16. How could a triclinic shear zone be distinguished from a monoclinic shear zone? Further Reading Other structural geology textbooks discuss fault classification and geometry from different viewpoints. Some, such as those by Davis et al., Twiss and Moores, and Pollard and Fletcher, include fault mechanics in their general treatment of faulting. It would be worthwhile to compare our approach with those in several of these other texts. Billings, M. P., 1973, Structural geology, 3rd edition: New York, Prentice–Hall, 606 p. Davis, G. H., Reynolds, S. J., and Kluth, C. F., 2012, Structural geology of rocks and regions, 3rd edition: New York, John Wiley & Sons, 864 p. Hills, E. S., 1963, Elements of structural geology: New York, John Wiley & Sons, 483 p. Park, R. G., 1983, Foundations of structural geology: London, Chapman & Hall, 135 p. Pollard, D. D., and Fletcher, R. C., 2005, Fundamentals of structural geology: New York, Cambridge University Press, 500 p. Twiss, R. J., and Moores, E. M., 2007, Structural geology, 2nd edition: W. H. Freeman and Company, 532 p. van der Pluijm, B. A., and Marshak, S., 2004, Earth structure, 2nd edition: New York, W. W. Norton & Company, 656 p. READINGS ON FAULT ZONE KINEMATICS Hanmer, S., and Passchier, C., 1991, Shear-sense indicators: A review: Geological Survey of Canada Paper 90–17. A useful summary of the literature and of criteria for determining shear-sense in rocks. Passchier, C. W., and Trouw, A. J. W., 2005, Microtectonics, 2nd edition: Berlin, Germany, Springer, 366 p. Discusses a wide variety of deformation processes and phenomena, including shear-sense indicators. Simpson, C., 1986, Determination of movement sense in mylonites: Journal of Geological Education, v. 34, p. 246–260. Discusses both shear-sense indicators and properties of fault rocks. 11 Fault Mechanics Thus far we have discussed the geometry, classification, and kinematics of fractures and faults but have yet to place these structures into their proper mechanical context. What forces are responsible for making faults slip? How are the stress states that generate thrust and normal faults different? What roles do fluids play in the generation of faults? In this chapter we provide a historical overview of fault mechanics and then outline modern concepts relating to the mechanics of faulting. Our understanding of fault mechanics is garnered from theoretical models, laboratory experiments, and field observations. We do not know who first recognized a fault, or when or where. Probably, it was many centuries ago, when someone noted ground breakage after an earthquake. The word “fault” was likely coined by eighteenth century English coal miners when they recognized offset coal seams, and considered this offset a defect or “fault” in the perfect deposition they expected in nature. Miners also are responsible for coining the names “normal fault,” for faults that have “normal” displacement (hanging wall down relative to the footwall), and “reverse faults,” for faults that have the opposite—reversed—movement sense (hanging wall up). It was also in the eighteenth c entury that Coulomb formulated the failure criterion that bears his name (Chapter 5), recognizing that shear and normal stresses are interdependent with respect to the cohesive shear strength and the coefficient of internal friction of a material. In the 1800s, Playfair, Lyell, Kotô, and other geologists wrote about faults much in the modern sense. Otto Mohr in 1882 related the Coulomb failure criterion to both shear stress and normal stress (Figure 5–9), and so the criterion is frequently referred to as the CoulombMohr criterion of failure. During the late 1800s, Bailey Willis and H. M. Cadell experimented with some of the first geologic models, exploring the nature of faults and other structures (Figure 11–1), but it was not until Anderson (1942, 1951) systematically examined the three fundamental types of faults that modern study of fault mechanics began. Anderson’s clear and simple—and rigorous—assumptions form the basis for most later studies of fault mechanics. . . . rupture by shearing would be expected to occur along planes oblique to the axis of greatest and least intensity of compressive stress, but (if the material is isotropic) inclined at angles of less than 45° to the axis of greatest stress. L. M. HOSKINS, 1896, Sixteenth Annual Report of the U. S. Geological Survey 269 270 | Fractures and Faults with depth, because of the increase in the weight of the overlying column of rock. Anderson made several important assumptions regarding stress in the Earth that are still used in fault mechanics: (1) the crust was initially “intact” and unfractured; (2) one principal stress direction is vertical; (3) the two other principal stresses, which are perpendicular to the first and to each other, must be horizontal and probably maintain a constant orientation for thousands to millions of years; and (4) forces must balance each other in a body in equilibrium. Assumption 2 actually recognizes that the Earth’s surface is a surface of no shear (that is, not subject to a shear traction); therefore, one principal stress must be vertical (at depth, however, this relation may be more complex). These assumptions produce a direct relationship between the orientation of stresses and the types of faults. Following up on his assumptions, Anderson suggested three possibilities for deviation from lithostatic stress conditions: 1. 2. 3. FIGURE 11–1 Bailey Willis’ pressure-box model consisting of layers of differing strength that produced a faulted fold as they were compressed from the ends. The deformation sequence is from top (undeformed) to bottom. (From B. Willis, 1893, U.S. Geological Survey, Thirteenth Annual Report, Part II.) Anderson’s Mechanics and Fundamental Assumptions Anderson (1942) defined three groups of faults that may be related to principal and shear stresses in the Earth. In doing this, he first defined a “standard state.” Accordingly, his standard state represents a stress system made up of two parts: (1) the force of gravity, and (2) a superposed horizontal (tectonic) stress that remains constant in any horizontal plane but increases Principal stresses σ1 and σ2 are horizontal. The least principal stress σ3 is vertical, and the dip on the fault plane will be 45° − ϕ/2 (about 30°). Maximum and minimum principal stresses σ1 and σ3 are horizontal, implying that the intermediate stress σ2 is vertical and that the fault plane will have a nearvertical dip. Principal stress σ1 is vertical. Therefore, the fault plane will dip 45° + ϕ/2 (about 60°). These three sets of conditions describe the stress in each major fault group: thrust faults, strike-slip faults, and normal faults. In essence, which principal stress is vertical controls the type of fault that develops. We will discuss each class in greater detail in the next section and in the following three chapters. Long after Coulomb formulated the theory of shear fracture in 1776, Navier observed in 1833 that rupture does not occur on the planes of maximum shear stress that bisect the angles between the greatest and least principal stresses. He suggested instead that “internal friction” was responsible for the difference and proposed a constant he called the coefficient of internal friction to account for it. The observation that σ1 (maximum principal stress) bisects the acute angle between the conjugate shear planes of the stress ellipsoid is called Hartman’s rule. This angle (2α) commonly is closer to 60° than to 90° because the shear angle depends on the angle of friction (ϕ) in the Mohr diagram (Figure 11–2), so that ± α = 45° − ϕ/2.(11–1) From the Mohr diagram in Figure 11–2, it is also evident that σmax (the maximum shear stress) is at 45° to σ1 Fault Mechanics τ Coulomb-Mohr failure envelope +2α ϕ σ3 –2α +2θ σ1 σn –2θ FIGURE 11–2 Mohr diagram showing relationships among ϕ, θ, α, and the Coulomb-Mohr failure envelope. (see also Figure 5–10). The significance of this relationship lies in the ability to predict the angles produced by faults and other shear fractures, which occur on planes of less than maximum shear stress (where frictional resistance is lower). Anderson’s Fault Types Separation of stress regimes into the three fundamental possibilities just outlined gives rise to Anderson’s three basic fault groups. The mechanics are easy to understand if his scheme is followed. Type 1. Thrust Faults Ideal thrust faults may be defined mechanically as faults produced by maximum and intermediate principal stresses oriented horizontally, with the minimum principal stress oriented vertically (Figure 11–3a). A state of horizontal compression is thus required for thrust faulting. Strict adherence to Anderson’s concept of thrust faults does not account for the steep dips (> 45°) of reverse (high-angle thrust) faults, or for near-horizontal thrusts, because of the initial assumption of a homogeneous Earth. Variations in the relative strength and other properties of different rock types, however, permit more steeply and shallowly dipping segments to form in nature and do not violate Anderson’s basic concepts. The two shear planes are potential fault planes; ideally, a fault should form parallel to each shear plane, but | 271 commonly only one dominant shear plane becomes a fault. The alternate shear plane may form a fracture or series of fractures with minor displacement. The result is a thrust fault with the upper block (the hanging wall) moved up relative to the lower block (the footwall). Mohr-circle analysis of thrust faulting (Figure 11–4) may involve successively increasing values of σ1, producing circles of increasing radii until the failure envelope is reached. Alternatively, the value of a vertical σ3 can be decreased by erosion to permit the failure envelope to be reached. Type 2. Strike-Slip Faults If the maximum and minimum principal compressive stress axes are horizontal and the intermediate principal stress axis is vertical, conditions are right for strike-slip faulting (Figure 11–3b). As with all faults, the intermediate principal stress axis will lie within any fault plane that forms, and, as a result, must in this case be vertical. The corresponding stress ellipsoid for strike-slip faulting also contains vertical planes of maximum shear stress, which ideally lie at 45° or less to the axis of minimum stress; shears commonly form at angles more acutely and symmetrically about the axis of minimum strain (and maximum stress), mainly because of an optimum combination of high shear stress and low normal stress—and thus occur in isotropic rocks. In addition, inhomogeneities and the pre-rupture strain history in most rock masses play an important role in formation of faults. Mohr-circle analysis for strike-slip faults can be the same as for thrusts (Figure 11–4), if sufficient differential stress exists to increase the size of the circles to reach the Mohr failure envelope for any of the Anderson fault types. Type 3. Normal Faults Normal faulting involves extension in one horizontal direction, with the maximum principal stress (σ1) vertical (Figure 11–3c). Shear planes may be expected at 45° or less to the axes of maximum and minimum principal stress and strain, respectively. They therefore form steeply dipping fault planes located symmetrically about the vertical axis. Both shear planes are frequently utilized in complex normal fault zones. Similarly, as with thrust faults, Anderson’s mechanics do not account for the formation of lowangle normal faults. Mohr-circle analysis of normal faulting may be thought of as starting at a large confining pressure, with σ3 decreasing (producing extension) until the size of the circles produces a stress difference (σ1 − σ3) large enough to reach the failure envelope (Figure 11–5). As with the other kinds of faults, other means may be used to increase the stress difference and cause failure. For example, depositional loading where σ1 is vertical can lead to normal faulting. 272 σ3 Thrust faults Minimum stress Planes of maximum shear stress Planes of actual faulting σ3 45° σ1 Maximum stress 30° σ1 σ1 σ1 σ1 σ2 σ2 (a) Strike-slip faults σ2 σ2 σ1 σ3 Maximum stress Minimum stress 45° σ3 σ3 σ1 σ1 σ1 (b) Maximum stress σ1 Normal faults σ1 σ1 σ1 45° σ3 Minimum stress σ2 σ3 σ3 σ2 (c) FIGURE 11–3 Mechanical and geometric qualities of Anderson’s three kinds of faults indicating the relationships between the three principal stresses, fault geometry, and the development of fault planes. (a) Thrust faulting. (b) Strike-slip faulting. (c) Normal faulting. Fractures and Faults Fault geometry | State of stress | Fault Mechanics τ τ Failure envelope Failure envelope ϕ ϕ ϕ ϕ 273 2α σ3 2θ σ1 σn FIGURE 11–4 Mohr-circle analysis of thrust faulting. As σ3 remains constant, σ1 increases (dashed circles) to failure (red circle). Role of Fluids Hubbert and Rubey (1959) applied Terzaghi’s observations from soil mechanics (Chapter 9) and demonstrated that fluid plays an important role in faulting. They recognized that the “lubricating” effect of fluid in a fault zone is really a buoyancy effect that reduces the shear stress necessary to permit the fault to slip, as the fluid pressure reduces the normal stress on the fault plane. The resulting stress is effective normal stress (S ), and we can determine it by subtracting the fluid pressure (Pw ) from the normal stress (σn). Mohr circles are shifted to the left toward the failure envelope and then touch it, leading to rupture and movement along the fault (Figure 11– 6). This concept is an oversimplification requiring resolution of both the horizontal and vertical components of effective normal stress. Horizontal effective normal stress is more easily assumed to be the same in all directions, whereas the vertical effective normal stress varies with the weight of the overburden minus the vertical component of fluid pressure. If higher-pressure fluid from a nearby layer under higher pressure (“overpressured”) is forced into a rock layer under lower fluid pressure, the values of σ1 and σ3 will be decreased by an additional amount (−ΔP). This causes a decrease in the values of σ1 and σ3 , but the size of the Mohr circle remains the same (Figure 11– 6) and the circle is still shifted toward the tensile field, so that an additional rise in pore pressure may lead to failure at values of zero or negative (tensile) effective normal stress (Mandl, 1988). 2α ϕ 2θ σ3 ϕ σ1 σn FIGURE 11–5 Mohr-circle analysis of normal faulting: σ3 decreases with σ1 contact (increasing the size of the Mohr circles, dashed circles) until the Mohr circle (red) intersects the failure envelope. τ Failure envelope Mohr circle for dry material σ1 – Pw σ3 – Pw σ3 1 σ1 σn 2 FIGURE 11–6 Mohr circles showing the effect of fluid pressure (Pw) on effective normal stress. Increasing fluid pressure reduces the strength of the material (dashed red circle) and forces it toward the unstable region outside the failure envelope. Note the curved envelope, indicating a component of ductile behavior. The effect of fluid on movement is illustrated vividly by landslides and snow avalanches. Conditions favoring landslides may exist for centuries in an area without initiating slides (Chapter 2); the influx of a large amount of water into the susceptible materials may reduce the effective normal stress and trigger a landslide. Snow avalanches travel at high velocity on a cushion of air—another fluid that decreases effective normal stress. In unconsolidated sediment in accretionary wedges and deltas, movement along 274 | Fractures and Faults faults is made easier in sections overpressured by fluid that cannot escape. Normal stress is borne by the confined fluid rather than by the sediment, facilitating movement. Some movement will occur on any fracture produced by shear. If appreciable movement is to occur on an existing fault surface, the coefficient of friction along the fault must be overcome. Two laws concerning friction were probably first discovered by Leonardo da Vinci and then were rediscovered by Guillaume Amontons (1663–1705), a French physicist who first presented them to a scientific gathering in 1699 (Suppe, 1985). Amontons’ first law states that the tangential force parallel to a fracture surface necessary to initiate slip is directly proportional to the force perpendicular to the fracture surface. Dividing force by area, Amontons’ first law may be stated as τ = μσn(11–2) where τ is tangential (shear) stress, σn is normal stress, and the proportionality constant μ is the coefficient of friction [see Byerlee’s law (equation 11–4) in next section]. Amontons’ second law states that the frictional resistance to motion is independent of the contact area. This law has an important bearing on the nature of fault surfaces and resistance to movement. If fluid occurs in the fault zone, normal stress will be decreased by the quantity Pw, which is fluid pressure. Equation 11–2 then becomes τ = μ (σn − Pw) = μS(11–3) where (σn − Pw) is effective normal stress, S. Therefore, fluid lowers the shear stress required for failure and fault motion and allows movement to begin at lower values of τ. In 1959 Hubbert and Rubey illustrated the effective stress relationship, using only an empty beer can on a glass plate (Figure 11–7). First, they placed the can (open end down) on the dry plate and lifted one side of the plate until the can moved—requiring an angle greater than 15°. Then they lowered the plate and wetted it with water, chilled the can, and again placed it on the wet surface. This time, when they raised one side of the plate, only a slight incline—about 2°—was needed for the can to begin sliding down the slope. As the can warmed and the air inside tried to expand, the buildup of air pressure along the wetted surface of the glass plate permitted movement of the can on an even lower slope. The weight of the can corresponds to a vertical force (Figure 11–7), and the air pressure corresponds to pA BEER Frictional Sliding Mechanisms A mg cos θ θ mg sin θ θ FIGURE 11–7 The Hubbert and Rubey beer-can experiment. If the glass plate is dry, θ > 15°; if wet, θ < 2°; m—mass of can, g—acceleration due to gravity, A—area of base of can, p—excess pressure of air inside can over that outside. (From M. K. Hubbert and W. W. Rubey, 1959, Geological Society of America Bulletin, v. 70.) the fluid pressure. A similar laboratory bench model experiment used a concrete block weighing several hundred kilograms. The block was smooth and rested on a smooth surface. As long as the surfaces remained dry, the block could be moved only with great difficulty, but when a film of water between the two smooth surfaces counteracted the total stress and buoyed up the block, the block moved so easily that Hubbert and Rubey said that it was dangerous to stand near the heavy and unstable block. Movement Mechanisms Movement on faults occurs in at least two different ways: by stick-slip (unstable frictional sliding) and by stablesliding (continuous creep). The stick-slip mechanism (Figure 11–8) involves sudden movement on the fault after long-term accumulation of stress (Scholz, 2002). This mechanism and the accompanying elastic rebound ( Chapter 5) produce earthquakes. The stable-sliding mechanism involves uninterrupted motion along a fault, so that stress is relieved continuously and does not accumulate. The difference in behavior may be produced along segments of the same active fault undergoing stable sliding where ground water is abundant, but other segments, with less ground water, may move by stick slip. Some segments of the San Andreas fault in California exhibit stick-slip behavior, others stable sliding. Other and more complex factors, such as curvature of the fault surface, may determine the mechanism involved in movement. Withdrawal of ground water may cause near-surface segments of active faults to switch mechanisms, from stable sliding to stick slip, thereby increasing the earthquake hazard. The converse may also be true, but there are difficulties. Pumping fluid into a “locked” fault zone has been proposed as a way to relieve accumulated elastic Fault Mechanics F V x u P (a) Stick-slip Stable sliding V (b) t FIGURE 11–8 (a) Moving an object connected to a spring by a line load (P) (e.g., a strong cable). The spring will stretch as the line is tightened at velocity (u) until friction (F) with the surface is overcome, and the object will move at high velocity (V) as the spring relaxes. If the spring remains tight and the block is not allowed to cease moving, the block will continue to move (x-direction) by stable sliding; if the block stops, friction will have to be overcome again, and the stick-slip cycle will be repeated. (b) Time (t, x-axis) versus velocity (V), illustrating stick-slip and stable-sliding mechanisms. (After James Byerlee, 1977, Friction of rocks, U.S. Geological Survey, Office of Earthquake Studies.) strain energy and reduce the likelihood of a large earthquake, but the rate at which fluid should be pumped into a fault remains unknown. Pumping fluid into a locked fault zone would raise the fluid pressure and lower effective normal stress, but if pumping is too rapid, it could trigger earthquakes artificially by allowing the stick-slip mechanism to go to completion, rather than slowly bleeding off accumulated stress by creep. Studies by Raleigh et al. (1976) on the fluid-induced seismic activity at Rangely, Colorado, and Simpson (1986) on reservoir-induced and other man-initiated earthquakes, suggest that the Earth must be in a state of near failure (high in situ stress) for increases in fluid pressure to have a significant influence. Geothermal projects in northern California and in Basel, Switzerland, injected large quantities of water into hot aquifers to fracture the bedrock and thereby increase permeability, allowing for more steam to be extracted. These hydrofracturing (fracking) projects resulted in numerous small earthquakes, and the projects have since been canceled due to concerns about human-induced seismicity and the associated hazards. The San Andreas fault in California is one of the best studied and documented active faults in the world. It has generated numerous destructive earthquakes and much effort is directed at understanding the mechanics of faulting along that structure. This fault has produced a series of moderate-size (Mw ~6) earthquakes at remarkably regular | 275 intervals near Parkfield in central California. Quakes occurred here in 1857, 1881, 1901, 1922, 1934, 1966, and 2004, having a recurrence interval of approximately 25 years. The U.S. Geological Survey has done intensive work in this area in an attempt to predict one or more of the regular earthquakes, with limited success. The San Andreas has been the focus of the EarthScope Plate Boundary Observatory, consisting of many seismometers and GPS sites, and a deep drill hole that penetrated the fault at depths where earthquakes are presently being generated. The goal is to better understand the behavior of this large strike-slip fault and to be able to apply what has been learned to other similar faults elsewhere in the world to be able to predict future earthquakes. Fault Surfaces and Frictional Sliding Fault surfaces between two large blocks are never perfectly smooth and planar, especially on the microscopic scale. Microscopic to megascopic irregularities and imperfections, called asperities (Figure 11–9), increase the resistance to frictional sliding, and, because of the overall irregularly shaped fault surface, they also reduce the percentage of surface area actually in contact. Bowden and Tabor (1950), both metallurgists, first suggested that because of asperities, even the best-prepared surfaces will not fit together and that breaking asperities increases the contact area. The initial contact area may be as little as 10 percent, but when motion begins, irregularities on the surface are removed, and as the displacement increases, the contact area increases (Teufel and Logan, 1978). Because asperities provide the surface with frictional strength and resistance to movement, they must be broken through in order for movement to occur. Rock-mechanics experiments on fault surfaces demonstrate that resistance to frictional sliding can increase after movement begins (strain hardening, Chapter 7), suggesting an increase in strength or number of asperities in the contact zone, but they also indicate dependence on both velocity and displacement (Scholz, 2002). The increase may result from the greater contact area, requiring that more asperities be broken to initiate movement, but the strength of the fault zone decreases again with continued movement. Thus, despite the increased contact area, additional movement ultimately reduces the asperity population and, hence, also the strength of the fault surface (an example of strain softening, Chapter 7). Byerlee (1977, 1978) showed experimentally (Figure 11–10) that, for low effective normal stress, S (< 0.2 GPa)—the usual condition in the upper crust— σmax S = 0.85,(11–4) where σmax is maximum frictional shear stress (in MPa). This relationship has been called Byerlee’s law of rock friction, and is an important statement regarding faulting and the brittle behavior of most rocks under stress in the 276 | Fractures and Faults Fault surface σ1 σ1 Asperities (Asperities must be broken to overcome friction on fault surface) Open spaces (a) (b) FIGURE 11–9 (a) Asperities and contact-surface area along a fault. Note that because of the irregular nature of the fault surface, asperities reduce the area in contact with the opposing fault surface. (b) Holes and grooves in the footwall (limestone) of a near-horizontal thrust fault at Vellerat near Choindez in the Jura Mountains, Switzerland. The holes were produced either by irregularities—asperities—on the footwall surface that were broken and removed during movement or by asperities in the hanging wall that gouged and plucked mate rial from the footwall. The curved fractures above (south of) the large hole are extension fractures that indicate relative south-to-north motion of the hanging wall. Grooves (slickenlines) in the fault surface were also produced by irregularities on both the hanging wall and footwall surfaces. (Locality courtesy of Hans P. Laubscher, University of Basel, Switzerland. RDH photo.) upper crust. That Byerlee’s ratio for most rock types is 0.85 (Figure 11–10) indicates that the coefficient of friction in Amontons’ laws is independent of rock type and depends solely on values of shear and normal stress. Byerlee also showed that for values of S between 0.2 GPa and 2 GPa, These conditions probably occur at greater depth in the crust. There is some doubt that the 0.85 value for the coefficient of friction is valid—it is probably closer to 0.6—particularly because earthquakes occur in the shallow crust at a shear stress much below that suggested by Byerlee’s experiments (Alsop and Talwani, 1984). Fluid, some clay minerals, or anything else that weakens rocks could cause failure at values lower than predicted. Shear (Frictional) Heating in Fault Zones Data gathered from frictional sliding experiments and the occurrence of pseudotachylyte veins (literally, false glass, Figure 11–11) in many fault zones indicates that heat is 80 Shear stress, τ (MPa) σmax = 50 MPa + 0.6 S.(11–5) 100 τ= σ 85 0. 60 40 20 0 0 20 40 60 Normal stress, σn (MPa) 80 100 FIGURE 11–10 Least-squares fit of points derived from experimental measurement of maximum shear stress (τ) and normal stress (σn), producing a curve with the equation τ = 0.85σn. Note that these measurements were made on sawed dry rock specimens, not fresh fractures. (Modified from James Byerlee, 1977, Friction of rocks, U.S. Geological Survey Office of Earthquake Studies.) Fault Mechanics | 277 FIGURE 11–11 Veins of pseudotachylyte (dark bands) in lowercrustal gneiss from the Ivrea zone, Valle dell Infierno near Ornavasso, Italy. (Locality courtesy of Hans P. Laubscher, U niversity of Basel, Switzerland. RDH photo.) generated along faults. The amount of work (W) accomplished in overcoming friction is related to the shear stress (τ) along the fault surface and the displacement (d) during a single movement event as W = τd. (11–6) The amount of heat (q) generated by the work done can then be estimated from q= W ddττ , = J J (11–7) where J is the mechanical equivalent of heat (4.186 joules calorie–1 gram−1 at 15° C). The heat generated can be related to an increase in temperature (T) by q = mCT, (11–8) where m is the mass of rock heated and C is the specific heat of the rock mass. Amount of heat (here heat flow, q) can also be related to movement velocity (v) and mean shear stress along the fault as q ≤ vτ. (11–9) According to Scholz (1990), equation 11–9 predicts that if the velocity of motion of a fault is greater than 1 cm/y and shear stress is greater than 50 MPa, shear heating as a consequence of faulting will be significant. Scholz (1980) suggested that for the effects of shear heating to be recognized in geologic systems, temperatures must be increased by several hundred degrees Celsius within several kilometers of the fault and must be maintained long enough for metamorphic reactions to occur. The primary evidence for the effects of shear heating is twofold: (1) pseudotachylyte (Figure 11–11), dark vein fillings of glass-like material thought to form by brittle failure, friction-generated heat, and local melting of rock (Sibson, 1975); and (2) metamorphic reactions in subduction zones and accretionary complexes where greenschist- and blueschist-facies metamorphism in the fault zone can be directly related to heating of the overriding block by friction with the downgoing slab (Pavlis, 1986; Peacock, 1992). Frictional melts that produce pseudotachylyte seem to be concentrated along very thin fault zones (< 1 cm, Sibson, 1973) and occur in a variety of tectonic settings. In addition, metamorphic aureoles in footwall rocks beneath ophiolites (Williams and Smyth, 1973; Jamieson, 1986) have been cited as evidence for shear heating (e.g., Scholz, 1980), although it is difficult to prove that the heat was not acquired at greater depth in the crust before emplacement, and an already hot slab overthrust a cool footwall. Platt (2015) concluded from experiments and modeling that shear heating for 5 m.y. just below the ductile-brittle transition would increase the temperature by 80° C and up to 120° C just below the Moho. Scholz (1980) cited the Alpine fault in New Zealand as an excellent example of the direct relationships between a large crustal fault and metamorphic isograds that 278 | Fractures and Faults FIGURE 11–12 Tectonic map showing the location of the Alpine fault and the related plates; plate motions are also indicated. AUSTRALIAN PLATE TR ENC H North Island d an 40°S l ea au air W w Ne lt au f ine M AD EC Z t aul re f ate w A fault Hope p Al PU YS 45°S UR EG CH EN R T R KE 50mm/yr – A NG TO lt fau 40mm/yr PACIFIC PLATE South Island 30mm/yr 0 100 200 300 kilometers 170°E indicate increased grade closer and subparallel to the fault (Figure 11–12). Fault rocks within the Alpine and many other crustal fault zones, however, contain deformed retrograde (lowered or decreased grade compared with the surrounding rocks) hydrous minerals such as chlorite and muscovite (Reed, 1964). This suggests that the fault zone served as a conduit for rapid fluxing of large amounts of water and dissipation of heat during deformation, rather than as a locus for heat accumulation and regional metamorphism. Geochemical and isotopic evidence suggest large quantities of water move through crustal fault zones to convert anhydrous minerals (e.g., feldspars, garnet, kyanite) to hydrous minerals (e.g., muscovite, chlorite) and selectively remove particular elements and isotopes (e.g., Sinha et al., 1988). Friction-related heating along faults is a process that clearly occurs in the Earth, but it is difficult to demonstrate except along faults and landslides containing pseudo tachylyte (or hyalomylonite) and within subduction zones. Glassy melt has even been documented along the weak surfaces where landslides initially propagate (Erismann et al., 1977; Heuberger et al., 1984; Weidinger and Korup, 2009). This remarkable occurrence is the most convincing evidence of significant amounts of frictional heat on fault surfaces, because the pre-landslide materials would be at surface temperatures and pressures. 175°E 180° Reality of Fault Mechanics Models for understanding basic fault mechanics are very useful for learning about the differences in the three fundamental types of faults and why they exist. The problem with Anderson’s mechanics, or other ideal models, is that rocks in the Earth’s crust are mostly not homogeneous materials on the outcrop to map scale, and this heterogeneity produces variations in dip, curvature, displacement, and many of the other basic properties of real faults in the field. Even so, some faults are knife-sharp contacts on the outcrop scale, whereas others consist of an array of faults or a fault zone (Figure 11–13). Sedimentary and many volcanic rocks contain layered anisotropies—primarily bedding—that provide opportunities to be exploited by faults as they propagate through a sedimentary sequence. A fault may begin to propagate at a high angle across bedding in a mechanically strong rock type, like sandstone, limestone, or dolostone, but may then encounter a layer of weak material such as shale, coal, or salt and change dip to propagate along the weak layer by expending less energy than it would take to continue to propagate across the sequence of strong layers. Fault Mechanics | 279 (a) (b) FIGURE 11–13 (a) Knife-sharp brittle fault contact (gray-tan boundary) of Cambrian clastic rocks (tan) thrust over Ordovician limestone (gray) near Inchnadamph in the Northwest Highlands, Scotland. (b) Complex array of brittle thrust faults in Pennsylvanian sandstone and thin interbeds of shale near Dunlap, Tennessee. Low-angle faults (near hammer) propagated both along shale beds and across sandstone beds forming wedges and imbricate slivers of sandstone. (RDH photos.) 280 | Fractures and Faults Regional metamorphic rocks may contain both a foliation and original bedding that provide even more opportunities for faults to propagate. Propagating faults may follow foliation or relict bedding, exploiting the differences in strength parallel to rather than across the foliation, or occasionally even follow the contact between rocks of strongly contrasting strength, such as slate and quartzite. Igneous rocks may be the most homogeneous of all rock types, if they crystallize by uniform cooling of a static magma. Many igneous rocks, however, flowed as the pluton moved to higher parts of the crust and crystallized during the final stages of emplacement, so they, too, may contain a foliation. Dikes and sills of different strengths from the enclosing igneous rock mass also can provide anisotropies for localization of faults along contacts. Even so, the interlocking nature of crystals in an igneous rock mass adds an additional microtextural element of strength in three dimensions not present in sedimentary and lowgrade metamorphic rocks. ESSAY Study of real faults in the field reveals that they are frequently not single planar structures, but form multiple anastomosing, curved, and branching (splaying) surfaces (Figure 11–13). Brittle faults form discrete surfaces, but occasionally form zones of cataclasite as breccia and gouge, whereas ductile faults form wide zones of plastic deformation. The same fault may produce brittle fault surfaces in the upper crust, but, as it extends deeper into the crust, the same fault may produce a broad zone of mylonite below the ductile-brittle transition (Chapter 13). Moreover, the same fault that moved the first time as a ductile fault may be reactivated millions of years later as a brittle fault as the Earth’s surface is eroded so that the fault is closer to the surface and is now above the ductilebrittle transition. This ends our discussion of fault mechanics. Now we turn to a more in-depth discussion of the three main fault types beginning with thrust faults. Artificial Earthquakes Should we try to artificially relieve accumulated elastic strain energy on large faults otherwise certain to cause sizeable earthquakes? The San Andreas fault is likely to produce an earthquake of magnitude 8 or larger in southern California before the year 2025. One proposal is that we pump fluid into a locked segment of the fault zone at a suitable rate so that the strain energy will be relieved by very small earthquakes and thus minimize damage and loss of life. No one has ever successfully carried out such an experiment, however. Should southern California cities be evacuated before pumping? Who will pay for damages produced by the small earthquakes? What if pumping triggers a large earthquake and devastates the region anyway? Who bears legal responsibility? Such questions discourage attempts to try the experiment. Artificial earthquakes were produced unintentionally in the early 1960s as a by-product of disposal of toxic chemicals in a 12,045-foot well at the Rocky Mountain Arsenal near Denver, Colorado. In 1965, geologist David M. Evans suggested that the occurrence of earthquakes after disposal of fluid there from 1962 until 1965 showed that it was possible to influence the mechanism and timing of release of accumulated elastic strain (Evans, 1966). He plotted the occurrence of earthquakes from March 1962 to November 1965 and correlated them with the pumping of fluid into the well at the arsenal. His data showed that earthquakes began within a month after pumping started, decreased markedly from S eptember 1963 through September 1964 when no fluid was injected— and resumed with greater frequency when pumping was restarted in September 1965 (Figure 11E–1). The waste fluid was pumped into Precambrian crystalline basement rock beneath the Paleozoic to Cenozoic sedimentary cover, with disposal in fractures that did not communicate with the present-day surface ground-water system. The fluid was initially injected under pressure, with the pressure relieved by flow along existing fractures enlarged in the crystalline rocks. New fractures were expected to form by hydrofracturing during injection. Although seismic activity was not unknown, no earthquakes had been felt or recorded in the Denver area between 1882 and the beginning of pumping in 1962. From April 1962 until September 1965, local seismic stations recorded 710 earthquakes with epicenters in the vicinity of the Rocky Mountain Arsenal. Magnitude ranged from 0.7 to 4.3 on the Richter scale, and about 75 of the earthquakes were felt. Most foci were determined to be from 4.5 to 5.5 km deep (Evans, 1966)—about the same depth as the bottom of the well. Low-level elastic strain energy accumulated and was relieved by fluid pressure, reducing the effective normal stress so that elastic strain could be relieved by shear on appropriately oriented fracture surfaces. No one doubts that the Denver earthquakes were produced by deep-well injection. Public outcry brought an end to the pumping, and contractors at Rocky Mountain Arsenal (remarkably) devised a chemical means of breaking down the toxic waste in order to dispose of it conventionally. The problem of disposal fluid–induced earthquakes has surfaced again, this time in Oklahoma, Ohio, Texas, Kansas, and elsewhere, with disposal of fluids used in fracking Fault Mechanics 90 Earthquakes/month 281 FIGURE 11E–1 Correlation of earthquake frequency with the injection of liquid waste at Rocky Mountain Arsenal from 1962 to 1965. (From D. M. Evans, 1966, Geotimes, v. 10.) Earthquake frequency 80 | 70 60 50 40 30 20 10 0 9 Contaminated waste injected 7 6 5 4 3 2 1964 horizontal wells to increase oil or gas production (see Essay 1 in Chapter 9) causing sizeable earthquakes. Earthquakes as large as Mw = 5.8 have occurred in Oklahoma since 2010, and a clear relationship of fluid disposal and earthquakes has been demonstrated (Walsh et al., 2015). The events in Denver during the 1960s and more recently in Oklahoma prove that we can induce earthquakes, but to enter a major active fault zone and attempt to relieve stored elastic strain energy artificially—before nature releases it suddenly and without warning—requires detailed knowledge of the fracture system associated with the fault at great depths. We do not have the data necessary to predict how much fluid should be pumped, where it should be pumped, and how rapidly it should be pumped into the NOV JUL SEP MAY JAN MAR SEP NOV JUL MAY NOV JUL 1963 SEP MAY JAN MAR NOV JUL 1962 SEP MAY MAR JAN 0 JAN No fluid injected 1 MAR Millions gallons/month 8 1965 system to lower the effective normal stress and bleed off the excess energy. Apparently, the crust in the Denver area did not contain a great excess of accumulated and stored elastic strain energy like the crust along the San Andreas fault in southern California. Before we can attempt to drain off energy from a large and active fault zone, we must answer many questions—scientific, sociological, political, and legal. References Cited Evans, D. M., 1966, Man-made earthquakes in Denver: Geotimes, v. 10, no. 9, p. 11–18. Walsh, F. R., III, and Zoback, M. D., 2015, Oklahoma’s recent earthquakes and saltwater disposal: Science Advances, v. 1, no. 5, p. 1–9. Chapter Highlights • Anderson’s models for fault movement are based on the assumption that principal stresses in the crust are either horizontal or vertical, and that the type of faults that develop are governed by the orientations of the principal stresses. • Faults slip when the state of stress is sufficient to overcome the frictional resistance acting on the fault— increased fluid pressure lowers the effective stress and facilitates slip. 282 | Fractures and Faults • Faults can move via stick-slip behavior (frictional sliding) or stable sliding (continuous creep). Earthquakes are generated by stick-slip behavior. • Frictional heating occurs during slip on faults, and can be sufficient to locally melt rock producing pseudotachylyte. Questions 1. Why are Mohr diagrams for normal and thrust faults constructed of nested circles of oppositely increasing radii? 2. How is Amontons’ first law related to Byerlee’s law? 3. How do Anderson’s fundamental assumptions relate to real faults? Can you suggest an alternative scheme of orientation of principal stress (strain) axes that will work? 4. How does water affect the normal and shear stress on a fault? Explain. 5. Describe the transformation of part of a fault from a stickslip mechanism to a stable-sliding mechanism. What are the reasons for the transformation? 6. If a fault in a gneiss has a maximum shear stress of 68 MPa and an effective normal stress of 77 MPa, what is the coefficient of sliding friction for the fault? 7. Explain in terms of fault mechanics the mechanism by which earthquakes were produced in the Denver area soon after deep injection of fluid. Further Reading Anderson, E. M., 1951, Dynamics of faulting and dyke formation with applications to Britain: Edinburgh, Oliver and Boyd, 206 p. A classic and readable work discussing the characteristics and mechanics of the three major types of faults. Mandl, G., 1988, Mechanics of tectonic faulting: Amsterdam, Elsevier, 407 p. Mathematical presentation of fault mechanics preceded by a discussion of the different geometric attributes of faults. A second section is a thorough discussion of the concepts of stress and strain and their application to faulting. Scholz, C. H., 2002, The mechanics of earthquakes and faulting, 2nd edition: Cambridge University Press, 471 p. Contains a more in-depth summary of fracture and fault mechanics than is provided here; provides useful insight into the mechanics of faults leading directly to earthquakes as a consequence of faulting. 12 Thrust Faults Thrust faults are fascinating structures, consisting of low-angle faults that transport thin sheets of rock—a phenomenon regarded as physically impossible when they were first discovered in the mid-nineteenth century. Many thrust sheets cover huge areas and have moved rocks horizontally tens to hundreds of kilometers. The Moine thrust in the Northwest Highlands of Scotland consists of an extensive thrust sheet with a minimum displacement of 50 km, placing Middle Proterozoic rocks on a suite of early Paleozoic rocks (Figure 12–1). Thrusts form some of the largest structures in mountain chains, comparable in size to large accreted terranes or microcontinents—hundreds of kilometers long. Thrusts affect the migration of ground water, oil and gas, and ore-bearing fluids during movement and also form traps for hydrocarbons and metallic minerals. Thrust, or “overthrust,” faults occur in mountain chains—orogenic belts. A belt of thrust faults, called a foreland fold-thrust belt, occurs between the undeformed craton and the metamorphic core of nearly every mountain chain (Figure 12–2). Most examples contain stratigraphic sequences formed from stable trailing margins, like the present-day Coastal Plain and Continental Shelf, Slope, and Rise on the East Coast of the United States. Much larger slabs of metamorphic rock underlain by thrust faults occur in the interiors of mountain chains, where some thrusts form under ductile conditions at moderate to high temperatures. Thrusts also form in subduction zones as the overriding plate scrapes sediment off the descending sea floor, producing an accretionary wedge. Subduction zones are actually megathrust systems that form at convergent plate boundaries. Thrust faults also form at the toe of masses of sediment along continental margins that move down slope under the influence of gravity. These have proved to be prolific sources of hydrocarbons off the West Coast of Africa, and along other margins, and consequently are well studied. The petroleum industry has long explored thrust-faulted terranes, gathering extensive drilling and seismic reflection data to help understand thrust geometry and behavior. Several very important concepts, such as thin-skinned thrusting and fluid involvement, were either proved or formulated by petroleum company structural geologists. Eight great faults [occur in East Tennessee as] ribbon-like masses or blocks . . . crowded one upon another, like thick slates or tiles on a roof, the edge of one overlapping the opposite edge of the other. JAMES M. SAFFORD, 1856, A Geological econnaissance of the State of Tennessee R 283 Fractures and Faults 5°30' W 4°30' W 5° W Loch Eriboll 58°30' N Arnaboll th ru st The Minch th ru st | Mo ine 284 Stack of Glencoul Assynt (a)(1) Loch Shin WSW 58° N ss nei M oin g Knockan Crag e thrust ESE ean Ullapool Arch 20 0 ite Mylon kilometers qua e r tzit Dalradian and post-Caledonian rocks Caledonian igneous rocks an Cambri Cambro-Ordovician sedimentary rocks Neoproterozoic intrusions Moine rocks — undivided (a)(2) Morar group FIGURE 12–1 (a)(1) Arnaboll thrust in the Moine thrust complex near Loch Eriboll, NW Scotland. Archean Lewisian gneiss in the hanging wall is thrust from left to right (white arrow) over bedded Cambrian quartzite in the footwall. Note that the foliation in the gneiss curves into the fault zone, providing shear sense. A 0.3 to 0.5 m-thick dark-colored mylonite zone occurs just above the thrust. Geologist for scale is Robert H. Butler. (Photo courtesy of Arthur J. Merschat, U.S. Geological Survey.) (a)(2) Sketch of photo. (b) S implified tectonic map of NW Scotland showing the location of the Moine and related thrusts. E riboll is in the northeastern part of the map. (From R. Strachan and J.R. T higpen, 2007, Field guide, graphic by J. Ryan Thigpen, University of Kentucky.) Nature of Thrust Faults Thrusts are gently dipping faults in which the hanging wall has moved up relative to the footwall. A variety of thrusts exists, and their behavior varies with the types and strengths of the rocks involved, the temperature at the time of formation, and the degree to which water was involved during movement. Thrust faults occur in mountain belts and their eroded remnants. They occur most commonly in a Torridon group Stoer group Lewisian Gneiss Complex Lewisian Inliers within Moine rocks (b) continentward-thinning wedge of sedimentary rocks above an undeformed basement in foreland fold-thrust belts (Figure 12–2). The undeformed mass of continentalmargin sediments has a characteristic wedge shape—a shape that is maintained throughout the deformation of the belt. This characteristic is inherited from the shape of the original continental margin on which the thrust belt is developed, because trailing-margin sediments thicken oceanward. Wedge geometry in thrust belts (Figure 12–2) was first recognized as a fundamental property of thrust belts by Elliott (1976). After studying active structures in Thrust Faults Interior of mountain chain Semi-rigid crystalline thrust sheet A 285 Continental interior Foreland foldthrust belt (FFTB) Free surface ry nda r ppe | β bou U α ry Lower bounda B Undeformed rigid basement Basal detachment (a) Continental margin Continental interior Tectonic transport Deformation propagating outward in time Metamorphic core Suture Older structures Ductile deformation dominant Younger structures FFTB Brittle deformation dominant T A (b) FIGURE 12–2 (a) Wedge-shaped foreland fold-thrust belt formed by deformation between two almost rigid plates, the undeformed basement below, and an advancing semi-rigid crystalline thrust sheet above that pushes the foreland fold-thrust belt in front of it. The yellow units represent weaker rocks where the basal detachment forms. A—Ancient rift normal fault beneath the crystalline sheet nucleates an antiformal stack duplex (see later) that arches the crystalline sheet. B—Older rift fault beneath the platform nucleates one or more foreland fold-thrust belt thrusts. α—Dip on basement beneath foreland fold-thrust belt. β—Topographic slope angle. (Modified from Hatcher, R. D., Jr., Lemiszki, P. J., and Whisner, J. B., 2007, Boundaries and internal deformation in the curved southern Appalachian foreland fold-thrust belt, in Sears, J. W., Harms, T. A., and Evenchick, C. A., eds., Geological Society of America Special Paper 433.) (b) Sequence, style, and rheology of deformation in the inner and outer parts of an orogen. Note that (a) is contained in the right-hand part of (b). the Taiwan thrust belt and formulating dynamic geometric models, Suppe (1981) concluded that the wedge shape is preserved during deformation through a combination of surface erosion and slumping. During thrusting, the principal change is that the wedge is shortened and thickened until it reaches a steady-state condition termed a critical wedge (Chapple, 1978; Suppe, 1981; Dahlen, 1990). Woodward (1987) suggested that the critical wedge models developed primarily from study of modern accretionary wedges may not survive rigorous application to foreland fold-thrust belts, because of contrasts in mechanical properties of the rocks and in the amount of fluid present. Despite this, we now know that the dip on the basement surface, and the mechanical properties of the basal weak unit (the detachment), strongly influence the amount of displacement that may occur in the deforming wedge, and that a large amount of internal deformation is not required within the wedge. Metamorphic rock—either as basement slices or as progressively metamorphosed sedimentary rocks— appears on the thickened side of the wedge in the transition to the metamorphic core of a mountain chain (Figure 12–2). Thrusts involving metamorphic and ig neous rocks are called crystalline thrusts. Those closer to the foreland form under brittle conditions; those farther into the metamorphic core form under conditions ranging from ductile to brittle, depending on temperature, availability of water, and strain rate during movement (Hatcher and Williams, 1986; Hatcher and Hooper, 1992; Hatcher, 2004). Thermal or strain softening of the crystalline mass may be required before faulting is initiated, if low-angle thrust faults are to propagate through crystalline rocks. The thrust plane may be initiated by local ductile behavior, but the sheet is transported as brittle mass. A source far inside an orogen may produce warmer thrust sheets than one on the outer flanks. 286 | Fractures and Faults Detachment Within a Sedimentary Sequence The concept of thin-skinned deformation is based on common properties of thrusts in foreland fold-thrust belts (see Essay 1 in this chapter). The purpose of this section is to introduce the properties and components of a thin-skinned foreland fold-thrust belt. Foreland thrusts are characteristically low-angle faults that place older rocks over younger rocks. They frequently include high-angle segments and (rarely) may bring basement rocks to the surface; they commonly repeat the same oldest rock unit across the entire belt. The oldest unit most commonly is a shale, evaporite, coal, or other weak (incompetent) rock type. Thrusts generally propagate along these layers, which are called detachments or décollements (French for “detachments” or “ungluing”). Because they represent translation along bedding, they are also called bedding-parallel thrusts. Décollements may occur as the result of either folding or faulting (Figure 12–3), but the net result is relative displacement of the upper layers. Many thrust faults form in a concave-up, spoon-shaped geometry and are called listric thrusts (Figure 10–3). Ramp-flat geometry is common in thrust sheets (Figure 12–3). High-angle segments (the angle is high relative to bedding, not necessarily forming a steep dip) exist where a thrust cuts across the stratigraphy, typically across a strong (competent) unit, from one detachment to another (Figure 12–4). A high-angle segment is a ramp, and these segments may occur on all scales crossing units from a few centimeters to a kilometer or more thick. Massive limestone, dolostone, sandstone, or other competent rock types may compose strong units that cause thrusts to ramp. The thickness of strong units (also called a strut) limits the amplitude of folds associated with thrusting. The flat component of the ramp-flat geometry is commonly localized in an incompetent (e.g., shale, evaporite) unit. Folds commonly form in association with thrust faults. Suppe (1983) defined fault-bend folds (Figure 12–5a) as those formed as the thrust surface changes from steeper to shallower dip in an up-dip direction. Fault-bend folds are similar to Willis’s shear thrusts. A thrust sheet wherein dip flattens as it passes over a ramp would produce a fault-bend fold. Suppe (1985) also recognized fault-propagation folds, which are thrusts that form along the common limb between an anticline and syncline during folding of a sedimentary sequence (Figures 12–5b and 12–5c). Fault-propagation folds may evolve into faultbend folds as displacement increases, perhaps accounting for the comparatively larger number of fault-bend folds in most foreland fold-thrust belts. Both fault-bend and fault-propagation folds are common types of forced folds. Detachment thrusts are commonly horizontal thrusts that form above a weak layer and deformation may be Strong unit 3 Weak unit C Strong unit Weak unit B Strong unit 2 Weak unit A Strong unit 1 Flat Ramp (a) Limit of displacement Flat (b) (c) Ramp Chaotic zone FIGURE 12–3 Formation of a décollement in a sequence of alternating weak and strong rock units. Dashed line in (a) is the path of a future décollement. Décollement follows weak units and ramps (or refracts) across strong units. Ramping occurs because of a change in the physical properties of a weak unit, as in weak unit A, B, or C in (a), or because of the thinning of a weak unit, as in the weak unit in (b). The entire sheet moves over the undeformed footwall, forming a ramp anticline (or fault-bend fold; see Figure 12–5). (c) Folds may also form by this mechanism above a décollement. Basal detachment B Future imbricate faults Ramp B Strong B Weak B 2 3 1 Strong A Weak A Ramp A Basal detachment A (master décollement) (a) 2 1 3 (b) FIGURE 12–4 Properties and propagation of thrusts in cross section. (a) Undeformed. (b) Deformed. The fault labeled 1 moves first; that labeled 3 moves last. The dip of thrust sheet 1 increases as thrust 2 forms and moves; the dip of both 1 and 2 are increased as 3 forms and moves up the ramp, arching and steepening the earlier-formed thrust sheets. Thrust Faults Fault-bend fold (a) Early-stage fault-propagation fold Unslipped Slipped | 287 FIGURE 12–5 (a) Fault-bend fold. Rocks passing over the faultbend (ramp) are ideally folded, and then unfolded. (b) Initial development of a fault-propagation fold as a blind thrust. (c) Well-developed fault propagation fold containing a hangingwall anticline and a footwall syncline. (d) Detachment thrust formed as pressure solution takes up internal strain in the rock unit(s) above the thrust, so the displacement equals the amount of pressure-solution shortening within the hanging wall (Geiser, 1989). A fold may form above the detachment increasing the amount of displacement on the thrust, and the structure is called a detachment fold. (b) Fault-propagation fold Trishear zone 60° Fault tip Trishear angle (c) Pressure solution cleavage Detachment thrust 30° Fault ramp angle (d) FIGURE 12–6 Geometry of a fault-propagation fold and the r esultant triangular-shaped zone of deformation known as a trishear. accompanied by both folding and development of a pressure solution cleavage (Figure 12–5d). As a fault-propagation fold hinge tightens, commonly becoming more overturned and converging downward, a triangle-shaped zone of (frequently penetrative) deformation forms from the tip of the propagating fault (Figure 12–6). The triangular zone of deformation associated with a fault-propagation fold is called a trishear (Erslev, 1991; Allmendinger, 1998). Folds that form near the thrust surface during movement are called drag folds (Figure 10–15a). Drag folds are a product of friction along the thrust surface and may range from open to tight folds (Chapter 15), depending on the strength of the rocks being deformed. The greater the amount of weak material in a stratigraphic sequence, the tighter the drag folds. Thrusts may occur as isolated faults, but they commonly occur in groups consisting of a master fault with several associated smaller faults; the smaller ones are imbricate thrusts (Figure 12–7a). The term imbricate zone may also be used to describe the series of thrusts making up such a group, or the entire foreland thrust belt. Imbricates probably form by branching from a master décollement as the thrust sheet moves. As one segment “sticks,” an imbricate propagates beneath it. In most cases, propagation is toward the foreland, but the term does not imply a propagation direction. Repetition of the sequence results in an imbricate stack. An accretionary wedge forms as the sediments in a subduction zone are scraped off the descending slab, and consists of an imbricate stack of thrusts (Figure 12–7b). Duplex structures occur where two subparallel thrusts of approximately equal displacement are separated by a stack of imbricates (Figure 12–8a). The upper of the two master faults is the roof thrust, and the lower is the floor thrust. Smaller imbricates connect the two master faults. Imbricates typically dip more steeply than the roof or floor thrusts and gradually merge with the master faults. Duplexes occur in most thrust-faulted terranes and were recognized more than a century ago by Peach et al. (1888) along the Glencoul and Moine thrusts in Scotland. They form as the roof thrust ramps and then 288 | Fractures and Faults Footwall broken sequentially forward as hanging wall locks and master fault continues to move Paths of thrusts if open-ended imbricates form Ocean-floor sediment Subducted ocea nic Accretionary wedge thrust complex Overriding plate crust (b) 4 3 2 1 Paths of future thrusts Duplex Open-ended imbricates 4 1 3 2 4 Imbricates (a) 3 Roof Arched hanging wall 2 1 Imbricates (horses) Floor Evolved (antiformal stack) duplex (c) FIGURE 12–7 (a) Formation of imbricate zones and duplexes. Younger imbricates steepen the dip of older faults as they move. (b) Formation of accretionary wedges. (c) A hinterland-dipping duplex may evolve into an antiformal stack duplex by continued motion on the thrust sheet and imbricates, resulting in arching of the hanging wall. FIGURE 12–8 (a) Cross section of the Limestone Cove duplex, Tennessee, showing deformed (above) and retrodeformed (below) sections. p –Cb—Basement rocks. –Cu—Unicoi Formation. –Che—Hampton and Erwin Formations. –Cs—Shady Dolomite. –Cr—Rome Formation. –Cc— Consauga Group. O –Ck—Knox Group. (From F. A. Diegel, 1985, Geological Society of America Southeastern Section Guidebook.) (b) Exposure of a small duplex in Lower Devonian limestone in a quarry at Fuera Bush, south of Albany, New York. (c) Relationships between different elements in the duplex. Dm—Manlius Formation. Dc—Coeymans Formation. Dk—Kalkberg Formation. [(b) and (c) courtesy of Stephen Marshak, University of Illinois–Urbana.] Limestone Cove inner window Stony Creek syncline SE NW Shady Valley sheet Pulaski fault system O Ck Cr Cs Cu Shady Valley sheet O Ck Cc Cr he C _he p Cb 0 (a) locks, breaking the footwall, and new imbricate faults form, ramp, and lock, allowing formation of the floor thrust and continued movement of the entire thrust complex. Duplex development is a fundamental property of foreland fold-thrust belts, and frequently results in arching the thrust sheet above the duplex as it is built by duplication of rocks beneath the sheet (Boyer and Elliott, 1982; Hatcher, 1991). Mitra (1986) concluded that duplex Cs 5 kilometers vertical and horizontal geometry is governed by a combination of ramp angle and height of the ramp, spacing between imbricates, and total displacement in the duplex system. In some imbricate thrusts, a roof thrust exists with only minor displacement, but in others the roof thrust is easily identified and has considerable displacement (Banks and Warburton, 1986; Morley, 1986). Antiformal stack duplexes result as the imbricate stack forms and rotates forward so that the Thrust Faults | 289 (b) Bend in section S N SSW Outcrop-scale duplex Dm Dc NNE Dk Dm Dc Dc Dm Dm Dm plex du Mini- Talus (c) RDH 8/18 Talus Person for scale 0 20 meters FIGURE 12–8 (continued) dip of imbricates in the duplex becomes nearly horizontal (Figures 12–7c and 12–8). Geiser (1989) recognized three categories of thrusts using fold geometry and deformation mechanisms: layer-parallel shortening, fracture, and fold thrusts. Geiser’s fracture thrusts are the same as Willis’s shear thrusts and Suppe’s fault-bend folds, and his fold thrusts are the same as Willis’s break thrusts and Suppe’s faultpropagation folds. Combinations are also possible. The layer- parallel shortening mechanism would account for only 15 to 25 percent strain, if it depended solely on pressure solution as the dominant strain mechanism in the thrust sheet. Over a thrust belt 100 km wide, however, this mechanism could produce 15 to 25 km of displacement (decreasing with distance from the direction of thrusting). Other layer-parallel shortening mechanisms, such as contraction faulting (see next section), may result locally in 50 to 60 percent shortening. Pressure solution has been well documented by Geiser and Engelder (1983) in the Appalachian Plateau in New York and by Alvarez et al. (1976) in the northern Apennines in Italy. 290 | Fractures and Faults Propagation and Termination of Thrusts A thrust fault moves until the energy that causes it to move is spent, or until something stops it from moving, and the remaining energy is transferred to another existing fault or propagates a new fault. A thrust belt rarely consists of a single thrust, and so there must be some reason that motion is transferred from one thrust to another or for the unbroken sequence to form a new thrust. Movement along a thrust may become difficult or diminish where the thrust passes over a ramp. Frictional resistance to movement is greater in the high-angle segment of the fault plane than along low-angle segments. If the fault geometry changes such that the force necessary to overcome the frictional resistance exceeds the strength of the footwall rocks, a new thrust may form and propagate through the footwall from an existing detachment. New thrusts may form at any level, depending on where the older thrust surface becomes locked and a suitable detachment is present for continued propagation of the thrust. This is also the duplex-forming mechanism described earlier. A thrust may ramp to a higher décollement because of stratigraphic pinch-out of the detachment unit, by facies changes within the detachment (reducing the amount of weak material), or by basement irregularities. Facies changes may also weaken the strong unit. Imbricate thrust faults project down dip until they join a larger fault. The line of intersection of two fault surfaces is a branch line (Figure 12–9). Imbricates have only one branch line, but a horse is terminated at each end by leading and trailing branch lines. Thrusts may terminate up dip in several ways. A thrust may intersect the surface as an emergent (sometimes e rosion) thrust (Figure 12–10). In that case, surficial materials may be caught up and overridden by the advancing thrust sheet. The amount of movement that occurs after the surface is reached depends on the available energy. Emergent thrusts, documented by De Paor and Anastasio (1987) in the Spanish Pyrenees, where unconformities—formed beneath debris eroded from the advancing thrust sheet—were deformed by the sheet. Smaller thrusts may terminate in the sedimentary section, either within a detachment or as a series of branching splays that distribute motion on the smaller faults (Figure 12–11). The opposite of an emergent thrust is a blind (hidden) thrust, in which displacement decreases upward within the sedimentary section; it never reaches the surface. An active blind thrust was responsible for the destructive 1994 Northridge earthquake in the Los A ngeles area (Figure 5E–1). Terminations of thrusts along strike sometimes yield information about subsurface and up-dip behavior. T' T C S B B' (a) S B'1 B'2 B (b) U X X' B B U (c) FIGURE 12–9 Branch lines. (a) Diverging splay S, which has a single tip line T and a map termination T', and one branch line B that intersects the erosion surface at B'. (b) Rejoining splay S with a single branch line B that intersects the map at two branch points B'1 and B'2. (c) Horse surrounded by fault surfaces. Two fault surfaces meet at a single closed branch line B with two cusps, U. Cross section within block illustrates half of horse cut along section X–X'. (Modified from S. E. Boyer and D. Elliott, AAPG Bulletin, v. 66, © 1982. Reprinted by permission of American As sociation of Petroleum Geologists.) A thrust may splay up dip or along strike and distribute movement among several smaller thrusts before terminating (Figures 12–11a and 12–11b). A single thrust or a group of splays may strike into the axial zones of anticlinal folds that plunge and die along strike away from the main thrust from which they were derived (Figure 12–11b). Folds and splays frequently strike at angles of 15° to 30° into the hanging wall of the thrust 291 | Thrust Faults Erosional debris from the advancing thrust sheet, soil, and other surficial deposits Tear fault k roc Bed Cross-section view (a) Bedrock A 0 (a) Map view (b) (d) 20 kilometers No displacement Maximum displacement 0 (1) 20 No displacement kilometers Map view (c) Tear fault Cross-section view (a) A B B' A A A' B A B' T Map view 0 Map view (b) (d) 20 kilometers No displacement Maximum displacement 0 (3) (c) 20 kilometers Map view 0 1 No displacement kilometers 2 T Cross-section view 0 (2) A' 20 kilometers FIGURE 12–11 Termination of thrusts. (a) Branching splays, which take up displacement up dip (cross section) or along strike. (b) Decreasing displacement and Elliott’s bow-and-arrow rule. Displacement decreases away from the approximate center of the thrust sheet (map view). (c) Along-strike splays into plunging anticlines. Main thrust splays into smaller thrusts, and then into plunging anticlines (map view). (d) Tear faults (map view with cross sections A–A' and B–B'). A—away from the observer; T— toward the observer. Lower Miocene Upper Eocene–Oligocene Lower–Middle Eocene Upper Cretaceous–Paleocene Triassic (b) FIGURE 12–10 (a) Emergent thrusts break the surface and involve surficial materials. Sometimes they break the erosion surface on land, while in others, the surface broken is an ocean-bottom surface. (b) Sequential development of an emergent fold-thrust system in the Pyrenees Mountains in northeastern Spain. As the thrust advances (1–2), erosional debris is shed into the adjacent foreland basin. (3) Active thrust has overridden its footwall syncline, shedding erosional debris into the adjacent foreland basin. (From K. R. McClay, J. A. Muñoz, and J. Poblet, 1999, Thrust tectonics 99, Pyrenees field trip guidebook: Egham, England, Geology Department, Royal Holloway School of Mines, University of London, 172 p.) sheet from the strike of the main fault, a result predicted by Andersonian mechanics. Thrust faults commonly break off and grind material along the fault surface. Pieces or blocks of material called horses, or slices, measuring up to several kilometers in maximum dimension, may be transported within the fault zone beneath a thrust sheet. A general rule applies: the age of the material composing horses is usually intermediate between the ages of the hanging-wall and footwall rocks (Figure 12–12). An exception occurs where the horse consists of crystalline basement. Horses may roll or slide along and, in the process, be folded and intensely fractured. As a result of the mode of formation and transport, these blocks are commonly made of 292 | Fractures and Faults FIGURE 12–12 Exposure of the Champlain thrust at Lone Rock Point on Lake Champlain near Burlington, Vermont. The gently dipping fault zone contains a horse of white Lower Ordovician Beekmantown Dolomite (right side of the photo) separating the hanging wall composed of gray Lower Cambrian Dunham Dolomite and footwall of black Middle Ordovician Iberville Shale. (RDH photo.) Dunham Dolomite Beekmantown Dolomite Iberville Shale H H Strong un it FIGURE 12–13 Formation of horses (H) in cross section. strong materials most frequently derived from the footwall, but horses derived from the hanging wall also exist. Less commonly, they are composite strong/weak materials, with strong dominating. Horses are completely surrounded by fault surfaces (Figure 12–13). A horse may also be thought of as a slice that remains an integral part of the thrust sheet and is not transported far from its point of origin, but many geologists use the terms “horse” and “slice” synonymously. Some thrusts terminate along strike and up dip by decreasing displacement until the fault terminates in bedding. The bow-and-arrow rule, formulated by Elliott (1976), stated that maximum displacement on a thrust is determined by a line perpendicular to the chord connecting the ends of the thrust sheet at the point of maximum distance from the chord (Figure 12–11c). Elliott’s rule works best if displacement is approximately symmetrical to the ends of the sheet and reaches a maximum in the center. A more realistic application of this principle is in log-log displacement-length plots, where mapped fault length is compared with best estimate of displacements (Fermor, 1999; Hatcher, 2004) (Figure 12–14). While Elliott’s bow-and-arrow rule may underestimate thrust displacement by as much as 50 percent, these plots provide better estimates, because they more precisely describe a nonlinear process. The ends of a thrust sheet may also terminate in strikeslip faults (tear faults), which at depth flatten to become part of the thrust sheet (Figure 12–11d, and the Jacksboro and Russell Fork faults in Figure 12E1–3a). Along-strike changes in detachment level of a thrust may also occur where the thrust is forced to ramp to a higher level—a lateral ramp. The timing of faulting in a foreland fold-thrust belt is commonly not the same everywhere. A normal-sequence (or in-sequence) thrust pattern describes faults that propagate outward from the internal parts of a mountain chain, such that faults closer to the hinterland slipped first and then deformation was translated to new faults farther out in the foreland (Figure 12–15). Sometimes a moving thrust sheet will lock or achieve a geometry that causes the hanging wall to break back of the leading edge, producing out-of-sequence thrusts with respect to the normal insideout geometry (Figure 12–15). | Thrust Faults 100 Displacement (km) Oldman River McConnell– Simpson Pass Livingstone Brazeau Meade McConnell– Crawford Absaroka Livingstone Moose Mtn Sulphur Mtn Bighorn-Nikanassin Highwood Darby Rundle Prospect 1 Sorge 10 4 5 (a) 1 2 4 3 5 6 (b) Turner Valley Burnt TimberLimestone 3 Hogsback Waterton 10 2 1 Bourgeau Paris–Willard (a) Interior of mountain chain Lewis-Eldorado 293 Mountain Park Jumping Pound Robb CoalbranchLovett Lookout Butte Pincher Creek 100 1000 Length (km) FIGURE 12–15 In-sequence (“normal”) (a) and out-of-sequence (b) thrusts. A normal sequence (1, oldest, through 5 or 6, youngest) involves progression of thrusts from one side of a foreland fold-thrust belt to another. Out-of-sequence thrusting (b) (thrust 4 in shaded square) formed by breaking through the hanging wall of thrusts (shaded square 3) that already had formed. 1000 Great Smoky Whiteoak Mtn Pulaski 100 Saltville Displacement (km) Holston Mtn Sequatchie Knoxville Pine Mtn Narrows Dumplin Valley Rocky Valley 10 St. Clair Cumberland Plateau Wildwood Dunham Ridge 1 Browns Mtn Murphrees Valley Horton 0.1 10 (b) Chestnut Ridge Deer Park Elkins Valley Glady 100 Length (km) 1000 FIGURE 12–14 (a) Log-log displacement-length plot for thrusts in the Alberta-British Columbia and Wyoming thrust belts. Names of Alberta Foothills thrusts and triangle zones are shaded light yellow. Canadian Rockies and Alberta Foothills thrusts are indicated with light blue circles; Wyoming-Utah-Idaho thrusts with orange circles. [Modified from P. Fermor, 1999, Geological Society of America Bulletin, v. 111. Additional data on Canadian Rockies thrusts from Price and Mountjoy (1970) and Price (1981).] (b) Similar plot for southern and central Appalachians thrusts. Cumberland and Allegheny Plateau thrusts have light brown shaded names, while others are Valley and Ridge thrusts. Thin, red dashed line corresponds to the heavy red line in (a). Note the similarity in slope and relationships between thrusts in the southern Alberta Rockies, and the southern and central Appalachians. The long-dashed blue line represents a best fit for several central Appalachian thrusts below the main line, while the purple dashed line appears to better fit a small group of large-displacement Valley and Ridge thrusts. (From Hatcher, R. D., Jr., 2004, Properties of thrusts and the upper bounds for the size of thrust sheets, in McClay, K. R., ed., Thrust tectonics and hydrocarbon systems: Tulsa, Oklahoma, American Association of Petroleum Geologists Memoir 82.) Features Produced by Erosion Thrust sheets characteristically have a large areal extent, and their fault surfaces commonly dip at low angles; also, many thrust sheets are folded during or after emplacement. This produces several important erosion-related features. Erosion may produce “holes” in a thrust sheet, exposing rocks in the footwall. Footwall rocks are thus completely surrounded by the hanging wall, producing a feature called a simple window, or fenster. A window commonly develops where a thrust sheet has been antiformally folded (domed), causing part of the sheet to have a higher elevation than adjacent parts (Figure 12–16a). A thrust sheet may undergo renewed movement during or after folding. An antiformal fold thus produced may prevent the entire thrust sheet from moving and lead to imbrication of the sheet near the crest of the antiform. Erosion may then expose a more complex window into the footwall rocks, but the window is opened along the trace of a fault and will appear to be partly closed because the elongate outcrop pattern parallels the fault trace (Figure 12–16a). Oriel (1950) first used the term eyelid window to describe this complex geometry in the North Carolina Blue Ridge. Many windows in overthrust terranes expose footwall duplexes (Figure 12–8a), suggesting an interactive relationship between the growth of duplexes and the arching of a thrust sheet during thrust emplacement (Boyer and Elliott, 1982; Hatcher, 1991). Many examples of isolated domes occur in large thrust sheets; breached windows that expose duplexes in their footwalls include the Grandfather Mountain and Mountain City windows in the southern Appalachians (Boyer and Elliott, 1982; Diegel, 1986) and the Assynt window in the northwestern Scottish Highlands (Elliott and Johnson, 1980). 294 | Fractures and Faults A' K (b) Chief Mountain W Klippe W EW W Roof thrust A Imbricate thrust Imbricate thrust A W u K Imbricate thrust Floor (Lewis) thrust A' EW (a) (c) FIGURE 12–16 (a) Erosional features along thrusts: W—simple window; EW—eyelid window; K—klippe. Windows and klippes may be used in estimating minimum amount of transport (u). Rocks of the thrust sheet are striped. Younger thrust shown by open teeth on hanging wall. (b) Chief Mountain, Montana, the top of which is a klippe in the Lewis thrust complex that transported Middle Proterozoic Belt Supergroup rocks over Upper Cretaceous sedimentary rocks. The Lewis thrust is located along the base of the mountain, beneath the massive Belt Supergroup carbonates. Boyer and Elliott (1982) concluded that the upper—nearly horizontal—boundary forms the roof of a duplex structure in the Belt Supergroup rocks. The inclined faults in the carbonates are imbricates in the duplex, so the floor is the Lewis thrust, and the roof thrust is the fault beneath the subhorizontal rocks in top of the mountain. (Bailey Willis, 1893, U.S. Geological Survey.) (c) Sketch of Chief Mountain by Willis (1902), modified by J. Dyson, reproduced in Nevin (1949), and slightly modified here. Some geologists use the term “window” to describe any erosionally exposed rock unit that is surrounded laterally by the unit above it. If the contact between the two is not a fault, but a stratigraphic contact or unconformity, the proper term is inlier, because the rocks are still in stratigraphic order, with the oldest on the bottom. In thrust-faulted regions, true windows involve younger rocks exposed by erosion through a faulted sheet of older rocks. Erosion also frequently isolates parts of a thrust sheet. Segmentation of a thrust sheet by erosion may leave a remnant called a klippe (Figures 12–16b and 12–16c). A klippe sometimes results from folding of the thrust sheet, where the preserved part remains in a synform, but erosional dissection of a nearly flat thrust sheet may also preserve parts of the sheet as klippen (plural of klippe). Klippen are erosional outliers of thrust sheets, but not all outliers are klippen. A large, isolated remnant of the hanging wall is called an allochthon, although the term is also used for a large single thrust sheet. The opposite is an autochthon—a mass of rock in its original site of formation. Windows and klippen are useful for estimating the minimum transport distance of a thrust sheet (Figure 12–16a). The minimum horizontal transport is the distance measured across strike from the outcrop trace of the thrust on the down-dip side of a window to the outcrop trace of the thrust on the up-dip side of a klippe, or leading edge of the sheet. This assumes the rocks in the window are younger than rocks in the klippe, that the thrust cuts stratigraphically upward, and that transport was across strike. Displacement is better measured on a map than on a cross section, because a cross section is more interpretative; sections based on modern digital seismic reflection data (Chapter 4) are usually more reliable. Thrust Faults ESSAY Thrust Jurassic clastic and carbonate rocks 295 Debate About Thrust Faults According to Willis (1923), the phenomenon of low-angle thrusting was first recognized in 1826 by Weiss near Dresden, Germany, where Paleozoic granite occurs above a horizontal fault contact with Cretaceous rocks. During the 1830s, Arnold Escher von der Linth, a Swiss geologist, first recognized thrust faults on the northwest side of the Aar massif in the Alps, and then in the 1840s was the first to correctly interpret the Glarus overthrust in Switzerland. He called these structures Überschiebung (German for “overpushing”). Shortly afterward, Safford (1856) recognized the Appalachian thrusts in Tennessee and visualized their geometry. In 1848 British geologist Roderick Impy Murchison examined the Glarus thrust and agreed with Escher’s conclusion, but later refused to agree with Nicol’s (1861) conclusion that thrust faults also exist in the Scottish Highlands (Bailey, 1935). This dispute became known as the “Highlands controversy” (e.g., Oldroyd, 1990). Charles Lapworth, representing Her Majesty’s Geological Survey, went to the Assynt District in the Northwest Scottish Highlands, where six weeks of study convinced him that Nicol was right and a large thrust fault, the Moine thrust, is the best interpretation of the structure (Figure 12–1). (He also recognized the importance of mylonite and coined the name.) Unfortunately, he fell mentally ill, believing the Moine thrust was still moving and threatening his cabin near the base of Knockan Crag, and became so disabled he never finished his work there. Other British geologists later sought to disprove the existence of Scottish thrusts by testing the Moine as a candidate structure in the Northwest Highlands near Loch Eribol and Assynt. Later in the nineteenth century, several members of Her Majesty’s Geological Survey, including B. N. Peach, J. Horne, C. T. Clough, and H. M. Cadell, Permian Verrucano redbeds | mapped the same region in an attempt to dispose of any notion of large-scale horizontally transported thin sheets of rock in the British Isles. Instead, in 1884 they published compelling evidence that at least 16 km of transport had occurred along the Moine thrust. The usefulness of their geologic maps of this region (Peach et al., 1888), including the Moine thrust (Figure 12–1), is likely to outlast the stone monument to their work that now stands on a low hill near Inchnadamph. The Assynt District has been remapped by modern British Geological Survey geologists and they have published a new geologic map of the Assynt District (Krabbendam et al., 2007). As shown by studies of the Glarus (Figure 12E1–1) and Moine thrusts, thrust faults have long provoked controversy. First, the very existence of horizontal sheets of rock that had been transported great distances was disputed; later, basement involvement in foreland thrusts was debated. (Basement consists of crystalline rock that is the product of an earlier orogenic cycle and underlies a less deformed and less metamorphosed cover.) During the 1950s and 1960s, geologists focused on whether or not the motive force for thrusting is gravity or compressional stresses, and then more recently on thrust mechanics and modeling dynamics of thrust and other faults using computers. Great strides toward understanding the geometry and mechanics of thrust faults were made during the 1970s and 1980s, but even recent mechanical models leave room for further improvement of our understanding of thrust mechanics. Thus, controversy and fascination continue with these structures. Thrusts have historically been debated as either thinskinned, with no basement involved, or thick-skinned, with basement involved (Figure 12E1–2). Because basement is not FIGURE 12E1–1 Sketch of the nearly horizontal Glarus thrust near Glarus, Switzerland. The hanging wall of the fault consists of Permian Verrucano redbeds that were thrust over Jurassic clastic and carbonate rocks. From E. B. Bailey (1935). 296 | Fractures and Faults ESSAY k k cr k cr k mPz cr k mPz Saltville fault Whiteoak Mountain fault mPz m uPz k s cr Cs cr p=b Cb 10 SE Cs k k 0 k mPz uPz mPz cr cr Great Smoky fault uPz mPz Rockwood fault Sequatchie Valley fault NW continued k cr k k p=b Cb kilometers kilometers p=b Cb mPz uPz mPz k mPz k k c k m|z mP 0 c 5 c k c s s p=b Cb kilometers kilometers Saltville fault Great Smoky fault uPz Whiteoak Mountain fault uPz Rockwood fault NW Sequatchie Valley fault (a) c k mPz c k c c c c c s s s s c s s s k c s c c s SE s s p=b Cb (b) NW mPz cr cr 0 0 k 5 5 kilometers kilometers p=b Cb Helena fault uPz k cr p=b Cb SE NE Jones Valley fault Opossum Valley fault NW p Cs p=b Cb cr mPz k cr SE mPz uPz uPz cr cr cr cr k Tchi-Q Thua, Tarc basement p=b Cb (c) 0 10 kilometers (d) FIGURE 12E1–2 (a) Thin-skinned (no basement) thrusting versus (b) thick-skinned, basement-involved thrusting along nearly the same cross section through the Appalachians in Tennessee and western North Carolina. [(a) From a cross section by RDH; (b) from John Rodgers, 1953, Kentucky Geological Survey Series 9, Special Publication 1.] (c) Cross section from the Appalachian Valley and Ridge in Alabama showing control of thin-skinned structures by older faults in the basement. (From W. A. Thomas, 1986, Virginia Tech Geological Sciences Memoir 3.) uPz—Upper Paleozoic rocks. mPz—Middle Paleozoic rocks. k—Knox Group carbonate rocks (Cambrian-Ordovician). c—Cambrian shale and carbonate. cr—Conasauga Group and Rome Formation (Cambrian). s—Shady Dolomite and Chilhowee Group rocks. p –Cs—Precambrian sedimentary rocks. p –Cb—Precambrian basement rocks. (d) Thick-skinned, basement-involved thrust from the Sierra Pampeanas, Argentina. The structural style here is very similar to that in the Colorado Rockies, and is not in a classic foreland foldthrust belt setting. (From P. E. Garcia and G. H. Davis, 2004, American Association of Petroleum Geologists Bulletin, v. 88.) commonly observed at the surface in foreland fold-thrust belts, many geologists came to believe that basement was also not involved in the subsurface. The thin-skin concept was first originated with Buxtorf (1916), working in the Jura Mountains in Switzerland and France. Rich (1934) outlined most of the principles of thin-skinned deformation during his classic study of the Pine Mountain block in the southern Appalachians (Figure 1 2E1–3a). Even so, R odgers (1949, 1964) Y X Pine M o untain th ru st Jacksoboro fault Chestn ut Ridge 10 Hu n ter anticlin e Vall ey Duffield Powell thrust Va lley Clinchport thrust 20 N anticline ult fa 0 Ewing Y' t Kingston thrus X' VA thrust Vall ey KY rk Wallen TN anticli ne Middlesboro syncline Fo Powell Chattanooga thrust Va lley VA Z R usse ll KY Ro ck Fac y fau e lt Pineville 297 | Thrust Faults Z' kilometers (a) KY TN KY VA Pineville Ewing VA TN Duffield (b) NW X 2,000 X' Pine Mountain thrust Om M-D – 8,000 – 12,000 Pine Mountain thrust Y 2,000 Feet WV T M-D – 4,000 Omu-S – 8,000 O Ck Crc – 12,000 pC BT II Middlesboro syncline Z Feet – 4,000 – 8,000 – 12,000 – 16,000 BT I PMT Powell Valley anticline Z' Pine Mountain thrust HVT P M-D Omu-S O Ck Crc PM T pC 0 (c) T Y' Borehole P Sea level CL Powell Valley anticline Middlesboro syncline Sea level u-S WVT PMT Omu-S O Ck Crc pC – 4,000 2,000 SE P Sea level Feet Powell Valley anticline Middlesboro syncline 5 10 kilometers FIGURE 12E1–3 (a) Attributes of the Pine Mountain thrust sheet, Tennessee, Virginia, and Kentucky. The three lines X–X’, Y– Y’, and Z–Z’ locate the sections in (c). (b) Digital elevation model for the map area shown in (a). Note the clear correlation of structures with topography. (c) Sections through the Pine Mountain block showing the fault-bend fold character of the Pine Mountain thrust (PMT). WVT—Wallen Valley thrust. CLT—Clinchport thrust. P—Pennsylvanian rocks. M-D—Mississippian and Devonian rocks. Omu-S—Middle to Upper Ordovician and Silurian rocks. O –Ck—Cambro-Ordovician (Knox Group) carbonate rocks. –Crc—Cambrian clastic rocks. p –C—Precambrian basement rocks. O –Ck, Omu-S, and P are strong rock units; –Crc and M-D are weak units. HVT—Hunter Valley thrust. BT I and BT II in the middle cross section are Bales thrusts I and II. [(a) and (c) from S. Mitra, 1988, Geological Society of America Bulletin, v. 100.] 298 ESSAY | Fractures and Faults continued and Cooper (1964) took opposing sides in a renewal of the thin- vs. thick-skinned debate in the Appalachians. Ironically, the debate was resolved not in the Appalachians but in the Canadian Rockies where petroleum company geologists and geophysicists Bally et al. (1966) employed surface geology, seismic reflection, and drilling data to demonstrate that basement is not involved (Hatcher, 2007). Mitra (1988) later used seismic reflection and existing drill data to show that the subsurface Pine Mountain fault was more complex than Rich had thought (Figure 12E1–3c), but reconfirmed Rich’s fundamental conclusions about the thin-skinned nature of the Pine Mountain block. Seismic reflection, drilling, and surface geologic data in fold-thrust belts throughout the world have clearly demonstrated that thin-skinned deformation is the dominant style. Today we know that thick-skinned thrusts (as originally defined) exist, and that we still need to better understand how all thrusts form (Figures 12E1–2b and 12E1–2d). Gravity and tectonically generated compressional stress are two possible alternative primary forces for producing foreland fold-thrust belts. This produced another debate among structural geologists that raged into the 1970s. Hubbert and Rubey (1959) argued that it would be very difficult to push a thin sheet of rock very far horizontally without breaking it up, because its internal strength is too low; they reasoned that the magnitude of shear stress necessary to move a rock mass would be greatly reduced if the base of the mass were under high pore-fluid pressure (Chapter 11). They maintained, however, that body forces—gravity—were necessary to move a thrust sheet, making gravity an appealing mechanism. Milici (1975) pointed out that the pattern of overlap suggested by outcrop traces of thrust faults in part of the Appalachian foreland thrust belt yields a crosscutting pattern in which the oldest thrusts formed on the outer fringe of the belt, and successively younger thrusts form deeper in the core of the orogen (Figure 12E1–4a). Gravity would be required to produce such a pattern. The Bergamasc Alps of northern Italy were once considered a classic example of “gravitational gliding” tectonics (de Sitter, 1949). De Sitter concluded that Paleozoic basement was uplifted during the Alpine orogenies, and the cover slid (glided) gravitationally southward off the basement high along weak evaporites in the Triassic carbonates (Figure 12E1–4b). Laubscher (1990), Schumacher (1990), and Schönborn (1992a, 1992b), have shown that basement is indeed involved in deformation of the cover here and basement probably drove cover deformation south of the moving basement blocks (Figure 12E1–4c). This clearly makes primary compression the favored mechanism. Model experiments by Ramberg (1967) (see Figure 1–6) and field work, including studies of accretionary wedges in subduction zones (Stockmal, 1983; Dahlen et al., 1984), demonstrate that most thrust belts result from outward (continentward) propagation of thrusts from the core of the orogen. Similar map patterns exist in many foreland foldthrust belts where it can be shown independently that the deformation plan is inside out. Independent evidence has also shown that the oldest thrusts—not the youngest—are in the interior of the orogen and that deformation there generally occurred long before deformation in the foreland. Such evidence led Hans Stille in the 1930s to suggest that an orogen, including the foreland fold-thrust belt, is deformed from the inside out, concluding that compression is the primary force that produced deformation. Another objection to the gravity mechanism is the basement dip direction beneath the foreland. Nowhere in the world is there a foreland fold-thrust belt where the basement surface slopes away from the interior of an orogen: all are inclined toward the interior. The original wedge shape of the foreland wedge also argues against a reverse slope. It is difficult to envisage gravity pushing thrusts (or water) up-slope. Price (1974) attempted to resolve the problem with his alternative mechanism of gravitational spreading, based partly on earlier observations and studies of models by Walter Bucher and Ramberg. Price suggested that as the core of an orogen is shortened and buoyantly uplifted during compression, metamorphism, and plutonism, the orogen compensates for uplift by flowing laterally under the influence of gravity, as a large ice sheet may push lobes uphill (Price, 1974; Elliott, 1976). Lateral spreading provides stress that deforms the foreland and pushes thrusts up the otherwise hinterland-dipping basement surface, but the amount of uplift actually needed to produce the observed deformation greatly exceeds most estimates. For this reason alone, Price’s mechanism seems unworkable. Add the requirement of an internal zone of stretching and attenuation of structures (none have been discovered except in very unique systems, such as the Gulf of Mexico or the Thrust Faults Older r er Y ung ge un Yo r ge oun r Olde 299 Yo Older r de Ol | Younger (a) N Mid dle E. Bergamasc Alps Low er T S Tria ssi rias c Camino thrust sic Middle Triassic Late Paleozoic basement Permian Lower Triassic gypsiferous dol. and marl (b) Cretaceous Valtorta fault 0 5 kilometers No vertical exaggeration 1 1' 1 sea level Jurassic (Maiolica) Rhaetian Upper Triassic Carnian Middle Triassic Lower Triassic Permian and older Basement 2A 2 2B 3 (c) Thrust system 1 (Orobic thrust) Thrust system 2 (Coltignone thrust) Thrust system 3 (Lecco thrust) FIGURE 12E1–4 (a) Milici’s geometric relationships suggesting development of thrusts by a break-back mechanism, based on the map pattern (mostly) of hanging-wall (southeast) truncations. (From R. C. Milici, 1975, Geological Society of America Bulletin, v. 86.) (b) Thrusts in the southern Alps of northern Italy interpreted as being the product of gravity forces. (From L. U. de Sitter, Structural Geology, 1964 © McGraw-Hill, Inc., p. 243.) (c) Cross section through the southern Alps showing basement (x or + pattern) involvement with cover deformation. (From G. Schönborn, Alpine Tectonics and Kinematic Models of the Central Southern Alps, Memorie Di Scienze Geologiche, 1992a, v. 44, p. 229–393.) West African continental margin that involve extensional movement down a slope with thrusting at the toe; see Chapter 14), and gravitational spreading becomes difficult to accept as a primary mechanism of foreland deformation. Price (1981), recognizing the problem, recommended abandoning the gravitational spreading concept. The deformed wedge, a weak basal layer, and the overall geometry of foreland fold-thrust belts all suggest that the compressional model for a wedge is correct. Mechanical models involving compression (see later)—despite initial objections to compression as the primary mechanism of foreland deformation—best explain how foreland fold-thrusts form. 300 | ESSAY Fractures and Faults continued References Cited Mitra, S., 1988, Three-dimensional geometry and kinematic evolution of the Bailey, E. B., 1935, Tectonic essays, mainly Alpine: Oxford, England, Clarendon Pine Mountain thrust system, southern Appalachians: Geological Society of Press, 191 p. America Bulletin, v. 100, p. 72–95. Bally, A. W., Gordy, P. L., and Stewart, G. A., 1966, Structure, seismic data, and Nicol, J., 1861, On the structure of the North-Western Highlands and the orogenic evolution of the southern Canadian Rockies: Bulletin of Canadian relations of the gneiss, red sandstone, and quartzite of Sutherland and Petroleum Geology, v. 14, p. 337–381. Ross-Shire: Geological Society of London Quarterly Journal, v. 17, p. 85–113. Buxtorf, A., 1916, Prognosen and Befunde beim Hauensteinbasis- und Oldroyd, D. R., 1990, The Highlands controversy: Constructing geologi- Grenchenburg-tunnel und die Bedeutung der letzteren für die Geologie cal knowledge through fieldwork in nineteenth-century Britain: Chicago, des Juragebirges: Naturforschende Gesellschaft Basel Verhandlungen, v. 27, University of Chicago Press, 438 p. p. 184–254. Peach, B. N., Horne, J., Clough, C. T., Cadell, H. M., and Dinhaus, C. H., 1888 Cooper, B. N., 1964, Relations of stratigraphy to structure in the south- (reprinted 1923), Assynt District: Geological Survey of Great Britain, scale ern Appalachians, in Lowry, W. D., ed., Tectonics of the southern 1:63,360. Appalachians: Department of Geological Sciences, Virginia Tech, Memoir 1, Ramberg, H., 1967, Gravity, deformation and the Earth’s crust as studied by p. 81–114. centrifuged models: New York, Academic Press, 241 p. Dahlen, F. A., Suppe, J., and Davis, D., 1984, Mechanics of fold-and-thrust Rich, J. L., 1934, Mechanics of low-angle overthrust faulting as illustrated by belts and accretionary wedges: Cohesive Coulomb theory: Journal of Geo- Cumberland thrust block, Virginia, Kentucky and Tennessee: American As- physical Research, v. 89, p. 10,087–10,101. sociation of Petroleum Geologists Bulletin, v. 18, p. 1584–1596. de Sitter, L. U., 1949, Le style structural Nord-Pyrénéen dans les Alpes Rodgers, J., 1949, Evolution of thought on structure of middle and south- Bergamasques: Société Géologique de France Bulletin, v. 19, p. 617–621. ern Appalachians: American Association of Petroleum Geologists, v. 33, de Sitter, L. U., 1964, Structural geology: McGraw-Hill Inc., p. 243. p. 1643–1654. García, P. E., and Davis, G. H., 2004, Evidence and mechanisms for fold- Rodgers, J., 1953, The folds and faults of the Appalachian Valley and Ridge ing of granite, Sierra de Hualfín basement-cored uplift, northwest Province: Kentucky Geological Survey Special Publication 1, p. 150–166. Argentina: American Association of Petroleum Geologists Bulletin, v. 88, Rodgers, J., 1964, Basement and no-basement hypotheses in the Jura and p. 1255–1276. the Appalachian Valley and Ridge, in Lowry, W. D., ed., Tectonics of the Hatcher, R. D., Jr., 2007, Confirmation of thin-skinned thrust faulting southern Appalachians: Virginia Polytechnic Institute Department of Geo- in foreland fold-thrust belts and impact on hydrocarbon exploration: logical Sciences Memoir 1, p. 71–80. Bally, Gordy, and Stewart, Bulletin of Canadian Petroleum Geology, 1966: Safford, J. M., 1856, A geological reconnaissance of the state of Tennessee: American Association of Petroleum Geologists Search and Discovery, Nashville, Mercer, 164 p. http://www.searchanddiscovery.com/documents/2007/07038hatcher/ Schönborn, G., 1992a, Alpine tectonics and kinematic models of the central index.htm. Southern Alps: Memorie Di Scienze Geologiche, v. XLIV, p. 229–393. Hubbert, M. K., and Rubey, W. W., 1959, Role of fluid pressure in mechanics Schönborn, G., 1992b, Kinematics of a transverse zone in the Southern of overthrust faulting: Part 1. Mechanics of fluid-filled porous solids and its Alps, Italy, in McClay, K., ed., Thrust tectonics: London, Chapman and Hall, application to overthrust faulting: Geological Society of America Bulletin, p. 299–310. v. 70, p. 115–166. Schumacher, M. E., 1990, Alpine basement thrusts in the eastern Seenge- Krabbendam, M., Goodenough, K. M., Leslie, A. G., Key, R. M., Loughlin, S. C., birge, Southern Alps (Italy/Switzerland): Eclogae Geologicae Helvetiae, v. 83, and Pickett, E. A., 2007, Assynt, Scotland, special sheet, bedrock: Keyworth, p. 645–663. Nottingham, England, 1:50,000 geology series. Stockmal, G. S., 1983, Modeling of large-scale accretionary wedge deforma- Laubscher, H. P., 1990, The problem of the deep structure of the Southern tion: Journal of Geophysical Research, v. 88, p. 8271–8288. Alps: 3-D material balance considerations and regional consequences: Tec- Thomas, W. A., 1986, A Paleozoic synsedimentary structure in the Appala- tonophysics, v. 176, p. 103–121. chian fold-thrust belt in Alabama, in McDowell, R. C., and Glover, L., III, eds., Milici, R. C., 1975, Structural patterns in the southern Appalachians: Evidence The Lowry volume: Studies in Appalachian geology: Virginia Tech Depart- for a gravity slide mechanism for Alleghanian deformation: Geological Soci- ment of Geological Sciences Memoir 3, p. 1–12. ety of America Bulletin, v. 86, p. 1316–1320. Willis, B., 1923, Geologic structures: New York, McGraw-Hill Book Co., 295 p. Thrust Faults Crystalline Thrusts Crystalline thrusts involve transport of metamorphic or igneous rocks, or both, as part or all of a thrust sheet (Figures 12–17 and 12–18; Table 12–1). They have been known for many decades in the Alps, the Appalachians, the Scandinavian and British Caledonides, and other orogens. Geologists once thought that their propagation and motion involved a process totally different from those producing thin-skinned foreland thrusts in a sedimentary sequence, but many attributes of thin-skinned thrusts also occur in crystalline thrust sheets. That they are low-angle thrusts indicates an important similarity to thin-skinned thrusts, but how does a subhorizontal thrust surface propagate through a crystalline mass so that part of the mass becomes separated and moves as part of the thrust sheet? There must be important differences, however, in view of the different material properties of sedimentary and crystalline rocks. After studying the Moine thrust zone in Scotland, Elliott and Johnson (1980) concluded that thrusts follow weakness zones in crystalline rock, as they do in a sedimentary section. Hatcher and Williams (1986) 301 came to a similar conclusion about propagation of thrusts in crystalline rocks and also observed that their shared properties with thin-skinned thrusts lead to a general rule of crystalline thrusts: the largest crystalline thrust sheet in an orogen is always larger than the largest foreland thrust. The rule no doubt partly reflects the greater inherent strength of crystalline thrust sheets (Hatcher, 2004). The zone of weakness along which detachment occurs could be an appropriately oriented mechanical weakness, such as a preexisting fault or a strong foliation, but more likely it is the ductile-brittle transition in the large composite sheets discussed later. Crystalline thrusts may form as large slabs wherein materials appear to exhibit brittle to semibrittle behavior. They may also form during ductile folding where large crystalline isoclinal recumbent folds (fold nappes) are produced. Hatcher and Hooper (1992) called the large slab-type thrusts Type C (for composite) crystalline sheets (Figure 12–17), and those related to ductile folding Type F (for fold-related) crystalline sheets (Figure 12–17). These form because continued transport attenuates the overturned limb between an antiform and synform, finally producing a ductile thrust. Fold nappe (Type F) Transition from foreland fold-thrust belt Ophiolite Basement horse Cross section Kårmøy Bay of Islands Semail Troodos Purcell Holston-Iron Mountain Winters Pass, Cabin (a) | Sgurr Beag Six Mile Pennine Alps (b) (c) Map view Laramide uplift Composite (Type C) (crystalline slab) (d) Wind River Sierras Pampeanas Blue Ridge-Piedmont Austroalpine Yukon-Tanana (e) FIGURE 12–17 Varieties of crystalline thrusts. (a) Basement chip at the base of the sedimentary section, that commonly occurs in the transition between a foreland fold-thrust belt and the interior of a mountain chain. (b) Ophiolite, a section of sediment, ocean crust, and mantle rocks ideally composed of sedimentary rocks, pillow basalt, sheeted dikes, cumulate gabbro, cumulate ultramafic rocks, and peri dotite. The petrologic Moho separates the cumulate gabbro from cumulate ultramafic rocks. (c) Type F sheets result from plastic folding and heterogeneous deformation and thus have lobate outcrop patterns in map view. (d) Laramide (basement) uplift. (e) Type C sheets are produced by detachment of a strong, largely brittle slab along the ductile-brittle transition as a product of continent-continent, terrane, or arc-continent collision. (From R. D. Hatcher, Jr., and R. T. Williams, Geological Society of America Bulletin, v. 97, 1986.) 302 | Fractures and Faults km 5 Appenzell St. Gallen N (a) PLIOCENE LAND SURFACE (b) Cd Pz Cd d -C Cv Cdd C 0 SILVRETTA (c) African basement African basement Pz Pz Cd Cd Cd Cd Cd Cd Cd Pz Cd Cd Pz Cd Cd Cd Nm ? Nm Cd Cd Cd Cd AAR MASSIF –10 Sch Sch Cd African basement NORTH ALPINE BLOCK Ru 6°E Cd- TAVETSCH No vertical exaggeration 9°E 12°E 48°N 48°N Zürich BASEMENT TERTIARY INTRUSIVES MESOZOIC No Alpine penetrative deformation Bergell (granodiotite & tonalite) Helvetic/In Heterogeneous penetrative Alpine overprinting Novate (granite) Ultrahelvet Verrucano (Permocarboniferous metasedimentary and metavolcanic rocks related to rifting of Pangea and opening of the Tethys ocean) Austroalpi OPHIOLITES ±Coherent complexes Ophiolitic mélange Milan 45°N ° 0 9°E 9°E Localities (present day) 100 kilometers 45°N 45°N Stratigraphic contact Tectonic contact Intrusive contact Axial traces 12°E FIGURE 12–18 Cross section through part of the Swiss Alps showing foreland fold-thrust belt structure in the Molasse Basin (a) and Helvetic Alps (b) to the north and the involvement of basement in the structure farther into the mountain chain. Note that the Type C Silvretta nappe (thrust sheet) (c) in the center of the section is composed of African basement (same as at the south end of the section). Several named Type F thrust sheets (nappes) in the deeper parts of the section (Aar and Gothard Massifs, and Suretta, Tambo, Adula, and Simano nappes) (d) involve European basement and are part of the Pennine Alps. The suture (Insubric zone) between African and European crust is located at (e). (From A. G. Milnes and O. A. Pfiffner, 1980, Tectonic evolution of the central Alps: Eclogae Geologicae Helvetiae, v. 73.) TABLE 12–1 Types and Properties of Crystalline Thrust Sheets NAME S LUCOMAN GOTTHARD PLACE OF EMPLACEMENT IN MOUNTAIN CHAIN T-P CONDITIONS OF FORMATION T-P CONDITIONS OF EMPLACEMENT Thin-skinned thrusts transporting basement Inner foreland/outer metamorphic core Low Low (greenschist or below) Ophiolites Inner edge of foreland, metamorphic core, accreted terranes Low to moderate; may be high in fault zone Low; may be moderate T at base of sheet Type F (“Fold nappes”) Metamorphic core Low to high, depending on rheology; may form at low P-T in weak rocks, e.g., salt and ice Low to high Basement uplifts Foreland; edge of craton Low; faults initiated brittle in upper crust, ductile in lower crust Low Type C (Composite sheets) Metamorphic core; may involve inner foreland after emplacement of sheet Moderate to high low in fault zone, higher along initial base Moderate to low African basement (d) ? Nm Nm ? Nm Sch Sch Sc Fe Fe Av Av Sch Nm Av Nm Fe ? SURETTA Mx ? Cd ? Cd ?Nm Pa Mx SOUTH ALPINE BLOCK To –10 ADULA Ru Cd- TAVETSCH ADULA TAMBO ? Fe Cr ? ? Cd African basement km 5 0 NOVATE Fe ? S ? Fe Fe Fe h African basement (e) BERGELL Sch 303 Como Chiavenna African basement Andeer TTA (c) F | Thrust Faults Tonale Line SIMANO LUCOMANGO GOTTHARD Milnes & Pfiffner, 1980 Digital drafting by A. L. Wunderlich, 2008 NTRUSIVES MESOZOIC COVER Pennine TERTIARY COVER odiotite & tonalite) Helvetic/Infrahelvetic Briançonnais (Schams) Molasse te) Ultrahelvetic Briançonnais (Falknis/Sulzfluh) Helvetic Flysch Austroalpine/Southern Alps Suretta Trias Pennine Flysch (in part u. Cret.) Bündnerschiefer plexes Bündnerschiefer with intercalated mafic/ultramafic rocks nge FIGURE 12–18 (continued) Tectonic contact Axial traces ESSAY Gravity Model Foldbelt If all of the mechanical elements are present, an ideal foldthrust system can form on a small scale under the influence of gravity. In December 1974, RDH observed such a foldthrust belt alongside a frozen, moss-covered logging road in the North Carolina Blue Ridge (Figure 12E2–1). The soil beneath the thin moss was water-saturated and had frozen overnight. As it froze, it expanded, forming needle ice that lifted the moss layer, increasing the slope angle and forming a detachment between the more rigid moss layer above and the more rigid (drier) soil below. The surface layer moved down the slope above the detachment under the influence of gravity, perhaps lubricated by a film of water that had not yet frozen. The sliding mass developed thrusts, drag structures, faultpropagation folds, transfer zones, and tear faults as it moved downslope above the detachment (Figure 12E2–1c). Both folds and thrusts could be traced to termination points, with many terminations overlapping the terminal zones of other folds and thrusts. As the sheet moved, it began to fragment, but mostly remained intact. The only motive force that created the mossy fold-thrust system was gravity—a phenomenon easily and frequently observed—and, until the 1980s, gravity was the mechanism commonly invoked to explain most foreland fold-thrust belts in mountain chains. Hansen (1971) described a similar gravity-driven, small-scale, multiple-fold system in partly frozen surficial materials (solifluction lobes) in south-central Norway. Large-scale gravity-related thrusts have long been recognized along continental margins by oil companies exploring for hydrocarbons, for example, the Perdido and Mississippi fan fold-thrust belts formed in the Gulf of Mexico at the toe of the basinward-moving Mississippi Delta sediment mass (Figure 14–13). Compare the gravity-driven model described in Figure 12E2–1 with the small thrust in northern Italy at a similar scale in Figure 12E2–2. This fault formed in limestone at a time when the rock was strong enough to fracture and form a drag fold along the leading edge of the sheet as it moved. The displacement on this thrust sheet varies along it, indicated by the change in strike of the drag fold and the 304 ESSAY | Fractures and Faults continued (a) (a) Needle ice Knife Undeformed area (b) (c) FIGURE 12E2–1 Small-scale, fold-thrust system developed on a slope covered by a thin layer of moss that froze; the moss detached, moved downslope under the influence of gravity, and produced thrusts, fault-propagation folds, tear faults, and other features characteristic of a fold-thrust belt. (a) View of needle-ice-covered upper slopes from which a layer of moss has detached and slid downslope. (b) Close-up of the detached moss layers showing the variety of structures developed. (RDH photos.) (c) Sketch of structures in (b). Tear faults Thrust Faults | 305 Horse (?) Transfer zones Hammer Imbricate thrusts (a) (b) FIGURE 12E2–2 (a) Mesoscopic-scale thrust sheet in Lower Triassic Raibler limestone and shale between Monte Pora and Clusone, in the Italian Alps. Note the drag fold along the leading edge of the sheet, the decreasing displacement downslope along the trace of the fault, and the internal fractures (tear faults or transfer zones) that compensate for additional variations in displacement within the internal parts of the sheet. (b) Sketch of relationships shown in (a). (Locality courtesy of Gregor Schönborn, Chevron Corporation. RDH photo.) fault near the lower end and the internal dismemberment of the sheet by tear faults (fractures) oriented perpendicular to the fault plane and the fault trace. Could this thrust also have formed by gravity? Or, is it more likely that, because the large thrust sheets in this region ultimately become involved in basement deformation (see Figures 12–3b and 3c; Schönborn, 1992), the mesoscopic thrust here may be Cross-Section Construction and the Room Problem The construction of accurate cross sections in thrust belts is of paramount importance, because properly locating structural traps (both laterally and at depth) is vital to the petroleum industry. Seismic reflection data (Chapter 4), particularly the large amount of data produced in exploration for hydrocarbons, have greatly clarified our another product of the compressional regime that formed this part of the Alps? References Cited Hansen, E., 1971, Strain facies: New York, Springer-Verlag, 207 p. Schönborn, G., 1992, Alpine tectonics and kinematic models of the central Southern Alps: Memorie Di Scienze Geologiche, v. 144, p. 229–393. view of the subsurface geometry of thrusts, provided more precise measurement of depths to basement, and confirmed the thin-skinned concept for deformation of foreland areas. Seismic reflection data from the 1970s and 1980s COCORP (Consortium for Continental R eflection Profiling) Project helped to confirm existence of large crystalline thrusts in the Appalachians and regional listric normal faults through much of the upper crust in the Basin and Range in Utah (Allmendinger et al., 1983; Cook et al., 1983). Fractures and Faults be partly solved by area (instead of line) balancing. Understandably, deformation out of the plane of the section requires construction of sections in several directions— a form of three-dimensional analysis. Strongly curved segments of orogens, such as the Ligurian Alps in Italy, are impossible to balance, except by employing three- dimensional balancing techniques. Laubscher not only pioneered the rigorous use of two-dimensional balancing, but also developed the technique of three-dimensional balancing and applied this to crustal balancing of the Alps (Laubscher, 1983, 1988; Laubscher et al., 1992). Accurate coupling of surface and subsurface data in cross-section analysis aids reconstructions that enhance our ability to formulate and improve mechanical models. Note that in this kind of analysis the component of movement parallel to strike ultimately prevents balancing sections if the sections cross into the metamorphic core. Another problem with balancing sections in complexly deformed rocks lies in estimating the amount of internal strain within rock units (Woodward et al., 1986). A poor estimate may prevent balancing a section otherwise correctly drawn. Students constructing and restoring their first cross sections in foreland fold-thrust belts commonly end up 1 2 2 4 3 6 4 8 (a) 0 1 Two-way travel time (s) FIGURE 12–19 (a) Seismic reflection profile of snake-head structure from the Appalachians buried beneath the Coastal Plain of Alabama. (b) Crosssection interpretation of the structure in the profile. Two-way travel time (s) Seismic reflection data are essential when constructing palinspastic (balanced or retrodeformed) cross sections through brittlely (mostly nonpenetratively) deformed thrust-faulted terranes (Figure 12–19). Although several geologists attempted to palinspastically restore structural sections (e.g., Hayes, 1891), cross-section balancing, originally invented by Laubscher (1962) and expanded upon by Dahlstrom (1969), has today become an iterative process that can be done with a computer. An oft-quoted rule is that “if a cross section will not balance, it cannot be correct; if it does balance, the section may be correct.” Balancing may be accomplished by measuring the lengths of deformed lines, and using these line lengths to restore the section to an undeformed condition (Figures 12–20 and 12–21; Woodward et al., 1985). If the section can be retrodeformed and reconstructed to an undeformed condition, the interpretation may be correct. Balancing by areas (thickness of rock units times length) is also possible by taking the areas of units in the section and restoring them to an undeformed condition. Major problems arise with construction and balancing of any section if internal deformation occurs within rock units, or if strike- or oblique-slip deformation has occurred out of the plane of the section. The problem of internal deformation may Depth (km) | E k Sna D ucture ad str e-he 3 F GG F 2 E D C C 4 B A B B A 4 (b) E G F 2 Angular unconformity Younger sedimentary rocks Older rift faults Apparent anticline produced by velocity anomaly in geophysical data 6 8 Depth (km) 306 | Thrust Faults 307 FIGURE 12–20 Retrodeforming a ypothetical block using the technique h of line (or bed-length) balancing. (After C. D. A. Dahlstrom, 1969, Canadian Journal of Earth Sciences, v. 6.) Deformed l0 ‒ Δl l0 l0 ‒ Δl Undeformed Deformed Folds form above detachment surface SW NE Mt. Crandell T MC T MC LR K CT M sea level T Lewis thrust sea level 0 Deformed length 1 2 kilometers vertical and horizontal Retodeformed length MCT Datum LRT MCT Datum Lewis thrust FIGURE 12–21 Section through part of the Canadian Rockies (above) and a restored (retrodeformed) version (below). The light blue unit is a strong unit. MCT—Mt. Crandell thrust. LRT—Livingston Range thrust. K—Cretaceous. (From S. E. Boyer and D. Elliott, AAPG Bulletin, v. 66, © 1982. Reprinted by permission of American Association of Petroleum Geologists.) with unfilled voids or overlapping rock units in their sections. This may initially suggest not enough rock or too much space (or vice versa) is present—a statement of the room problem in structural geology and tectonics. Usually, the problem lies in the skills of the person constructing the section, as large voids do not exist in the crust at depths of several kilometers, where most structures form. Many thrust faults form in regions where the local deformational style is governed by slip of layers past each other—flexural slip—(Chapter 15) and where ideally there is no ductile flow of material into voids, either potential or real. In a deformational realm dominated by horizontal compression, there should be no void space larger than pores or small fractures even in rocks being brittlely deformed. Thrusts may also form in the cores of brittle (flexuralslip buckle) folds—generally, anticlines—as the folds tighten and a room problem arises in the more tightly folded inner layers (Figure 15–25). A single thrust fault may 308 | Fractures and Faults propagate, tighter folds may form, or two or more thrusts may dip in the same directions as the limbs of the fold and opposite each other (Figure 12–22b). The last comprise a triangle zone or structure. Triangle zones commonly form in the outer or upper parts of the foreland fold-thrust belt where the overburden is relatively thin, but this is not a hard and fast rule. Two kinds of triangle zones have been identified by Couzens and Wiltschko (1996): simple, exemplified by triangle zones in the Appalachian Plateau in West Virginia, and complex, like the triangle zone in the Alberta Foothills of the Canadian Rockies (Figure 12–23). Duplexes may form at greater depths and serve the same purpose. Fold curvature, along with thickness and nature of the stratigraphic section involved, may alter the mechanical solution to the room problem. Most folds in a foreland fold-thrust belt are rootless and are transported along thrusts as they form. As they tighten, thrusts may form in the core as a single imbricate, as multiple imbricates, as antithetic thrusts (triangles just described), or as thrusts that work their way up through a fold as a series of branching splays or imbricates (Figure 12–22). The mechanics of thrust faults have been studied intensively ever since their discovery in the nineteenth century. Some of the early insights were derived from work with pressure boxes in which a piston deformed layers of different materials with contrasting properties and colors (Figure 12–24). In such experiments, the end opposite the piston is buttressed and the upper surface remains confined only by a layer of iron or lead pellets, so that deformation may proceed internally. By using pressure boxes, Cadell (1890) in Great Britain and Willis (1893) in the United States made several contributions toward our understanding of thrust mechanics. Let’s consider the character of thrust faulting in two dimensions by employing the stress and strain ellipse concepts (Figure 12–25). Ideally, thrust faults will dip 30° or less and form on shear planes that are bisected by σ1 (which is horizontal). As the crust shortens by thrust faulting, the bulk strain ellipse develops such that the minimum principal strain axis (Z), which is also the maximum shortening direction, is horizontal and the maximum principal strain axis (X) is vertical. This is, of course, a two-dimensional simplification, but applies well to thrust belts. Probably the most significant paper on thrust faulting published in the twentieth century was by Hubbert and Rubey (1959), who showed that fluid pressure along a zone of weakness facilitates motion with much less energy expended than if the zone is dry (Chapter 11). Their calculations of the force required to move a thrust sheet, such as the McConnell thrust in Alberta (Figure 10–1), always exceeded the inherent strength of the sheet if they assumed the hanging wall slid on a dry fault—indicating that it would fragment before motion could occur and therefore should not exist in nature. They concluded that the buoyant (a) (a) Thrust Mechanics (b) (b) (c) FIGURE 12–22 Possible solutions to the room problem in thrust-fold systems. (a) Single thrusts and splaying imbricates. (b) Triangle (delta) structures. (c) Duplexes. FIGURE 12–23 Two varieties of triangle zones. (a) Simple, or Appalachian, type. (b) Complex, or Canadian Rockies Foothills, type. (From B. A. Couzens and D. V. Wiltschko, 1996, The control of mechanical stratigraphy on the formation of triangle zones: Bulletin of Canadian Petroleum Geology, v. 44, no. 2.) Thrust Faults | 309 the observations of Terzaghi (Chapter 9), the Coulomb– Mohr criterion may be modified to |τc| = τ 0 + (σn − Pw ) tan φ, (12–1) where τc is the critical shear stress at failure, τ 0 is the inherent cohesive shear strength of the material, σn is normal stress, Pw is the pore pressure [(σn − Pw) = S, effective normal stress], and φ is the internal friction angle. If τ 0 is small, equation 12–1 reduces to |τc| = (σn − Pw ) tan φ. (12–2) σ3 σ2 σ1 (a) X fault plane Z conjugate plane Y (b) FIGURE 12–24 Thrusts produced in a pressure-box experiment. The sequence from top to bottom represents a fold formed in a pressure box that on continued deformation develops a thrust (a break thrust or fault-propagation fold). Layers are made of clays of slightly different properties. (B. Willis, 1893, U.S. Geological Survey, Thirteenth Annual Report, Part II.) effect of fluid in a mass of rocks would lower the frictional resistance to fracturing and subsequent motion—enough to show how a very large thrust sheet can exist in nature. They suggested that after fracture is initiated, following l − Δl (c) FIGURE 12–25 Stress (a) and strain (b) ellipse for thrust faults in cross section. (c) Sequential sections of crust before and after thrust faulting and contraction, showing displacement taking place primarily as horizontal shortening. 310 | Fractures and Faults Effective normal stress is an important factor in movement along thrusts and other faults (Chapter 11), as well as in the general process of rock deformation. Pore pressure reduces the normal stress and in effect reduces the overall strength of the rock mass. Thus fluid on the fault surface promotes the development of large thrusts, but fluid in the hanging wall inhibits their development, because increased pressure would not force the fluid downward into the fault zone. Hubbert and Rubey (1959) assumed that after movement begins, cohesive shear strength along the fracture becomes negligible; stress is then transferred to the fluid, producing a buoyant effect and greatly enhancing motion. In the preceding discussion in Chapter 11, we saw a useful analogue to the buoyant-fluid concept— Hubbert and Rubey’s beer-can experiment (Figure 11–7). This experiment demonstrates the importance of buoyant force in decreasing effective normal stress. As pointed out by Hsü (1969), Hubbert and Rubey’s simplification applies only if renewed movement occurs on an existing fracture. In all other situations, we must consider the cohesive shear-strength term (τ 0). Study of thrust sheets in the Muddy Mountains in Nevada led Brock and Engelder (1977) to conclude that thrust sheets (or other fault blocks) may be too permeable to maintain fluid pressure of the kind Hubbert and Rubey postulated. Fibers of calcite and other minerals on many fault surfaces also suggest that deformation occurs by a creep mechanism, and may further indicate that the overpressure mechanism is not viable for all thrusts. Fibers and mineral growth along many faults, however, indicate that fluid was present. The mechanical analysis of foreland fold-thrusting by Chapple (1978) may prove as significant as the earlier study by Hubbert and Rubey. Chapple outlined five characteristics of foreland fold-thrust sheets that are now considered fundamental: (1) They are thin-skinned, and all deformation occurs above a basal layer without basement involvement. (2) The basal layer in the thrust sheet consists of a weak material such as shale, coal, or evaporite. (3) Before deformation, the entire stratigraphic section of a foreland belt is wedge-shaped. The wedge thins toward the interior of a continent, with depth to basement increasing toward the sea (or an ancient sea); the surface of the wedge is initially flat or slopes gently away from the continent before collision. (4) As deformation proceeds, the wedge is continuously lengthened as more faults form, shortened as thrusts override each other, and thickened, but it maintains its overall shape throughout deformation (Figures 12–2 and 12–26). (5) The entire deforming foreland fold-thrust belt behaves plastically on the regional scale. Dynamic thrust models developed by Suppe (1981) from study of the active accretionary wedge thrust belt in Taiwan suggest that an equilibrium angle (critical taper) is maintained throughout deformation of the wedge and that materials composing thrust sheets are Coulomb (brittle) materials (Figures 12–26 and 12–27). T β α+β rface ic su raph opog Horizontal α Basa l thru st fau lt FIGURE 12–26 Ideal Coulomb wedge: α is the dip of the basal thrust; β is the topographic slope angle; α + β is the angle at the apex of the wedge. Thus, Davis et al. (1983) have called this deforming wedge a Coulomb wedge and, from experiments on dry sand, developed the Coulomb wedge theory (Dahlen, 1990). The basal angle α is the dip of the basement surface, and the critical taper angle α + β is maintained by internal deformation within the wedge, out-of-sequence and synchronous thrusting, or by active erosion, which removes the steepened part of the shortened end of the wedge. These angles are also related to the coefficient of internal friction µ, which equals tan φ for the rock mass. In addition, the surface-slope angle is partly influenced by climate; for example, in an arid climate the surface equilibrium angle would be maintained by increased landsliding, whereas in a humid climate, stream and slope erosion processes would maintain the angle. Coulomb wedge theory was developed from experiments on dry sand, with the Taiwan accretionary wedge thrust belt serving as a natural analogue. These materials are not the same as the contrasting strong and weak stratigraphic sequences in foreland fold-thrust belts, but the behavior of an entire thrust belt resembles that of a Coulomb wedge. Weak units may deform plastically, however, while strong units may deform brittlely. To formulate an ideal mechanical model for thrust faulting, we must understand how materials involved in thrusting deform under stress (that is, their rheology), as well as know their strengths. It is also essential that we understand the degree to which internal (penetrative) deformation (such as cleavage formation) affects the thrust sheet during initiation and emplacement. Different ideal- behavior modes—such as elastic, viscous, and plastic— may be used in model experiments to duplicate natural behavior, but it may not be possible to describe material behavior exactly in terms of an ideal rheology. Consequently, we must first make assumptions about rheology in order to devise a mechanical model for foreland thrusting. The mechanical model formulated by Chapple (1978) embodies both elastic and plastic behavior. Chapple assumed that the basal weak layer and the total wedge behave as ideal plastic materials. As a result of his analysis, thrust Thrust Faults 2.9° Chiai 4.5° Chengkung 6.5° 311 | Sea level 6° 0 50 Philippine Sea Asian Plate Plate kilometers μ = 0.85 0.95 1.05 6° 1.15 1.25 μ = 0.4 0.7 0.8 0.9 0.97 6° Sea level μb = 0.85 λ = 0.675 Sea level μb = 0.85 λ = 1.03 FIGURE 12–27 Thrusts in Taiwan maintaining the wedge shape and equilibrium surface angle of 2.9°. µ—Coefficient of friction. µb— Coefficient of friction along base of wedge. λ—Pore-fluid pressure, obtained from a ratio of pore-fluid pressure to lithostatic load pressure. (From D. Davis, J. Suppe, and F. A. Dahlen, Journal of Geophysical Research, v. 88, p. 1153–1172, 1983, © American Geophysical Union.) faults are considered a manifestation and consequence of shortening of the wedge. A second conclusion is that plastic flow under compression is an attribute of foreland foldthrust belts, and that compression provides most of the shear stress along the basal weak layer to drive deformation of the wedge. Elliott (1976) concluded from his mechanical analysis that gravity is primarily responsible for deformation of foreland fold-thrust belts. He did not assume a specific rheology, but did make preliminary assumptions about stress distribution within thrust sheets. He assumed that σ1 is oriented at 45° to the basal layer in thrust sheets, and so he did not incorporate a weak basal layer with its attendant properties in his analysis. Thus, the fundamental strength of the entire thrust sheet must be the same as that of the basal layer. In contrast, Chapple assumed that the strength of the remainder of the thrust sheet was much greater than that of the weak basal layer. A consequence of Elliott’s approach is that horizontal compression is not necessary to form a foreland fold-thrust belt, leading to the additional consequence that high shear stress is not produced in the basal layer—contrary to Chapple’s conclusion. Involvement of basement in the more internal parts of thrust belts, however, confirms that gravity cannot be the primary force, and that plate-derived compressional stresses are likely the primary force producing thrust belts. Mechanics of Crystalline Thrusts The mechanics of crystalline thrusts remain a partly unsolved mystery. Recall that crystalline thrusts share many properties with thin-skinned thrusts, as they are transported along low-angle faults, occur in sheets up to a few kilometers thick, and may follow zones of weakness in the footwall sequence, but there are important differences (Figure 12–28). Crystalline thrust sheets are among the largest structures in orogenic belts: they develop along no obvious lithologic plane of weakness, and may form as large brittle sheets as part of the thick foreshortened wedge, but can also form either as huge detached thrust sheets (Type C) or as products of plastic folding (Type F) (Hatcher and Hooper, 1992) (Figures 12–18 and 12–28). 312 | Fractures and Faults Foreland fold-thrust belt Crystalline thrusts composite (Type C) Weak Fold-related (Type F) Brittle Strong Ductile Weak Continental or oceanic crust Continental crust Brittle Brittle Ductile (a) Continental or oceanic crust Strong 0 Ductile 5 kilometers (b) 0 5 kilometers 0 (c) 5 kilometers FIGURE 12–28 Three environments of thrust faulting: (a) Foreland fold-thrust belt, where thrusts are generated by an indentor by propagation into a wedge-shaped assemblage of sedimentary rocks with a weak basal unit (local ductile-brittle transition) and a strong structural-lithic unit that influences the size of thrust imbricates (after Fermor, 1999). (b) Type C crustal slab thrust sheet that detaches along the ductile-brittle transition, transporting all of the crust above the transition in the sheet. These thrust sheets serve as the indentors that push the foreland fold-thrust belt in front of them, generally in continent-continent collision zones. (c) Plastic, fold-related thrust sheets (Type F) that form with a lobate shape (map view) below the ductile-brittle transition, or cool and evolve into smaller Type C sheets. (From Hatcher, R. D., Jr., 2004, Properties of thrusts and the upper bounds for the size of thrust sheets, in McClay, K. R., ed., Thrust tectonics and hydrocarbon systems: Tulsa, Oklahoma, American Association of Petroleum Geologists Memoir 82.) Understanding the formation of detachments along which crystalline thrusts propagate is a difficult problem. Oxburgh (1972) suggested that crystalline thrusts form as “tectonic flakes” when two pieces of continental crust collide. Armstrong and Dick (1974) suggested that propagation and detachment of crystalline thrusts occur at the ductile-brittle transition in zones of high heat flow, as in back-arc basins. Oxburgh’s mechanism may account for single, large crystalline-thrust complexes, such as the Type C A ustroalpine sheets in the Alps, which can be directly related to a collision zone. Moreover, Armstrong and Dick’s mechanism may apply to generation and emplacement of ophiolite thrust sheets, but most crystalline thrusts are composed of continental crust and do not originate in situations described by either of the two models. The majority of crystalline thrusts occur in the metamorphic cores of mountain chains. The five basic types of crystalline thrust sheets identified by Hatcher and Williams (1986) became elements of a mechanical model to explain formation of the composite, ophiolite, and thin-skinned types. This model was simplified to two basic types by Hatcher and Hooper (1992) that embodies Armstrong and Dick’s idea of detachment within the ductile-brittle transition zone and also relates across-strike width to compressive stress, friction and dip on the basal thrust, and thickness of the sheet. Most geologists currently agree that faults beneath crystalline thrust sheets (and deep-seated listric normal faults, see Chapter 14) propagate within the ductile-brittle transition that occurs at a depth controlled by the thermal properties of the crust—thereby also controlling the thickness of these sheets. Their upper size limit is controlled by the overall strength of the sheet, determined by composition (the strength of quartz-bearing or pyroxene plagioclase-rich crust), thickness, and the thermal regime in which they originate (Hatcher, 2004). Thrust faults and thrust belts have long fascinated geologists. The mechanics of these structures will doubtlessly remain a subject for debate for future structural geologists. We now turn from thrust faults to the other class of faults that form under horizontal compression— strike-slip faults. Chapter Highlights • Thrust faults are a major fault type that form in compressional tectonic settings such as accretionary wedges and foreland fold-thrust belts (FFTBs). • Thrust faults typically develop within a critical wedge of deforming materials, whose overall shape is controlled by the mechanical properties of the material. • Thrust faults generally transport material toward the foreland, and can have displacements of tens to hundreds of kilometers. • Thin-skinned thrust faults occur above a detachment within a sedimentary sequence, whereas thick-skinned thrust faults occur where basement is involved. Thrust Faults • Forced folds such as fault-propagation folds and faultbend folds commonly develop in the hanging wall of thrust faults. • Erosion of thrust sheets can produce windows through the hanging wall into the footwall, and klippen as erosional outliers of the hanging wall. • Geologists have long debated the role of tectonic compression versus gravitational sliding in the formation | 313 of thrust faults, with compression occurring in most mountain chains. • The existence of large thrust sheets (thousands of km2) requires lowering the effective stress over vast areas along these faults. The largest thrust sheets are composed of very strong rocks (e.g., gneisses and massive plutonic rocks) and detachment likely occurs along the ductilebrittle transition. Questions 1. What evidence would you seek to prove that a large thrust fault exists—or not—in an area where none has been found before? 2. Why does a foreland wedge maintain its shape throughout deformation? 3. Why do thrusts have steeper dips on ramps than within detachments? 4. How and why do horses form? 5. How does fluid pressure reduce the amount of energy needed to move a thrust sheet? If this is so, why do castles of wet sand stand (have greater cohesive strength) and those of dry sand form more gently sloping surfaces (have less cohesive strength)? 6. Why does Chapple’s model for foreland fold-thrusting require a weak basal layer? 7. How does an eyelid window form? 8. How did Price’s concept of gravitational spreading partly dispel objections to a simple gravity model for thrusting? 9. How are potential voids filled beneath folds or in a stack of thrusts? 10. Why did Chapple choose an ideal plastic rheology for the foreland wedge even though evidence of brittle (elastic) behavior was abundant? 11. Why don’t the hanging walls of thrusts slide back down after they have been pushed up? 12. From the curve in Figure 12–14b, estimate the displacement of the Saltville thrust (in the southern and central Appalachians), which has a strike length of 680 km. Further Reading The literature on thrust faulting is voluminous and growing. These works, and the papers the authors cite, will help to open the door to better understanding of thrust faults. Boyer, S. E., and Elliott, D., 1982, Thrust systems: American Association of Petroleum Geologists Bulletin, v. 66, p. 1196–1230. Describes the terminology and geometry of thrusts, with examples from several mountain chains, in both maps and cross sections. Chapple, W. M., 1978, Mechanics of thin-skinned fold and thrust belts: Geological Society of America Bulletin, v. 89, p. 1189–1198. Lists the properties of a foreland fold-thrust belt, then derives a mechanical model. The first part of the paper and the conclusions will be particularly useful to undergraduates. Dahlen, F. A., 1990, Critical taper model of fold-and-thrust belts and accretionary wedges: Annual Review of Earth and Planetary Science, v. 18, p. 55–99. Summarizes critical wedge theory and its application to thrust systems. Dahlstrom, C. D. A., 1969, Balanced cross sections: Canadian Journal of Earth Sciences, v. 6, p. 743–758. Principles of balancing cross sections (mainly line balancing) are explained clearly and concisely, with examples mostly from the Canadian Rockies. Hatcher, R. D., 2004, Properties of thrusts and the upper bounds for the size of thrust sheets, in McClay, K. R., ed., American Association of Petroleum Geologists Memoir 82, p. 18–29. Discusses the properties of different types of thrusts, and compares and contrasts their properties and behavior. Hossack, J. R., and Hancock, P. L., eds., 1983, Balanced cross sections and their geological significance: Journal of Structural Geology, v. 5, p. 98–223. Special issue dedicated to David Elliott, containing 10 papers on balanced cross sections. Laubscher, H. P., 1988, Material balance in Alpine orogeny: Geological Society of America Bulletin, v. 100, p. 1313–1328. Outlines the principles of 3-D material balancing using the Alps as an example. 314 | Fractures and Faults McClay, K. R., ed., 1992, Thrust tectonics: London, Chapman and Hall, 447 p. McClay, K. R., ed., 2004, Thrust tectonics and hydrocarbon systems: Tulsa, Oklahoma, American Association of Petroleum Geologists Memoir 82, 667 p. These three books edited by McClay contain papers largely presented at meetings on thrust faults held about a decade apart that contain examples of thrust systems from different parts of the world as well as up-to-date treatment of mechanics, geometry, and concepts of thrusting. McClay, K. R., and Price, N. J., eds., 1981, Thrust and nappe tectonics: Geological Society of London Special Publication 9, 539 p. Mitra, S., 1986, Duplex structures and imbricate thrust systems: Geometry, structural position, and hydrocarbon potential: American Association of Petroleum Geologists Bulletin, v. 70, p. 1087–1112. This study of duplex and imbricate thrusts provides more details than do Boyer and Elliott (1982) on this aspect of thrust faulting. Cites good examples from several fold-thrust belts. Mitra, S., and Fisher, G. W., eds., 1992, Structural geology of fold and thrust belts: Baltimore, Maryland, The Johns Hopkins University Press, 254 p. Another compendium of papers dedicated to David Elliott. It contains a number of useful papers on thrust faulting in different regions, as well as several papers on thrust mechanics. Moores, E. M., 1982, Origin and significance of ophiolites: Reviews of Geophysics and Space Physics, v. 20, p. 735–760. Summarizes the structure and processes that form and emplace ophiolite sheets, with examples from various settings. Oldroyd, D. R., 1990, The Highlands controversy: Constructing geological knowledge through fieldwork in nineteenthcentury Britain: Chicago, University of Chicago Press, 438 p. Chronicles the history of acceptance of the Moine thrust as a thrust fault from the early to mid-nineteenth century. Stockmal, G. S., Beaumont, C., Nguyen, M., and Lee, B., 2007, Mechanics of thin-skinned fold-and-thrust belts: Insights from numerical models, in Sears, J. W., Harms, T., and Evenchick, C., eds., Whence the mountains? Inquiries into the evolution of orogenic systems: A volume in honor of Raymond A. Price: Geological Society of America Special Paper 433, p. 63–98. Presents a finite-element model for foreland fold-thrust belts based on several assumptions and comparisons with existing mechanical models. 13 Strike-Slip Faults On January 12th, 2010, the Enriquillo-Plantain Garden fault zone in southwestern Hispañola slipped, generating a Mw 7.0 earthquake that utterly destroyed Port-au-Prince, Haiti (Figure 13–1). The EnriquilloPlantain Garden fault is a left-lateral strike-slip fault developed along part of the boundary between the North American Plate to the north and the Caribbean Plate to the south. Earthquakes spawned along active strike-slip faults worldwide have had disastrous consequences in terms of lives lost and property damage. Notable examples include California, 1906; Guatemala, 1976; Turkey, 1999; Haiti, 2010; New Zealand, 2010. Such disasters justify intensive study of active faults aimed at improving our ability to predict earthquakes and enhance building design for safety. Routine prediction of earthquakes is not yet possible, but we have gathered an enormous amount of data and greatly increased our knowledge of strike-slip fault systems. Many of these large active strike-slip faults, such as the San Andreas in California (Figure 13–2), the Alpine in New Zealand, and the North Anatolian in Turkey, are located on plate boundaries and form integral parts of these dynamic boundaries. Others, such as the Great Glen fault in Scotland described earlier by Kennedy, and the Brevard fault in the Appalachians, have been known for decades—not because of their tectonic activity, but because of their distinctive and continuous linear traces. Strike-slip faults are also important because crustal blocks are transported hundreds to thousands of kilometers along these structures. Displacements of this magnitude enable terranes to be transferred along the length of an orogen and allow whole crustal blocks to escape from collision zones. In this chapter we discuss the geometric characteristics of strike-slip faults, the tectonic environments in which they occur, and mechanics of these structures. The powerful dislocation which intersects Scotland along the line of the Great Glen has, in the past, been regarded by most geologists as a normal or dip-slip fault. . . . A reconsideration of the entire problem now suggests . . . that the dislocation is, in reality, a lateral-slip [strike-slip] . . . fault with a horizontal displacement of approximately 65 miles. WILLIAM A. KENNEDY, 1946, Quarterly Journal of the Geological Society of London Properties and Geometry Strike-slip faults are those with motion parallel to the strike of the fault plane. The movement sense on a fault can be determined with relative ease following a large earthquake, using several different lines of evidence. 315 316 | Fractures and Faults 80° W 75° W 70° W Earthquake magnitude (Mw) 8.0–8.9 North American Plate 7.0–7.9 Cuba 20° N 6/21/1900 Mw 7.9 Septen trion a zone Oriente fault Gonâve Microplate Jamaica ne ult zo n fa Walto Kingston 6/14/1899 Mw 7.8 llo Enriqui 1/12/2010 Mw 7.0 1842 Mw 7.7 Haiti Garden fault z one -Plantain 1691 Mw 7.7 20° N 8/4/1946 Mw 8.1 Dominican Rep. Port-au-Prince Hispañola 8/8/1946 Mw 7.9 l faul t zon e Santo Domingo 4/24/1916 Mw 7.2 7/29/1943 Mw 7.9 1787 Mw 8.0 10/11/1918 San Juan Mw 7.5 Puerto 11/18/1867 Rico Mw 7.5 Caribbean Plate 15° N 80° W 0 75° W 70° W 300 15° N kilometers FIGURE 13–1 Tectonic map of the northeastern part of the Caribbean Sea and adjacent regions showing the locations of major faults and plate boundaries, and the location of the January 2010 Mw 7.0 earthquake (orange star) that destroyed much of Port-au-Prince, Haiti. (Modified from McCann, 2001.) One is accompanying ground breakage. If surface rupture occurs, topographic features, such as streams and ridges, will be offset, indicating movement sense (Figure 13–2). The linear trace of strike-slip faults (both active and inactive) allow these features to be readily identified with remote sensing technologies. Modern technologies such as LiDAR (light detection and ranging) enable lineaments, scarps, and other tectonic landforms to be identified even in regions that are heavily vegetated (Figure 13–3). Strike-slip faults are characterized by their steep dip and the predominance of horizontally displaced markers (Figure 13–4). Most dip more than 60°, and many approach the vertical. Shallow- to moderately dipping strike-slip faults also exist (Alpine fault, New Zealand), particularly where a fault changes orientation. Strikeslip faults are also called wrench, tear, and transcurrent faults, although Sylvester (1988) recommended the term FIGURE 13–2 The San Andreas fault is geomorphically well expressed in eastern San Luis Obispo County, California. View is toward the southeast. Can you determine the motion sense on the San Andreas fault from this photo? (Hint: look closely at the way stream valleys change trend as they cross the fault.) (U.S. Geological Survey.) Strike-Slip Faults 38 38°42'N 8°42 42 2N | 317 38°42'N Lineaments 1906 Holocene 0 100 200 meters 300 400 Quaternary 12 1 123°25'W 23°25 2 W (a) 123°25'W (b) FIGURE 13–3 (a) Shaded relief image generated from a bare-earth LiDAR DEM in a heavily vegetated region of the northern California coast southeast of Sea Ranch along the San Andreas fault. (b) Numerous lineaments can be easily identified by their topographic expression. Lines in (b) trace fault scarps formed during the 1906 and earlier Holocene and Pleistocene earthquakes. [Fault data from http://earthquake.usgs.gov/data/, LiDAR DEM downloaded from OpenTopography (http://opentopo.sdsc.edu/); data courtesy of the Sonoma County Vegetation Mapping and LiDAR Program (http://www.sonomavegmap.org).] Steeply dipping zone of anastomosing faults and splays from main fault Sinistral motion Fault zone with dominant motion parallel to horizontal FIGURE 13–4 Geometry and anatomy of a strike-slip fault. “wrench fault” be abandoned because of the confusion generated by the name. Transform faults (Wilson, 1966) are plate-bounding strike-slip faults and were originally predicted by Wilson as a consequence of plate motion on a sphere. Sinistral, or left-lateral, and dextral, or rightlateral, strike-slip faults should be familiar terms that were defined in Chapter 10. Strike-slip faults may branch and splay into smaller segments and other types of faults. They may contain horses plucked from either side of the fault and carried along in the same way that blocks are carried along thrust faults. Horses may be derived from either block, and so the general age-relationship rule applicable to thrusts (Chapter 12) does not apply here. The geometry and motion sense of a strike-slip fault may abruptly change along strike. The segment with the markedly different strike may become a thrust or normal fault (Figure 13–5). Folds may also form along a strikeslip fault, either as a consequence of a change in strike, 318 | Fractures and Faults FIGURE 13–5 (a) Transfer of motion from strike-slip into thrust or normal slip motion. (b) Gently plunging folds related to strike-slip motion. (c) En echelon segments of a dextral fault. (d) Map of the Pine Mountain block in Tennessee, Kentucky, and Virginia showing a thrust sheet bounded by tear faults. All are shown in map view. [(d) after J. L. Rich, 1934, AAPG Bulletin, v. 18. Reprinted by permission of American Association of Petroleum Geologists.] Ocotillo badlands San Francisco Bay Dead Sea Death Valley Note sense of motion on sides of faults adjacent to the ends of the step-over blocks Upthrown block (rhomb horst) bounded by thrust faults Arrows directed toward step-over on fault segments next to the step-over block reflect upthrown motion of central block Downthrown block (rhomb graben) bounded by normal faults Arrows directed away from step-over on fault segments next to the step-over block reflect downthrown motion of central block (a) Anticlines Synclines (c) (b) 83° W 84° W s Ru ll se Buck Knob anticline Gladeville anticline KY VA 37° N Pineville KY Rocky F ace f. Cum Jellico TN Dis tur be dz Cumberland Gap nd berla in nta Mou el Pow l Va ll e n ya tic hr ley t Val r e t un 0 s rk f aul t ust 10 20 30 kilometers VA ow nd Wi Fo 37° N e lin H M Pine A ult st fa thru n i ta oun Tear fault TN on e Speedwell A f. Tear fault oro ksb Jac Jacksboro Lee sandstone Pennsylvanian Cumberland Mountain A' Sea level 0 Thrust plane 84° W Thrust plane 5 A' Sea level kilometers 83° W (d) branching into either thrust or normal faults, which pass into folds as the displacement diminishes along the faults, or drag related directly to strike-slip motion. Shear sense on steeply plunging drag folds reflects the sense of motion of associated faults. Overlapping segments of en echelon (overlapping) strike-slip faults may indicate the motion sense from the nature of the structures in the overlap zone (Figure 13–5c). A strike-slip fault is commonly envisioned as a single brittle fault surface separating two oppositely moving blocks. Some do occur as simple planar faults, but absolute planar faults are not common in upper-crustal Strike-Slip Faults Earth’s surface Brittle faulting T A Cataclastic zone Brittle upper zone Ductile-brittle transition Mylonite zone T A Ductile lower crust FIGURE 13–6 Along a strike-slip fault, both the deformation type and kind of fault rocks vary with depth in the crust. T—motion toward the observer; A—motion away from the observer. rocks. Most strike-slip faults—like other large faults in the interior parts of mountain chains and at terrane and plate boundaries—are commonly not single, discrete, brittle surfaces. They most frequently occur as cataclastic zones consisting of anastomosing fault strands containing gouge and breccia (Figure 13–4) or—if erosion has exposed the deeper parts of the zone—a considerable thickness of mylonite (Figure 13–6). These are the classic shear zones discussed in Chapter 10. Evidence from inactive strike-slip faults and others eroded to expose lower-crustal segments suggests a continuous transition from brittle deformation near the surface to ductile deformation at middle- to lower-crustal depths (Figure 13–6). At the surface, elastic strain energy can be relieved by instantaneous strike-slip rebound (Chapter 11), as indicated by cataclastic rocks (breccia and gouge). At depth, this motion may occur as aseismic plastic creep, continuously producing mylonite and other ductilely deformed rocks. Also, comparison of brittle strike-slip faults with those in deeply eroded crust indicates that strike-slip fault zones near the surface are relatively narrow, but some ductile strike-slip fault zones in deeply eroded parts of orogens may be several kilometers wide (Chapter 10). The mineralogy and texture in these zones exhibit abundant evidence of ductile deformation at high temperature and pressure. Page (1990) suggested that a broad zone of “pseudoviscous” strain exists along the San Andreas fault at depths greater than the depths where the fault generates earthquakes. Tectonic Setting of Strike-Slip Faulting Many strike-slip faults (for example, the San Andreas in California, the Motagua in Central America, and the Alpine in New Zealand) are plate boundaries; they | 319 are fundamental accommodation structures. They also form the boundaries between many accreted terranes (Chapter 1) and the continent (or other terranes) to which accretion is taking place. Strike-slip faults also occur behind oblique convergent margins in mountain chains, like several large faults in southeastern Alaska (the Denali and Fairweather faults) and adjacent parts of the Yukon and British Columbia (Tintina fault), where deformation in the upper plate is transferred into strike-slip motion parallel to the margin. Structures in these environments, such as folds and smaller dip-slip faults, are formed by margin-parallel compression. Other strike-slip faults include tear faults that bound the ends of thrust sheets. Classic examples include the Jacksboro and Russell Fork faults at the southwestern and northeastern ends of the Pine Mountain thrust sheet in the Appalachians (Figure 13–5d). Geometry Related to Other Fault Types Wilson (1965), McKenzie and Parker (1967), and Morgan (1968), using the fact that the Earth is nearly spherical, recognized that because plate tectonics and spherical geometry govern the motion of both continents and ocean floors, major strike-slip and transform faults must follow small or great circles on the Earth (Figure 13–7). We can thus predict, using spherical geometry, that with any deviation of a fault plane from a small circle the sense of movement on the fault will include components of either normal or thrust motion (Figure 13–5). When the orientation of the fault plane deviates significantly from the primary orientation, motion along the fault passes from the realm of strike slip into the realm of normal or thrust motion (Figure 13–8). Relationships between en echelon or parallel segments of strike-slip fault systems that are not connected by segments of strike-slip faults have been described by Aydin and Nur (1982), although Wilson (1965) probably made the original observation of these relationships; they saw that motion may be transferred from one segment to another—by a step-over—through zones of extension or of contraction, depending on the relative motion of the fault segments and the sense of each step-over (Figure 13–9). As a result, an en echelon dextral strike-slip fault with right step-overs produces pull-apart, or rhomb-graben (or rhombochasm), basins. The same result is produced by left-lateral strike-slip faults with left step-overs. Two sides of the basin will be bounded by segments of the strikeslip fault with a significant component of normal slip. The other sides will be bounded by normal faults oriented obliquely to the primary direction of horizontal strike-slip 320 | Fractures and Faults FIGURE 13–7 Small-circle geometry relationship of strikeslip and transform faults. (a) Generalized diagram showing the motion of two blocks on a sphere that must follow small circles on the sphere concentric to pole A. (b) Transforms (dashed faults) in the present-day Atlantic Ocean relative to small circles (heavy solid lines) concentric to a pole at 62° N 36° W. Dashed lines represent active and inactive transforms. (Modified from W. J. Morgan, Journal of Geophysical Research, v. 73, p. 1959–1982, 1968, © American Geophysical Union.) Pole A Block 2 Block 1 (a) 20° N 60° W 40° W 20° W 0° 20° N 10° N 10° N ? ? on lin e ? 0° Ca me ro 0° (b) 40° W 60° W 20° W Alternative shear plane (anti-Riedel shear) not utilized Z Normal faults Thrust faults X Elongation Y-axis vertical Boundaries of strike-slip fault zone (a) Y Actual fault orientation (Riedel shear) 0° Boundaries of strike-slip fault zone Shortening (b) FIGURE 13–8 (a) Strain ellipse for strike-slip faults (map view). (b) Strain ellipse showing the possibilities for motion transferred to thrust or normal-slip domains. Motion transferred to thrust or normal faults must also occur on shear planes in appropriately oriented strain ellipsoids, not on the one shown here with a Y-axis vertical. Strike-Slip Faults Folds or pressuresolved areas Structurally high areas Extension cracks Structurally low areas (a) | 321 FIGURE 13–9 Transfer of motion between strike-slip fault segments producing rhomb-graben or rhomb-horst structures, depending on whether the step-over is in a right- or left-lateral sense (c) and (d). (After A. Aydin and A. Nur, Tectonics, v. 1, p. 91–105, 1982, © American Geophysical Union.) (b) or or (c) Upthrown block bounded by thrusts (d) motion (Figure 13–9). Burchfiel and Stewart (1966) first suggested the term “pull-apart” to describe the structure of the Death Valley region. Death Valley is such a topographically low area because it is part of a rhomb graben. Crowell (1974) and Dibblee (1977) later recognized the same relationships between step-overs and grabens and horsts along segments of the San Andreas fault. Dextral strike-slip faults with left step-overs or sinistral faults with right step-overs produce rhomb horsts, or push-up ranges. Strike-slip fault segments with significant thrust motion will bound two sides of a horst, and the other two sides will be bounded by oblique-slip thrust faults (Figure 13–5b). Small rhomb grabens and horsts have been identified at many places on the Earth (Figure 13–10). The Dead Sea and Rhomb graben Rhomb horst FIGURE 13–10 Rhomb-graben and rhomb-horst structures along a large and complex hypothetical fault system. (After A. Aydin and A. Nur, 1982, Tectonics, v. 1, p. 91–105, © American Geophysical Union.) the San Francisco Bay area have been interpreted by Aydin and Nur (1982) and Aydin and Page (1984; Figures 13–11a and 13–11c) as rhomb-graben structures. Similar conclusions were reached earlier for the Dead Sea structure by Freund (1965) and Freund et al. (1968). The Ocotillo Badlands and Borrega Mountains along the Coyote Creek fault in California have been interpreted by Aydin and Nur (1982) as rhomb horsts (Figure 13–11b). Each of these structures formed as part of a complex of interacting plate boundaries where relative motion has changed through time. Complex fault geometry frequently produces large rhomb grabens and horsts (Figure 13–10). Then, as noted by Aydin and Nur (1982), more faults form, producing smaller segmented grabens and horsts, which together form larger composite basins or uplifts. Aydin and Nur also noted a consistent ratio of length to width of pull-apart basins and push-up ranges varying from 2.4 to 4.3, with a mean of 3.2. The ratio appears to be scale independent, suggesting fractal (self-similar) behavior, because length-width ratios of basins and uplifts of all sizes fall within this range. Terminations of Strike-Slip Faults Strike-slip faults may terminate by splaying along strike into smaller faults, by changing strike and becoming thrust or normal faults (which may further splay into smaller faults or terminate in folds), or by diminishing displacement along the main fault until none is detectable (Figure 13–12a). Splays may develop as Riedel and antiRiedel shears (Chapter 11) off a main fault, reducing the total displacement. Fractures and Faults 30° E 40° N 40° E Black Sea 50° E 116°10' W Eurasia n Plate Turkish Plate Bitlis s utur e Aegean Sea 33°10' N Caspian Sea Za gr Mediterranean Sea Fold axis su Red Sea re Pe rs ia n Arabian Plate African Plate os Coyote Creek fault trace tu Dead Sea rhomb graben 30° N N 116°05' W 16 0 | 24 322 400 240 Gu lf 0 80 0 Ocotillo Badlands 80 500 160 kilometers (a) (1) N ult Easte r n b o undar y fa ult I N S E A Lisan diapir D D E A om f. f a u lt Sed Pacific Ocean fault 37° N (a) (2) Arava 35° E Livermore domain Jordan We s tern boundary (b) y Ba co n cis be ran gra n F mb Sa rho B A S Dead Sea Israel 31° N kilometers Jericho fa 32° N 33°05' N 3 0 0 40 N 0 kilometers 50 kilometers 122° W (c) FIGURE 13–11 (a)(1) Arrangement of plate boundaries in part of the Middle East showing the Dead Sea rhomb-graben and transform fault system. Arrows indicate plate movement directions. Rectangle shows location of detailed map in (a)(2). (After M. R. Hempton, 1987, Tectonics, v. 6, © American Geophysical Union.) (a)(2) Map showing the locations of the major faults of the Dead Sea Basin rhomb-graben structure. (Modified from J. Smit et al., 2008, Tectonophysics, v. 449, p. 1–16.) (b) Rhomb-horst along the Coyote Creek fault in California. Contours are in feet. (From R. V. Sharp and M. M. Clark, 1972, U.S. Geological Survey Professional Paper 787.) (c) Rhomb-graben fault system in the San Francisco Bay area. (After A. Aydin and B. M. Page, 1984, Geological Society of America Bulletin, v. 95.) A 0 4 (b) | Strike-Slip Faults A' kilometers A 323 A' A T A T A A T T Splays 0 Anticlinal folds (a) 10 0 20 1 kilometer kilometers (c) FIGURE 13–12 (a) Termination of strike-slip faults into thrust and/or normal faults, folds, and splays (map view). (b) Map view of flower structures. They may be a near-surface phenomenon—the flowers closing upward or downward in cross section into single fault zones—as convergence of faults along strike into a single fault is frequently observed on the surface. (c) Cross section of flower structure drawn along line A–A' shown in (b). A—movement away from observer. T—movement toward observer. A 0 4 A' kilometers (b) A A' In cross section, strike-slip faults frequently splay upward into outwardly A Tbranching segments that A T or horse-tail) configurations exhibit flower (or palm-tree (Figure 13–12b). AThese are more difficult to observe in A T T the field unless vertical relief exposes a cross section of the fault zone, or the fault zone has been tilted by later deformation and exposed by erosion. Existence of flower structures has been confirmed and observed as offset SW 0 0.0 0 1 1 kilometer 2 rock units in seismic reflection profiles. Some strike-slip motion involved in forming a flower structure must be resolved into dip slip. Faults associated with the Paleozoic Oklahoma aulocogen of southern Oklahoma exhibit flower and inverted rift structure (Figure 13–13; Harding, 1974). Flower structures are termed positive or negative, based on whether they branch upward (positive) or downward (negative). 3 4 5 6 7 8 NE 10 9 (c) p Ms M Ms yy y Ms Msp Oo c Msy 2.0 O oc Two-way time (seconds) 1.0 Ooc 3.0 y Ms 4.0 Ooc T A 0 2 kilometers FIGURE 13–13 Structure section constructed on a seismic reflection profile and drill data into part of the Ardmore basin in the Oklahoma aulocogen, illustrating flower and inverted-rift structures. Msp—Springer, Msy—Sycamore, and Ooc—Oil Creek are Paleozoic rock units. (After T. P. Harding, 1974, AAPG Bulletin, v. 58. Reprinted by permission of American Association of Petroleum Geologists.) 324 | Fractures and Faults Releasing and Restraining Bends Strike-slip faults, like other faults, rarely are perfectly planar structures and frequently have curved segments: slightly curved segments do not change movement kinematics or influence displacement, but moderate curvature creates problems with mechanics and kinematics that result in changes in the vicinity of the curved segment. The outcome depends on the direction of curvature relative to the movement sense on the strike-slip fault. Consider a dextral strike-slip fault that curves away (clockwise) from the right side of the fault (Figure 13–14a). As the fault moves, it will create extensional deformation and hypothetically a void space in the curved segment similar to a rhomb graben between two overlapping segments of a strike-slip fault. This segment becomes a releasing bend in the fault and the “void” is filled with sediment. The opposite situation arises where the same fault curves toward (counterclockwise to) the right side of the fault (Figure 13–14b) and a zone of enhanced contractional deformation similar to a rhomb horst forms in the area between two overlapping strike-slip faults. This is called a Fault segment curved toward right side of fault restraining bend. The magnitude 7.0 earthquake in Haiti in 2010 (Figure 13–1) may be the product of accumulation of compressional strain and sudden release of energy at a restraining bend along the sinistral Plantain Garden fault (Mann, 2007). Transtension and Transpression Resolution of strike-slip into significant contractional dip-slip motion is called transpression, which often results from oblique plate convergence where the dominant motion is strike-slip. Harland (1971) and Lowell (1972) were perhaps the first to describe transpression, in the course of their studies of Caledonian structures in Spitzbergen (Svalbard). It has since been reported in many places, including the Mecca Hills near the Salton Sea in California (Sylvester and Smith, 1976). Transpression and its opposite, transtension, involve nothing more than complex oblique-slip motion resolved from dominant strike-slip. It is surprisingly common, because most faults exhibit some form of oblique-slip. Basins produced along releasing bend Releasing bend (a) (b) Fault segment curved toward left side of fault Thrust blocks produced along restraining bend Restraining bend (c) (d) FIGURE 13–14 Blocks [(a) and (c)] containing dextral strike-slip faults with moderately curved segments. (a) Fault curvature toward the right-hand block (toward observer located south of block). (b) Movement on the fault in (a) as a releasing bend produces normal fault-bounded basins. (c) Fault curvature away form the right-hand fault block. (d) Movement on the fault in (c) along a restraining bend produces thrust fault-bounded, uplifted blocks. These are very important concepts, because many interactions at plate boundaries do not involve head-on collision or pulling apart—or pure strike-slip motion, but instead involve a major oblique-slip component. The kinematic histories of many plate boundaries, worked out using shear-sense criteria, rock unit displacements, and other fundamental techniques, have confirmed the transpressional or transtensional nature of many of these boundaries. Even the opening of the Red Sea did not occur perpendicular to the axis of the sea, but several tens of degrees off of this direction (Figure 13–11a). Transpressional and transtensional environments also produce distinct sets of structures, such as rhomb-graben and flower structures, that can serve as hydrocarbon traps. Tectonic plate movement that is not orthogonal (either in a contractional or extensional nature) will involve a component of oblique movement that leads to transpressional or transtensional structures. or transfer structures at plate boundaries. They form segments of convergent or divergent plate boundaries that are moving at different rates. The San Andreas fault fits this distinction between strike-slip and transform faults. It is an intra-continental transform, connecting the ends of the East Pacific Ridge, where it disappears beneath the North American continent in the Gulf of California, to the Gorda Ridge (via the Mendocino Transform) off the coast of northern California (Figure 13–15). It also is a strike-slip fault at a plate boundary. The connection through continental crust has not always existed, and the connection is regarded as temporary until the plate boundary shifts again either farther inland (to the Mojave Desert and Owens Valley region) or farther westward. Large earthquakes occurring during the early 1990s in relatively unbroken segments of continental crust suggest that the plate boundary may shift eastward, transferring Cascadia subduction zone Juan De Fuca Plate South Gorda Plate 40° N Can. USA Spreading center with bordering transform faults bia eau lumPlat o C Active subduction zone Volcano OR Basin and Range Province Mendocino triple junction rra N. American Plate s Mtn r ada nd y alle nA tV Sa ea Death Valley Colorado Plateau CA ea 40° N NV Nev Gr Pacific Plate Active and late Cenozoic faults, including transforms WA Sie s rlo ck f. Ga Mojave fau Desert lt 130° W Salton Trough ia rn lifo Ca PACIFIC OCEAN US A Me x. d lan er G f ul ja Ba 30° N Sonora of Ca lifo r a 120° W rni lifo Ca N ni a 0 400 kilometers FIGURE 13–15 San Andreas and related fault systems in California, northern Mexico, and in the adjacent Pacific Ocean. (After J. C. Crowell, 1987, Episodes, v. 10.) E ris ast P e a cifi c 30° N rd bo We have already discussed transform faults several times (see Figures 1–10, 10–9, and 13–7). Wilson (1966) first postulated that they exist to compensate differences in the rates and amounts of motion between adjacent plates, or segments of plates, whether at a spreading center (such as an oceanic ridge), or connecting segments in a subduction zone where some segments are consumed faster than others. Shortly after Wilson’s prediction, studies by Sykes (1967) of earthquake focal mechanisms along the Mid-Atlantic Ridge verified Wilson’s hypothesis. Several kinds of transforms have been described, including ridge-ridge transforms, ridge-arc transforms, and arc-arc transforms (see Figure 10–9b). The classic ridge-ridge transform has an apparent simple strike-slip displacement, but the real motion on the fault is opposite the apparent offset sense. Transforms are strikeslip faults that cut the entire lithosphere, so they are accommodation 120° W Juan De Fuca ridge Wil Casca lamette Va lley de Ra nge 130° W Transforms 325 | Strike-Slip Faults Rivera Plate 326 | Fractures and Faults the Sierran block, now on the North American Plate, to the Pacific Plate (Hauksson et al., 1993). Davis and Burchfiel (1973) earlier suggested that the Garlock fault east of the San Andreas in southern California is also an intracontinental transform (although it is not a plate boundary): they pointed out that two different tectonic styles are present on each side of its trace. Consider too, the Dead Sea fault in the Middle East (Figure 13–11a), the Alpine fault in New Zealand (Figure 11–12), and the Great Glen fault in Scotland. All may be intracontinental transforms, but keep in mind that transforms are only a special kind of strike-slip fault, and that, by changing fault geometry slightly, motion may become either thrust or normal. Mechanics of Strike-Slip Faulting A fundamental attribute of strike-slip faults is that they form by horizontal compression. Supporting evidence is threefold: (1) required for the Andersonian model of the strain ellipsoid for strike-slip faults, supported by experimental and field data that indicate the relationship between stresses and faulting (Figure 13–8a); (2) field evidence, including mesoscopic shear-sense indicators, drag folds, and the motion sense determined by offset marker units; and (3) first-motion studies of earthquakes produced by active strike-slip faults. The close association of strike-slip and thrust faults also shows that both form by horizontal compression. ESSAY Most strike-slip faults bear evidence of reactivation, and study of active faults indicates that reactivation is the rule over geologic time. As one example, the Ramapo fault in New Jersey and New York (see Chapter 14, Figure 14E–2) underwent recurrent strike- and dip-slip motion in the Paleozoic, Mesozoic, and Cenozoic over a period of about 400 m.y. (Ratcliffe, 1971). The Ramapo may even be active today, for many small earthquakes have been located along it (Aggarwal and Sykes, 1978). Moreover, geologic evidence indicates that the San Andreas fault that we see today has been moving blocks of continental crust past one another only since 5 Ma, and this motion has continued throughout the Holocene (Figure 10E–1; Sieh and Jahns, 1984; Powell et al., 1993). Before that time, segments of nearby faults were active at least since middle Miocene time (16–11 Ma). Various segments of the modern San Andreas have been active at different times. When accumulated elastic strain energy is relieved along a particular segment, other segments continue to accumulate strain to be relieved later, and so all segments of a large fault do not move at the same time. Geophysical evidence from the sea floor off California indicates that faults ancestral to the present San Andreas have been active throughout the past 30 to 35 m.y. (Atwater, 1970; Severinghaus and Atwater, 1990). Here we end our discussion of strike-slip faults with a note that even the largest and most widely known examples still deserve continued study, particularly because of the interrelated nature of all faults, and the seismic hazard posed by active faults. Rigid Indenters and Escape Tectonics A large system of intraplate continental strike-slip faults was first described by Molnar and Tapponnier (1975) in central Asia, where they found that known strike-slip faults interconnect (Figure 13E–1). As a result, they suggested that India acted as a rigid indenter (Figure 13E–2) when it collided with Asia, and that strike-slip deformation resulted when large parts of Asian crust moved laterally in response to the collision. The crust responded to the collision with the indenter by forming large strike-slip faults bounding blocks that moved laterally out of (“escaped” from) the collision zone, hence the term “escape tectonics.” North of the indenter in Asia, dextral strike-slip faults ideally would have moved blocks westward from the west side of the collision zone, and sinistral faults (again, ideally) would have moved blocks eastward and out of the eastern part of the collision zone. We recognize, however, that both dextral and sinistral faults bound the escaping blocks, because of the orientation of the more local stress fields and the shear planes that ultimately form faults. Deviation of actual motion from ideal behavior along the large faults was related to both the original shape of India as it collided with Asia (Figure 13E–1), which produced variations in stress trajectories, and also to the relative-motion vectors that brought Asia and India into collision. Tapponnier et al. (1982) built accurate scale models to better understand the process (Figure 13E–2). Burchfiel (2004) employed GPS data from the Himalayan and Southeast Asia region to reconfirm the motion based on studies on the ground and Tapponnier’s model. These data provide both magnitude and direction of present-day motion of different tectonic components of the collision zone and escaping blocks (Figure 13E–3). The Asia-India collision zone is one of Earth’s most populous regions, and so the earthquake hazard is of great Strike-Slip Faults 50° E 70° E 90° E 110° E | 327 130° E Baïkal rift system 40° N Tein Shan Tarim basin 30° N Tibet Kunlun faul t H In im du ala sT sa ya ng-Po s nf uture ron tal th r u st 20° N Normal fault Extinct volcanoes Thrust fault Active volcanoes Strike-slip fault Recent basaltic centers Folds Inferred zones of recent compression Inferred zones of recent extension FIGURE 13E–1 Tectonic map of Asia showing major active faults (heavy lines). Arrows indicate sense of motion. (From P. Tapponnier and P. Molnar, 1977, Journal of Geophysical Research, v. 82, p. 2905–2930, © American Geophysical Union.) ASIA ASIA F2 SOUTH CHINA SOUTH CHINA F1 SOUTH CHINA SEA SOUTH CHINA SEA INDIA INDIA INDOCHINA INDOCHINA ANDAMAN SEA ANDAMAN SEA 3 0 centimeters (a) (b) FIGURE 13E–2 (a) Plasticine model of escape tectonics involving a rigid indenter and several laterally moving blocks. (b) Sketch of the deformation in (a). Note the pull-apart basins along both faults (F1 and F2). (From P. Tapponnier, G. Peltzer, A. Y. Le Dain, R. Armijo, and P. Cobbold, 1982, Geology, v. 10, p. 611–616.) 328 | Fractures and Faults ESSAY continued 75° E 80° E 85° E 45° N i a 95° E 100° E a n S h T 90° E 105° E 110° E Gobi Desert 40° N n Ta r Ba im 40° N A lt Ordos Basin sin yn T h ag fa ult Qaid am Basin 35° N 35° N Sichuan Basin H i m a l a y a 30° N s 25° N 30° N Shillong Plateau GPS velocities 200 100 20 25° N mm/yr 0 20° N Indian Pla te 500 kilometers 75° E 80° E 85° E 90° E 95° E 100° E 105° E FIGURE 13E–3 Global positioning system (GPS) derived velocities (mm/yr) with respect to stable Eurasia from 553 control points within the Tibetan Plateau and around its margins, plotted on a shaded relief map. Arrow length is proportional to velocity. (Modified from Zhang et al., 2004, Continuous deformation of the Tibetan Plateau from global positioning system data: Geology, v. 32, p. 809–812.) importance. Thus, an additional incentive exists to study crustal deformation processes associated with the indenter mechanism and collision-related faults (both large and small), and to apply the results to earthquake prediction. Since the indenter mechanism was originally proposed, Davies (1984) has applied it to explain the origin of the Panafrican (Late Proterozoic) deformed belt in the Arabian Shield, and LeFort (1984) has used it to explain the structure of large faults and the curvature of the central Appalachians. No less important is the westward escape of the Turkish Plate from the northward-moving Arabian Plate indenter (Figure 13–11a), along a number of active faults. References Cited Burchfiel, B. C., 2004, New technology: New geological challenges: GSA Today, v. 14, no. 2, p. 4–10. Davies, B., 1984, Strain analysis of wrench faults and collision tectonics of the Arabian shield: Journal of Geology, v. 82, p. 37–53. LeFort, J.-P., 1984, Mise en évidence d’une virgation carbonifère induite par la dorsale Reguibat (Mauritanie) dans les Appalaches du Sud (U.S.A.), Arguments géophysiques: Bulletin Société Géologique de France, v. 26, p. 1293–1303. Molnar, P., and Tapponnier, P., 1975, Cenozoic tectonics of Asia: Effects of a continental collision: Science, v. 189, p. 419–426. Tapponnier, P., Peltzer, G., LeDain, A. Y., Armijo, R., and Cobbold, P., 1982, Propagating extrusion tectonics in Asia: New insights from simple experiments with Plasticine: Geology, v. 10, p. 611–616. Strike-Slip Faults | 329 Chapter Highlights • Most strike-slip faults are steeply dipping faults in which motion is directed parallel to the Earth’s surface along the fault. • Strike-slip faults form plate and other tectonic boundaries in both active and ancient orogenic belts, and may have displacements of hundreds of kilometers. • Changes in the orientation of strike-slip faults across restraining or releasing bends can produce upthrown blocks (rhomb horsts), rhomb grabens, folds, and even subsidiary normal and thrust faults. • Strike-slip faults are an integral part of foreland foldthrust belts, functioning as tear faults bounding thrust sheets and displacing thrusts. • Transtension involves both extension and strike-slip motion, whereas transpression involves both contraction and strike-slip motion. Both are common in orogenic belts. • Transform faults compensate differences in motion within a plate, requiring a fault to take up the difference. What may appear to be an ordinary strike-slip fault may have opposite motion sense dictated by plate motion. Questions 1. After reading this chapter, go back to Figure 13–2 and determine the motion sense on the San Andreas fault from the offset streams in the photo—is the San Andreas a dextral or sinistral strike-slip fault from your observations? 2. Why do strike-slip faults characteristically dip steeply? 3. How can strike-slip, normal, and thrust faults—as well as folds—all form in the same stress system? 4. Why do some strike-slip faults contain cataclastic material along their extent (or are single planar structures) but others contain mylonite and consist of zones several kilometers wide? 5. Why do some strike-slip fault zones contain mylonite that is cut through by later cataclasite? 6. What evidence supports the statement that some strikeslip faults are contractional structures? 7. Why must major strike-slip faults become some other type if they deviate from a small circle of the Earth? 8. How do strike-slip faults terminate? 9. Explain the origin of a rhomb graben. 10. Why does a ridge-ridge transform have a sense of motion opposite that of an ordinary strike-slip fault? 11. What distinguishes a ridge-ridge transform from a ridgearc transform? 12. What development in modern technology has assisted in the study of the kinematics of large faults and even plates? Further Reading Aydin, A., and Nur, A., 1982, Evolution of pull-apart basins and their scale independence: Tectonics, v. 1, p. 91–105. Describes strike-slip faulting and its relationships to the origin of pull-apart basins (rhomb grabens) and uplift (rhomb horsts), with numerous examples. Biddle, K. T., and Christie-Blick, N., 1985, Strike-slip deformation, basin formation, and sedimentation: Society of Economic Paleontologists and Mineralogists Special Publication 37, 386 p. Papers relating strike-slip faulting and formation of sedimentary basins. Several describe extensional settings; others, development of strike-slip faults and basins in compressional settings. Burchfiel, B. C., 2004, New technology: New geological challenges: GSA Today, v. 14, no. 2, p. 4–10. Provides a useful introduction to the use of GPS technology to address tectonic problems. Davis, G. A., and Burchfiel, B. C., 1973, Garlock fault: An intracontinental transform structure, southern California: Geological Society of America Bulletin, v. 84, p. 1407–1422. The Garlock fault—part of the San Andreas system—is interpreted as an intracontinental transform, in contrast with the San Andreas, which has been interpreted as a ridge-ridge transform as well as an intracontinental transform. Mann, P., 2007, Global catalogue, classification and tectonic origins of restraining-and releasing bends on active and ancient strike-slip fault systems, in Cunningham, W. D., and Mann, P., eds., Tectonics of strike-slip restraining and releasing bends: Geological Society, London, Special Publications 290, p. 13–142. doi:10/1144/SP290.2. An in-depth review of examples of restraining and releasing bends and discussion of the consequences of these features along strike-slip faults. 330 | Fractures and Faults McClay, K. R., and Bonora, M., 2001, Analog models of restraining stepovers in strike-slip fault systems: AAPG Bulletin, v. 85, p. 233–260. This paper summarizes the modern concepts and addresses the mechanics of formation of step-overs through deformation of layered clay models by varying the step-over width and geometry of the basement faults below that are reactivated to produce the deformation in cover sedimentary rocks. Powell, R. E., Weldon, R. J., II, and Matti, J. C., 1993, The San Andreas fault system: Displacement, palinspastic reconstruction, and geologic evolution: Geological Society of America Memoir 178, 332 p. A series of papers that chronicles the geologic history, geometry, and deformation along the San Andreas fault system in California. Quigley, M., and 12 others, 2010, Previously unknown fault shakes New Zealand’s South Island: Eos, Transactions, American Geophysical Union, v. 91, p. 469–470. Describes the effects of the September 4, 2010, magnitude 7.1 earthquake along a previously unknown fault, and the rapid scientific response to observe the effects of the earthquake. Illustrates the importance of immediate scientific observation of the movement on the Greendale fault, which had not moved in historic times. Sylvester, A. G., ed., 1984, Wrench fault tectonics: American Association of Petroleum Geologists Reprints Series 28, 374 p. Contains several classic papers on strike-slip faults. Several papers by J. C. Crowell, J. Tuzo Wilson’s paper defining transforms, J. S. Tchalenko’s paper on shear zones, and the comparative paper by R. E. Wilcox and others on wrench-fault tectonics all make good reading. Sylvester, A. G., 1988, Strike-slip faults: Geological Society of America Bulletin, v. 100, p. 1666–1703. An excellent review of the nature of strike-slip faults written for students, structural geologists, and other geologists. Tapponnier, P., Peltzer, G., Le Dain, A. Y., Armijo, R., and Cobbold, P., 1982, Propagating extrusion tectonics in Asia: New insight from simple experiments with Plasticine: Geology, v. 10, p. 611–616. Models the strike-slip tectonics of Asia, based on experimental work and the concept of a rigid indenter. The results are striking. 14 Normal Faults G. K. Gilbert’s recognition of the normal faulted structural style of the Basin and Range Province was one of the great discoveries in nineteenthcentury geology. Although chief geologist of the Wheeler reconnaissance, Gilbert was under the command of an army officer and had only three field seasons to explore the geology of large parts of Utah and Nevada. He was also conditioned to expect Appalachian geology in the Far West. He kept an open mind, however, and through careful observation together with hard work, hallmarks of a good scientist, he made many of the initial discoveries that provide some of the striking examples we will discuss in this chapter. Normal faults are dip-slip faults in which the hanging wall has moved down relative to the footwall (Figure 14–1). Normal faults are also the primary mechanism for extending and thinning the crust prior to the opening of a new ocean basin. At mid-ocean ridges normal faults control the morphology of the ridge itself and also greatly influence the nature of magmatism at these divergent margins. Only now are we beginning to understand the similarities and differences between extensional processes that form symmetrical rifts (such as the Gulf of California) and those producing asymmetrical extension (for example, the Basin and Range Province and the East African Rift). In many parts of the world, normal faults and their associated structures form important structural traps for hydrocarbon accumulation. Normal faults have been called gravity faults, implying that the primary motive force is gravity. They have also been called extensional faults because they typically extend layering, and thin the crust. Listric faults (Figure 14–2) have concave-up surfaces, flatten with depth, and steepen toward the surface. Listric faults may be either normal or thrust faults, as “listric” describes the geometry and not the sense of motion. Growth faults involve simultaneous deposition of sediment and fault motion. Many growth faults are listric normal faults and are common in sedimentary basins and along continental margins the world over. The labors of Pennsylvania geologists have rendered so familiar the structure of the Appalachians, that it has been accepted as typical of all mountains, and a comparison will facilitate an understanding of the basin ranges. Indeed, I entered the field with the expectation of finding in the ridges of Nevada a like structure, and it was only with the accumulation of difficulties that I reluctantly abandoned the idea. GROVE KARL GILBERT, 1874, Explorations and Surveys West of the One Hundredth Meridian 331 332 | Fractures and Faults N NE SW W 0 FIGURE 14–1 Tertiary normal faults cutting upper Pennsylvanian Honaker Trail Formation shale and sandstone northwest of Moab, Utah, on U.S. 191 directly across from the Arches National Park Visitor Center. (CMB photo.) 5 meters Properties and Geometry Earth’s surface Dip steeper up-dip toward surface Concave-up In many but not all instances, normal faults commonly have moderate to relatively steep angles of dip near the Earth’s surface. Early geologists inferred that normal faults propagate directly into crystalline basement beneath the sedimentary cover and terminate at depth in the crust without change in dip. With the accumulation of better field and geophysical data, however, it is clear that many normal faults are listric and flatten into incompetent units at depth, displaying many of the detachment properties of thrust faults. Others pass from the sedimentary cover into the crystalline basement (Figure 14–3). Modern Gentle dip becoming nearly horizontal at depth Motion can be either normal or thrust FIGURE 14–2 Characteristics of listric faults. Note that they apply to both normal and thrust faults. Confusion Range 0 kilometers 5 D Snake Range décollement House Range D M S S 10 15 20 25 Shot-point 1 number ? Pliocene–Quaternary Miocene–Oligocene Mesozoic Jurassic–Triassic Paleozoic Permian–Pennsylvanian Mississippian Devonian 200 ? Silurian Ordovician Cambrian limestone Cambrian clastics Precambrian clastics 0 Moho (?) reflections 10 kilometers 400 600 800 FIGURE 14–3 East-west cross section through the eastern Basin and Range Province in Utah showing flattening characteristics of listric normal faults (ticks), thrusts (solid teeth), and older thrusts inverted as normal faults (closed teeth with ticks). Section is based on the COCORP Utah #1 seismic reflection line. (From Allmendinger et al., 1983, Geology, v. 11.) (Continued on facing page.) Normal Faults 333 | Earth’s surface Brittle behavior Brittle upper crust Increasing ductile behavior with depth A Ductile-brittle transition 0 1 A' kilometer Ductile lower crust FIGURE 14–4 Listric (concave-up) normal fault flattens into the ductile-brittle transition. seismic reflection profiles, coupled with surface studies, suggest that many normal faults flatten into the crystalline basement at the ductile-brittle transition (5 to 15 km of depth) (Figure 14–4). More recent work has demonstrated that low-angle normal faults are more common than previously thought and, because of their geometry, facilitate a significant amount of crustal extension. Normal faults display many of the branching characteristics of thrust and strike-slip faults (Figure 14–5a). Splays occur along normal faults. Synthetic faults dip in the same direction as the master fault and join the master fault at depth (Figure 14–5b). Antithetic faults likewise join the master fault at depth, but dip in the opposite direction. Paired normal faults exist where related blocks are flanked by parallel-striking faults that dip either away from the blocks or toward them (Figure 14–6). A graben is a (a) Synthetic fault Surface A Antithetic fault Synthetic fault A' Antithetic fault 0 1 kilometer (b) FIGURE 14–5 Branching characteristics of normal faults. (a) Anastomosing splays: ball-and-stick pattern on faults indicates the downthrown side (map view). (b) Synthetic and antithetic faults (cross section). Sevier Desert Canyon Range Pavant Range thrust Gulf No. 1 Granning Canyon Range thrust O 0 ? 5 Base of shallow layered reflections Sevier Desert detachment 10 15 Numerous short, discontinuous seismic events 20 25 800 1,000 FIGURE 14–3 (continued) 1,200 1,400 1,600 kilometers ? 334 | Fractures and Faults Down-dropped central block (a) High central block (b) Asymetric down-dropped block (c) (d) FIGURE 14–6 Graben (a), horst (b), and half-graben (c) structures. (d) Oblique aerial photo of grabens and horsts in Canyonlands National Park, Utah. Here the valleys outline the grabens and the topographic highs define the horsts. Photo courtesy of Jesse Varner (https://www.flickr.com/photos/molas/53874036). structural trough developed between two normal faults that dip toward each other, with a down-dropped block between. A horst is a relatively upraised block flanked by symmetrical normal faults that dip away from the horst. Although horsts and grabens are common in many extensional settings (including planetary bodies such as Mars and Europa), the total amount of crustal extension generated across these structures is small due to the symmetric nature of the normal faults that must terminate at depth. The mountains and alluvium-filled valleys of the Basin and Range Province, which extend from southern Idaho southward into Mexico, may seem a classic graben-and-horst region, with the ranges as horsts and valleys as grabens, but crustal extension over geologic time has created a more complex geometry of tilted fault blocks and half-grabens. The Rhine graben region of Germany and Switzerland is dominated by a single, large down-dropped crustal block, but within it are many smaller horsts and grabens. A half-graben is a structural block bounded by a normal fault on one side that is commonly filled by sediment to form an asymmetric basin. The bounding normal fault for most half-grabens is listric, and in certain situations a suite of synthetic normal faults develops above the master listric fault. This can lead to a series of rotated normal fault blocks also known as a domino-style or book shelf fault system. In eastern North America, a suite of Triassic to Jurassic half-grabens (and to a lesser extent grabens) formed during the continental rifting 200 Ma that ultimately formed the Atlantic Ocean. Normal faults may also be related to folding. Some normal faults at depth pass into monoclinal folds near the surface or along strike (Figure 14–7). The shape of the fold is frequently related to the shape of the fault surface. Good examples occur in the Colorado Plateau, where some normal faults pass into monoclines along strike, although many of these have been interpreted as high-angle thrust Normal Faults (a) Monocline Normal fault (b) FIGURE 14–7 (a) Up-dip termination of a normal fault into a monoclinal drape fold (cross section). (b) Monocline grading along strike into a normal fault. faults. A normal fault may break and displace basement rocks but die out upward into the sedimentary cover, producing a drape fold in the sedimentary cover rocks. Drape folds also form in association with steeply dipping basement thrusts, as in the Rocky Mountain Front Ranges of Colorado and Wyoming. Drag folds (Chapter 10) form because of friction along the fault surface and occur along normal faults; they provide tangible evidence of fault kinematics due to the sense of shear of the folds along the fault. Reverse drag folds and rollover anticlines form along growth faults Breakaway zone Mylonite exposure Half-graben complex Low strain core of metamorphic rocks FIGURE 14–8 Schematic cross section illustrating the architecture of a typical metamorphic core complex. (Modified from G. S. Lister and G. A. Davis, 1989, Journal of Structural Geology, v. 11, p. 65–94.) | 335 where the part of the downthrown block close to the fault is displaced downward more than the parts farther away (see Figure 10–15). These structures are related to the listric shape of the faults on which they commonly form. Rollover anticlines are targets for petroleum exploration, and in the Gulf Coast have proved highly productive. The geometry and evolution of normal fault systems in the Gulf Coast region have been described by Cloos (1968), who modeled them in clay-block experiments. His experiments demonstrated the concave-up listric shape of these faults in three dimensions. Cloos also successfully modeled the map pattern of normal faults in Texas and Louisiana, where their concave shape faces southward toward the Gulf of Mexico. Low-angle normal faults were generally unrecognized because most low-angle faults were mapped as thrust faults and the mechanics of faulting (Chapter 11) indicate that normal faults should develop at dip angles of ~60°. Starting in the 1970s, however, low-angle normal faults were recognized in the Basin and Range as well as in orogens like the Caledonides and Alps. Seismic reflection data, generally acquired by the petroleum industry, indicate that low-angle structures are common in many sedimentary basins and extensional settings. Low-angle normal faults are also known as detachment faults and may be described as having both an upper plate and a lower plate. The recognition of detachment faults and metamorphic core complexes in the late 1970s and early 1980s dramatically changed the understanding of both the mode and magnitude of extension in the continental crust. Basin and Range core complexes represent midcrustal blocks that were tectonically exhumed during large-magnitude Tertiary extension (Davis and Coney, 1979; Crittenden et al., 1980; Davis, 1980). The basic architecture of a core complex includes mid-crustal rocks in the lower plate, a gently to moderately dipping detachment fault, and an upper plate with allochthonous cover rocks (Figure 14–8). Lower plate rocks are exposed in mountain ranges with a characteristic topographic form and bounded by the detachment fault on the range flank. In many core complexes, syntectonic basin deposits unconformably overlie the detachment fault and upper plate rocks (Figure 14–8). The detachment fault Transported cover rocks My loni te z one Basin fill Upper plate Detachment fault Lower plate ? 336 | Fractures and Faults commonly forms within the ductile-brittle transition, but because of the movement history of these faults, curviplanar mylonite zones are common in the lower plate immediately below the detachment fault (Figure 14–8). These mylonite zones are typically 1–2 km thick and pass downward into rocks with lower strain. Mylonites are commonly overprinted by brittle deformation upward toward the detachment fault, as the lower crustal rocks are exhumed into upper crustal conditions. Metamorphic core complexes form a distinctive element of the Basin and Range Province from Sonora in Mexico to British Columbia in Canada, but have also been recognized in Greece, Turkey, the Caledonides, Tibet, and along mid-ocean ridges. Extensional detachments and the underlying core complexes are intriguing structures. Most that can be closely examined in the Basin and Range (Figures 14–9 and 14–10) consist of a fault surface underlain by a thin (several centimeters thick) layer of microbreccia (extremely fine-grained breccia). These breccias are developed across thicker (up to several hundred meters) chloritized breccias that formed during the shearing and retrogression of footwall mylonitic gneisses. The mylonitic gneisses were formed at depth along the detachment faults by extensional ductile shear and then were carried upward in the footwalls of the faults. Upper-plate rocks typically exhibit only brittle deformation, usually by brittle normal faults (Coney, 1980; Davis, 1980). An excellent smaller-scale example of this are the Turtlebacks along the eastern flank of Death Valley in California (Figure 14–11), part of the strike-slip pull-apart system first described in this area by Burchfiel and Stewart (1966) (Chapter 13). Here, semi-consolidated continental B g C f c e d a b FIGURE 14–9 Typical Cordilleran metamorphic core complex. A—basement. B—cover. C—detachment. a—older metasedimentary rocks. b—older pluton. c—younger pluton (early to middle Tertiary). d—mylonitic foliation. e—mylonitic l ineation. f—marble (blue). g—lower to middle Tertiary sedimentary and volcanic rocks. (From P. J. Coney, 1980, Geological Society of America Memoir 153.) A Plio-Pleistocene sediments are brittlely deformed above a detachment zone that underwent a transition from a brittle upper part to near-ductile deformation in the lower portion (formation of microbreccia and protomylonite) at and below the detachment at the contact with the 1.8-Gaold Proterozoic basement. This transition is only about 2 to 3 m thick. The detachment had to be located within 5 km of the surface when it formed, although the actual ductile deformation may have been brought up from greater depth along the footwall. The thermal gradient could also have been steep at the time the detachment was active, producing high heat flow. Evidence of abundant fluid is present at the exposed contact in the form of chlorite formed as an alteration product of biotite in the ductilely deformed basement gneiss. The Whipple Mountains detachment in southeastern California (Figure 14–10) is another excellent example: in many places, moderately to steeply dipping upper-plate structures have clearly been truncated by the underlying detachment (Davis and Lister, 1988). Environments and Mechanics Normal faults are commonly described as brittle structures that develop only in the upper crust. Those formed near the surface generally have sharp contacts, “damage zones” with cataclastic rocks, and rotated blocks (or horses) characteristic of brittle fault zones; if formed deep in the crust, they exhibit ductile features—notably, mylonites—and develop thicker ductile shear zones. The large detachment-style normal faults produced by crustal extension, as in the Basin and Range Province, probably formed in the ductile-brittle transition. Let’s examine the character of normal faulting in two dimensions with the aid of the strain and stress ellipse and assume coaxial strain (Figure 14–12). Ideally, normal faults dip more than ~60° and form on shear planes that are bisected by a vertical (Z) axis, with the maximum principal strain axis (X) horizontal. The Y axis lies in the fault plane parallel to the intersection of the conjugate normal faults. The stress ellipsoid involves a vertical maximum principal stress (σ1) and a horizontal σ3, with σ2 lying within the fault plane (Figure 14–12). As with other faults and fractures, the rules for fluid pressure, buoyancy, and reduction of frictional resistance (Chapter 11) all apply to normal faults. Upward propagation of a normal fault—as argued by Price (1977)—may result from hydrofracturing by overpressured fluid, generally water. When pore-water pressure exceeds the tensile strength of a potential glide zone within part of a listric fault zone, hydraulic fracturing Normal Faults 337 | Elevation (m) (a) SW NE WDF 1,000 Tvs 500 SL Tvs WDF upxln 0 (b) mgr mgr 1,000 WDF mgr 500 SL 3 kilometers FIGURE 14–10 (a) View of the Whipple Mountains, California, looking southwest along the axis of the Whipple Peak antiform. The detachment fault is the light-dark contact that wraps around most of the range. Dark rocks in the upper plate consist of Miocene volcanic and sedimentary rocks, which were deposited on upper-plate crystalline rocks that form the light-colored area in the lowest portion of the photo. Light-colored rocks forming most of the range are lower-plate mylonitic gneisses that sit structurally beneath the nonmylonitic gneisses that compose the low-relief lower plate in the western part of the range (upper-right part of photo). (E. J. Frost, San Diego State University.) (b) Cross section across the Whipple Mountains, illustrating middle Miocene geologic relations before domal uplift and warping of the Whipple detachment fault (WDF). The cross section illustrates evidence for multiple phases of rotational normal fault displacement along the detachment surface. Tvs—Tertiary sedimentary and volcanic rocks. mgr—mylonitic granitic rocks. upxln—upper-plate crystalline rocks. (Modified from unpublished section courtesy of G. A. Davis, University of Southern California.) occurs. Frictional resistance to movement falls to zero, and the fault block moves, causing the fracture to propa gate upward—still under high water pressure—until the entire block moves along the fault. The block thus formed is bounded by a listric surface or is a rotational slide block. Many rotational blocks formed in the Government Hill landslide during the 1964 Mw 9.2 Good Friday earthquake in Prince William Sound near Anchorage, Alaska (Figure 14–13). Growth Faults Growth faults commonly form in relatively unconsolidated sediments during deposition and produce thickened stratigraphic units on the downthrown side (Figures 14–14 and 14–15). These sediments cannot sustain shear stress, so they move under the influence of gravity. Listric normal growth faults on modern continental margins are among the best examples of gravity faults because they can move 338 | Fractures and Faults FIGURE 14–11 The Turtlebacks along the eastern side of Death Valley National Monument, California. (a) Curved surfaces, such as the one here that gave the Turtlebacks their name, result from detachment faulting where PlioPleistocene sediments (light colored) have moved relatively down toward the valley in the foreground, leaving the erosionally exposed, 1.8-Ga Proterozoic basement gneisses (dark colored) visible in the footwall on the dome-shaped turtleback surface. (b) Close-up of a detachment zone. Ductile to semiductile deformation at the base of the fault zone in the Proterozoic rocks gives way upward to brittle deformation in the poorly consolidated overlying Plio-Pleistocene sediments. (Locality courtesy of John C. Crowell, University of California, Santa Barbara; RDH photos.) Precambrian P r b basement b Pr Pr b Precambrian b basement De h De Detachment fault P o-P -P P Plio-Pleistocene d sediments (a) (b) σ1 Primary fault plane σ2 (a) Z Conjugate fault plane Y σ3 l X (b) l + ∆l (c) FIGURE 14–12 Stress (a) and strain (b) ellipse for normal faults in cross section. (c) Sequential sections of the crust before and after normal faulting and extension, showing displacement taking place primarily as horizontal extension. A crustal segment of original length l is extended and thinned to a new length l + Δl, where the actual amount of extension, Δl = β (McKenzie, 1978). Normal Faults | 339 FIGURE 14–13 Normal faulting affecting the Government Hill Elementary School occurred as collateral damage during the March 28, 1964, Prince William Sound earthquake near Anchorage, Alaska. The downthrown side of the fault is to the left, producing a displacement of ~7 m (30 ft); tilting is related to the rotational nature of the normal faults. (U.S. Geological Survey.) Post-growth deposit Pre-growth sequence (a) Growth sequence (b) FIGURE 14–14 Geometry and characteristics of growth faults. (a) Uniform deposition before faulting. (b) Deposition continues during faulting, with excessive accumulation of sediment on the downthrown block of the fault. Movement ceases, but deposition continues on both sides of the fault. Compare with Figure 14–15. only under the influence of gravity. Their movement may be accelerated or slowed by the variations in load produced by different sedimentation rates. Loading of the downthrown side—the depocenter for rapidly deposited sediment—may accelerate motion. Frequently, the timing of slip on growth faults can be determined from sediment that has been deposited across the fault. Changes in relative thickness across the fault are therefore keys to timing of motion and also to recognition of the growth fault. The situation is unique because material is transported from one fault block to the other, both during and after movement on the fault. Xiao and Suppe (1986) presented evidence suggesting that the curvature of listric normal growth faults is related to compaction of unconsolidated sediments after deposition on the downthrown blocks of growth faults. The actual slip along growth faults, and possibly other large normal faults, could also be attributable to block rotation of the hanging wall (Xiao and Suppe, 1992; Groshong, 1993). In the Gulf Coast, overall movement along growth faults is toward the Gulf of Mexico basin. As a result, the faults tend to form arcuate, steplike patterns roughly concentric to the Mississippi delta and the Gulf Basin (Figure 14–16; Cloos, 1968). The term down-to-basin faults is frequently used because the downthrown side is always toward the Gulf Basin. These are also classic listric faults that flatten downward into a detachment in the sedimentary section. In the Gulf Coast, the detachments may be localized in either weak “geopressured” shales (actually unconsolidated shales—muds—containing excess trapped pore water), or they may propagate in the extensive underlying Jurassic salt unit. Blocks thus formed are analogous to rotational landslides and slump structures. Contraction and thrusting occur at the toes of both of these structures (Figure 14–17) because of the change during movement from extension at the rear to contraction at the toe. The entire process of down-to-basin faulting in the Gulf Coast and in other regions is intimately related to movement on either salt or other plastic materials (Figures 14–18, 21–20, 21–21, and 21–22). It has been modeled as a thin-skinned extension process in which the cover sediments behave 340 (a) FIGURE 14–15 Seismic reflection profile (a) and interpretation (b) showing the geometry of the Corsair fault complex—a major growth fault with many smaller synthetic and antithetic normal faults, and accompanying rollover along the Corsair trend in the U.S. Gulf Coast. (Courtesy of A. F. Christensen and Shell Offshore, Inc.) miles kilometers (b) FIGURE 14–15 (continued) 341 342 | Fractures and Faults 100° W 95° W 90° W 85° W AR East Texas basin Sabine uplift Louisiana salt g An sis si sal ppi t ba sin e LA Limit of salt Wiggins uplift FL 30° N 30° N Balcones fault zone AL Mis basin TX ur l flex ldwel a-Ca elin MS Monroe uplift North Northeast Gulf basin Rioande Gr Limit of salt ne t ymen emba ult ir zo Southern platform fa rsa Co ss ssi Limit of salt elt a ulip ma h Ta arc Mexico elt db fol ldb o fo Gulf of Mexico Pe rdid 25° N Burgos bas in Mi i ipp n Fa an s e Oc t rus c 90° W 25° N 0 100 200 300 kilometers 95° W 100° W FIGURE 14–16 Map of part of the U.S. Gulf Coast showing distribution of major regional growth faults (ticked lines) and salt diapirs (gold). The striped pattern covers the limit of salt—an area that has detached and moved toward the Gulf Basin. The southeastern edge has overthrust the sediments on the floor of the basin and produced the Perdido and Mississippi Fan foldbelts. (Modified from Plate 2, Principal Structural Features, The Gulf of Mexico Basin, compiled by Ewing and Lopez, in Salvador, The Geology of North America, Geological Society of America, v. J, 1991. Used by permission.) Listric normal faults Thrust faults 0 2 meters FIGURE 14–17 Cross section in a landslide or slump structure showing rotational character of normal faults and thrusting of the toes of listric faults in sediments. Curved arrows indicate counterclockwise rotation of blocks. Normal Faults | 343 Rift Zones 0 1 2 3 0 5 centimeters FIGURE 14–18 Salt tectonics in a region undergoing thinskinned extension above a salt detachment, from experiments by Vendeville and Jackson (1992a, 1992b) using silicone (gold) for salt and unornamented sand layers for brittle cover sediments (0). (1) Reactive stage; (2) active stage; (3) passive diapirism (or piercement) stage. Also see Figures 21–20, 21–21, and 21–22. (From Vendeville and Jackson, Marine and Petroleum Geology, v. 9, 1992. Used by permission.) almost passively in response to deformation in the underlying salt (Vendeville and Jackson, 1992a, 1992b). Thickening and thinning of the cover sequence, however, as products either of variations in the primary depositional framework and sediment dispersal patterns or of tectonic extension, provide zones where diapiric upwelling and piercement of salt can occur, forming most of the familiar salt structures (Chapter 2). Growth faults appear to be primarily aseismic. Areas where active growth faults are known to occur are commonly areas with little to no seismicity. Continuous and very recent movement on growth faults has been demonstrated in the Texas Gulf Coast, which is seismically one of the least active regions in North America. High fluid pressure in the fault blocks and the relatively unconsolidated nature of the sediments induce a state of stable sliding (Figure 11–8), and the blocks move (creep) aseismically toward the Gulf of Mexico. Narrow linear zones where the crust has been extended, producing grabens, half-grabens, and other structures associated with normal faults, are called rifts (Figures 14–19a and 14–20); they form major tectonic belts worldwide. Such rifts may presage formation of a new ocean basin or a major zone of crustal extension. Rifts have traditionally been thought to result from symmetric thinning of continental or oceanic crust, and the structure of rift zones along mid-ocean ridges supports that assumption. Based on earthquake epicenter locations and first-motion studies, McKenzie et al. (1970) concluded that such a symmetrical spreading pattern exists in the Red Sea and the East African Rift. They also concluded that, although spreading is symmetrical perpendicular to a rift axis, it may decrease to zero along the axis to a pole of rotation. These ideas have since become known as the “McKenzie model” of rift formation (Figure 14–20), although newer evidence suggests that the Red Sea and East African Rift formed by asymmetric rifting (Figure 14–19c). Aulocogens are large-scale tectonic troughs, bounded by normal faults that form within continental crust at a high angle to a nearby continental margin. Burke and Dewey (1973) suggested that aulocogens result from failed formation of a ridge-ridge-ridge triple junction above a mantle plume where two spreading ridges have developed, but the third does not continue to develop and spread apart beyond the initial rifting stage (Figure 14–19b). The result is a failed rift, or failed arm, which is typically filled with a great thickness of sediment. Examples include the Mississippi embayment, the southern Oklahoma/Wichita aulocogen, and the Lusistanian basin off the west coast of Iberia. Rift basins, such as the Triassic-Jurassic basins of eastern North America, commonly form as basins prior to the opening of an ocean. Formation of some eastern North American basins also involved a strike-slip component in addition to extension. In contrast, the Gregory Rift of the East African system has been shown to be an asymmetric rift (Bosworth et al., 1986); there, the master fault occupies the east side of the rift and is down toward the west for more than 100 km along strike (Figure 14–19c), but then changes to the west side and becomes down to the east for more than 100 km north and south. Regional Crustal Extension Large-scale extension of continental crust occurred in the Basin and Range Province during middle to late Tertiary time (Eaton, 1979; Coney, 1980; Wernicke and Burchfiel, 1982; Wernicke, 1985). The crust there has been vertically thinned by at least 25 percent during lateral extension, and in some areas more than 500 percent (Miller et al., 1983; Gans, 1987). Gans (1987), using crustal balance calculations, estimated the eastern Basin and Range across central Nevada has been extended 77 to 140 percent. 344 | Fractures and Faults Precambrian Crust Mantle Moho Oligocene Continental lithosphere Sea level Asthenosp here SL Early Miocene SL Middle Miocene SL ~3.5 Ma SL Salt Carbonate buildups ? Present 0 Ocean crust Salt New Moho theoretical position 100 kilometers (a) No vertical exaggeration Continent A Failed rift (arms) Continent A Continent B Line of future rift Continent B Successful rift begins to open, forming new ocean Continent A Future potential triple junction Continent A Sediment-filled aulocogen, or failed rift New ocean Continent B Potential failed arm (1) (b) Continent B (2) New ocean opens, deposition occurs along margins and in failed rifts FIGURE 14–19 (a) Cross section through the Red Sea Rift, constructed assuming rifting was symetrical. (From Lowell and Genik, 1972, AAPG Bulletin, v. 56. Reprinted by permission of American Association of Petroleum Geologists.) (b) Failed rifts and aulocogens formed at RRR triple junctions (Figure 1–10c). (c) (following page) Interpretive map (1) and cross section (2) of fault geometry in the Gregory Rift of the East African rift system made from LANDSAT images. Note asymmetry along the length of the rift, indicating that even supposedly classic symmetrical rifts may prove to have been formed by asymmetric extension. (From W. Bosworth, J. Lambiase, and R. Keisler, EOS, v. 67, © July 1986, American Geophysical Union.) Normal Faults Elgeyo Escarpment N Baringo–Bogoria subbasin Lake Baringo A' Movement on Elgeyo detatchment A Lake Bogoria Metkei Forest Lake Ol Bolossat Menengai Crater re da er st Ab ore F Metkei–Marmanet accommodation zone Breakaway zone for Aberdare detachment Lake Nakuru Nakuru–Naivasha subbasin Lake Elemenaita Lake Naivasha st ore uF Ma Movement on Aberdare detachment Susua 0 50 kilometers Nairobi Kedong–Ngiro accommodation zone Ngong Hills Gregory Rift Figure location Kavirondo Rift Kenya Lake Victoria Indian Ocean Tanzania Nguruman Nairobi t Escarpmen (c) (1) Elgeyo Escarpment A Baringo-Bogoria sub-basin Lake Magadi Magadi–Natron subbasin Lake Natron Stepped flexural margin A' Depth (km) 5 5 10 15 Brittle-ductile transition 20 Elgeyo detatchment 0 20 kilometers (c) (2) FIGURE 14–19 (continued) 1.5× vertical exaggeration 10 15 20 Depth (km) 0 0 | 345 346 | Fractures and Faults Gently dipping faults in the Basin and Range, now exposed at the surface, were at first interpreted as thrusts. Many geologists were surprised that there are low-angle normal faults in the Basin and Range. Thrusts do exist here, but many of these faults have been reinterpreted as segments of crustal-scale listric normal faults. They dip gently today because they either formed as low-angle segments that have been erosionally exhumed or are tectonically rotated steeply dipping faults. Steeply dipping upper crustal segments may flatten into the ductile-brittle transition during crustal spreading and thinning. Uplift and erosion have now exposed old low-angle detachments at the surface. Because of a constant heat flow rate, new levels of subhorizontal detachment form deep in the crust as the depth of crustal extension and detachment within the ductile-brittle transition remains constant. Uplift and erosion cause existing detachments to become inactive, and as extension continues, new detachments form beneath them (Eaton, 1979; Miller et al., 1983). Several models were proposed during the 1970s and 1980s to explain regional crustal extension (Figure 14–20). All are based on the fact that many low-angle fault surfaces in the Basin and Range are erosionally exhumed normal faults. Models have been developed involving one of these mechanisms: (1) symmetrical extension and pure shear, suggested by Proffett (1977), Eaton (1979), and Hamilton (1982), which is basically an application of the McKenzie (1978) model; (2) asymmetric extension involving simple shear zones and a master detachment cutting through the entire lithosphere (Wernicke, 1985); and (3) asymmetric extension and simple shear involving delamination of the lithosphere (Lister et al., 1986). The symmetrical-extension model explains thinning of the crust but not the asymmetric geometry of several extended regions, such as the Basin and Range; this model was undoubtedly based on consideration of symmetrical rifts such as the Gulf of California and the mid-ocean ridges. Many geologists who work directly with extended regions have accepted some form of Wernicke’s asymmetric-extension model, analogous to the structure shown in Figures 14–4 and 14–20b. They regard symmetrical extension as having only historical interest or being applicable in very specific circumstances. Symmetrical extension may, however, still be the mechanism for crustal extension that produced the major features, such as the opening of the Atlantic Ocean (Schlische et al., 2003) and the Red Sea. Formation of crustal listric normal faults and resulting large-scale extension has been suggested to explain the opening of the Bay of Biscay between France and the Iberian Peninsula (de Charpal et al., 1978). Seismic reflection McKenzie pure-shear model Lithosphere Brittle upper crust Ductile lower crust Ductile upper mantle (a) Wernicke asymmetric simple shear model Asthenosphere Magma 0 (b) 40 kilometers Delamination model No vertical exaggeration (c) FIGURE 14–20 Three models of extension of continental crust. (a) McKenzie “pure-shear” model: symmetrical rifting and pure shear. (b) Wernicke model: asymmetric rifting with simple shear. (c) Delamination model: asymmetric rifting with simple shear and delamination of the crust and lithosphere. (From G. S. Lister, M. A. Etheridge, and P. A. Symonds, Geology, v. 14, 1986.) Normal Faults 1069 1065 901 347 Hyperextension of Continental Crust and Mantle profiling in the Bay of Biscay reveals large normal faults that dip steeply in the upper crust and appear to flatten into a major detachment zone in the lower crust. The detachment horizon is interpreted as the ductile-brittle transition. Such faults are thought to be extensional normal faults like those in the Basin and Range Province. Stretching | Crust formed by extension taken to the extreme is called hyperextended crust (Figure 14–21). This phenomenon was discovered in seismic reflection profiles and rocks Post-rift sediments 0 Syn-rift sediments 10 30 Depth (km) 20 900 1067 Pre-rift sediments Upper continental crust Qtz-fsp-rich middle–lower continental crust Lower continental–mafic crust Embryonic slow-spreading oceanic crust 40 (a) Upper–rigid 1069 1065 901 0 1277 897 899 1070 Infiltrated mantle 10 1067900 1068 20 30 Lithospheric/asthenospheric mantle 1300° C Asthenospheric mantle Poly-phase deformation structures 40 (b) 899 1070 897 Exhumation 1068 900 1069 1067 Lithospheric mantle Serpentinized mantle Depth (km) Thinning Lower–plastic Accommodating shear zones Ocean Drilling Program drilling sites 1065 901 0 1277 20 30 Depth (km) 10 40 Sea-floor spreading 1276 1277 1068 900 899 1070 897 1069 1067 1065 901 0 10 20 30 40 (d) FIGURE 14–21 Extension stages involving hyperextension that lead to rifting and breakup of continents that had previously been joined. Evolution of rifting between Iberia and Newfoundland during the opening of the Atlantic. Parts a–d summarize the different modes of extension leading to continental break up. (a) The stretching mode involves high-angle listric faulting associated with halfgraben subsidence; continental crust is slightly stretched and sedimentary basins are developed independently, affecting a broad region. (b) The thinning mode involves conjugate decoupled systems of detachment faults that accommodate exhumation of deep crustal and/or mantle levels. (c) The exhumation mode involves detachment faults that crosscut the brittle crust and expose serpentinized mantle rocks on the sea floor. (d) Final sea floor spreading produces irreversible localization of thermal and mechanical processes in a narrow zone forming a proto-ridge. (From G. Péron-Pinvidic and G. Manatschal, 2009, International Journal of Earth Sciences, v. 98, issue 7, p. 1592.) Depth (km) (c) 348 | Fractures and Faults dredged from the ocean floor in the continental margins off Newfoundland and Iberia, and has also been discovered along the opposing Brazilian and Angolan margins (Unternehr et al., 2010). Mantle rocks (peridotite) exposed on the ocean floors have geophysical properties (poorly defined Moho, weak magnetic properties, etc.) that distinguish them from oceanic mantle, and were concluded to be hyperextended continental mantle (Péron-Pinvidic et al., 2007). Another property of this mantle and associated continental crust is that there was only intermittent melting of mantle to produce ocean-floor basalt, likely related to the large amount of highly asymmetric extensional deformation related to very slow sea floor spreading occurring here (Jagoutz et al., 2007). Over time, the spreading rate increases and normal oceanic crust (N-MORB) begins to form as spreading rate and melting increase. This process is preserved in the Err detachment in the eastern Alps (southeastern Switzerland) and the Briançonnais nappe in the French Pennine Alps (Masini et al., 2013). As the process that leads to continental breakup begins, the continental block undergoes stretching with deposition of first pre-rift followed by syn-rift sediments, together with some normal faulting on the flanks of the continental mass and in the interior (Figure 14–21a). This is followed by thinning of the continental crust and mantle, and uplift in the newly forming rift zone. This is the beginning of the hyperextension process (Figure 14–21b). Both upper and lower mantle material are brought up into the area beneath the rift. Hyperextension continues as highly altered continental mantle is exhumed and exposed on the newly formed non-volcanic sea floor (Figure 14–21c), but it is only at the close of this stage that seafloor spreading and significant melting occur, forming normal ocean floor basalt (Figure 14–21d). The rifting process initially appears very symmetric, but becomes very asymmetric to accommodate hyperextension and upwelling of mantle (Péron-Pinvidic et al., 2007; Péron-Pinvidic and Manatschal, 2009). Oceanic Core Complexes We discussed the formation of “metamorphic core complexes” earlier in this chapter as features on the continents that are the product of asymmetric extension and low-angle normal faulting that commonly preserves brittlely deformed, unmetamorphosed sedimentary and volcanic rocks in the hanging wall, and ductilely deformed metamorphic rocks in the footwall. The fault zone preserves a vertical transition from brittle to ductile deformation. Similar features have been discovered using both advances in imaging technology and deep drilling along slowly spreading, largely non-volcanic oceanic ridge segments (Dick et al., 2003; Smith et al., 2006; Escartin et al., 2008). Apparently, low-angle detachment normal faults occur here that are characterized by brittle deformation in the hanging wall and ductile deformation in the footwall analogous to deformation in continental core complexes. Oceanic core complexes are the products of low-angle detachment normal faulting that expose lower crust (gabbro) and serpentinized mantle rocks on the sea floor that are ductilely deformed into strongly lineated rocks near the contact with the hanging wall, with the lineation oriented perpendicular to the ridge axis (Figure 14–22). Spr ead all gw De in ng tac Depth below sea floor (m) 44°30 ̶5000 ‒3000 ‒1000 Ha hm ent fau lt s ing dire ctio n urfa ce 23°40 'N N Gabbro 23°35 Ma ntle 'W 44°35 'W 30 44°40 km per tite s& dik bb es ro Ga 'W 'N 23°25 'N 44°45' W 44°50 Depth (m) 23°30 Corrugations La va ido 'W xis ea idg R 'N 23°20 'N FIGURE 14–22 Block diagram of part of the Kane oceanic core complex at 23°30’ N latitude on the Mid-Atlantic Ridge. (Modified from John and Cheadle, 2010, American Geophysical Union, Geophysical Monograph Series 188.) 349 | Normal Faults These low-angle normal faults have a few to >10 km of displacement and accommodate a major part of the plate motion that occurs along the ridge (John and Cheadle, 2010). of “pull-apart” extension forming transtensional basins (Figure 14–24). Collapse Structures and Related Features Normal faults are important geologic structures as they facilitate crustal extension and in many instances lead to the development of sedimentary basins with their attendant hydrocarbon resources. Normal faults and the rift systems they generate lead to the break-up of continents and the formation of new ocean basins, where normal faulting continues at mid-ocean ridges. Detachment faults and core complexes produce large amounts of crustal extension, but are also the structures where the middle and deep crust are commonly exhumed in extensional settings. Some normal faults occur as collapse structures related to the subsidence of magma chambers, and they may deform volcanoes and the tops of plutons (Figure 14–23). They form calderas and other structures, and function in the overall process of magma emplacement (Chapters 2 and 20); they also provide conduits for magma to reach the surface. The impact of large extraterrestrial bodies (bolides) on the Earth produces rebound structures in which normal faults may develop concentrically or radially (see Figure 2–35). As a result, a series of concentrically arranged horsts and grabens are exposed in a deeply eroded impact structure. Such structures, also called astroblemes, are known in many parts of the world, and are attributed to asteroids or comets colliding with the Earth. Some, such as Meteor Crater in Arizona, were formed as recently as the Quaternary. Others (for example, the Wells Creek and Flynn Creek structures in Tennessee) are Paleozoic or Mesozoic structures, and the Vredefort structure in South Africa was probably formed by an impact during the Precambrian. Final Thoughts Future Cobequid Highlands Future Antigonish Highlands Ancestral Hollow fault Stellarton Basin Cobequid fault (a) Chedabucto fault Stellarton Basin (b) Relationship to Strike-Slip Faults The geometry and sense of motion of normal faults was at one time thought to be unique and invariably related to gravity or to crustal extension. Strike-slip faults (Chapter 13) can be related to the formation of isolated normal faults and of horsts and grabens (rhomb grabens and rhombochasms). Resolution of strike-slip faulting into an extensional sense results from the stepping over of strike-slip motion from one fault to another across a zone Doming around intrusion creates normal faults X X X Diapiric intrusion X X X X X X X X X X X X X (c) N Cobequid Highlands Cobequid fault Volcanic vent forms along normal fault X X Stellarton Basin FIGURE 14–23 Normal faults developed in association with volcanoes and plutons. (d) Stellarton Basin H w o oll lt fau Antigonish Highlands Chedabucto fault FIGURE 14–24 Formation of a transtensional basin along the Cobequid, Chedabucto, and Hollow strike-slip faults, Nova Scotia, in map view. (a) Pennsylvanian dextral fault with a releasing bend allows subsidence on south side of incipient pull-apart basin. (b) Deformation becomes localized along the north side of the basin, forming extensional faults in response to transtensional strain. (c) Extensional faults are distorted with continued shear, with deformation returning to the south boundary. (d) Basin is translated close to present position by (Permian?) shear along Cobequid and Hollow faults. Juxtaposition with northeast-striking Hollow fault leads to transpression. (From J. W. F. Waldron, 2004, Anatomy and evolution of a pull-apart basin, Stellarton, Nova Scotia; Geological Society of America Bulletin, v. 116, p. 109–127.) | ESSAY Fractures and Faults Inverted Faults and Tectonic Inheritance An inverted fault formed with one sense of motion and was later affected by a differently oriented deformation that reversed the original sense of slip. It may be that any fault not folded can be affected by a later stress field that reverses the original motion sense. Fewer faults undergo any such history, because reversal requires that the fault surface be suitably oriented with respect to the new stress field. Later crustal deformation, however, appears to occur perpendicular to continental margins and older zones of crustal weakness, so that perhaps 40 percent of existing faults may have recurrent motion in the same (original) sense. Consequently, the tendency for reactivation of old faults must be related to the alignment of newly formed plate boundaries in a later tectonic cycle. Intermediate block Main graben Normal faults formed by rifting of continental margins may be inverted and reactivated as thrusts (McClay and Buchanan, 1992). Butler (1989) concluded that preexisting basin structure influenced the geometry of later thrusts in the Alps, and Bailey et al. (2002) documented a set of Early Cambrian normal faults in the Virginia Blue Ridge that controlled rift sedimentation during the opening of the Iapetus ocean and were then tectonically inverted during late Paleozoic contractional deformation. Some geologists have speculated that the crust may undergo later extension and normal faulting in a direction exactly opposite the direction of compression that earlier produced thrusting. One example of such a reversal is in the Viking graben, in the North Sea (Figure 14E–1). The Viking graben is a complex of extensional structures formed during Cenozoic Schill Grund high 0 2 4 6 Depth (km) 350 Mid-Late Cretaceous (before inversion) 0 2 4 6 Upper Jurassic (end sedimentation) 0 2 4 6 End Middle Jurassic 0 2 4 6 End Early Jurassic 0 2 4 6 Depth (km) 4 Depth (km) 2 Depth (km) 0 Depth (km) Mid-Paleocene (after inversion) Depth (km) Deep crustal detachment zone ~12 kilometers FIGURE 14E–1 Balanced regional cross section through part of the North Sea with successive back-stripping of sediments to the end of Early Jurassic (JL) time, showing older faults that remain beneath the Middle to Late Permian Zechstein (Ze) evaporite sequence. These faults were reactivated contractionally near the end of the Mesozoic and beginning of the Tertiary, producing uplift and erosion of some of the Cretaceous sediments, before sedimentation resumed during the Tertiary. The Viking graben thus formed during Jurassic extension and then was subsequently inverted. TR—Triassic. J—Jurassic. K—Cretaceous; L—lower; M—middle; U—upper. S—fault active during sedimentation (red line). Tan unit represents the basement beneath the sedimentary sequence. (Modified and reprinted from Journal of Structural Geology, v. 5, A. D. Gibbs, p. 153–160, © 1983, with kind permission from Elsevier Science, Ltd., Kidlington, United Kingdom.) Normal Faults the late Mesozoic and early Cenozoic (Gibbs, 1983). Where high-quality crustal seismic reflection data have been acquired, the later normal faults appear to have reactivated older thrusts originally formed during the early Paleozoic Caledonian orogeny. Some thrusts had been reactivated earlier, during the Devonian, and formed the extensional Old Red Sandstone basins (McGeary, 1987). Most of the exposed Triassic-Jurassic basins in the eastern United States trend parallel to the strikes of major contractional Appalachian faults. Some basins are localized along the outcrop traces of older faults, indicating a further genetic connection. The Ramapo fault that crosses the New Jersey–New York border is the northwestern border fault for the Triassic-Jurassic Newark basin (Figure 14E–2). After detailed structural studies along the Ramapo fault, Ratcliffe (1971) showed that it formed as a contractional fault during the Paleozoic. He showed that it was reactivated during the Mesozoic as an extensional feature and that it also underwent strike slip during the same period. Historical earthquake epicenters and present-day seismic S-D FIGURE 14E–2 Geologic map of part of northern New Jersey and southern New York showing the northern end of the Triassic-Jurassic Newark basin and the Ramapo fault and its extension northeast into the Hudson Highlands. pЄ and pЄf—Precambrian rocks (orange and cross-hatch pattern is igneous and highgrade metamorphic rocks; magenta and fine dot pattern is metasedimentary rocks). ЄO—Cambrian and Ordovician rocks. S-D—Silurian-Devonian. Lavender with a dot-and-ellipse pattern is sedimentary rocks; purple and cross-hatch pattern is volcanic rocks. U—Upthrown; D—Downthrown block of fault. (Modified from N. M. Ratcliffe, Geological Society of America Bulletin, v. 82, 1971.) ꞒO Newburgh ꞒO NY NJ ꞒO H U Hu ꞒO D ds o n pꞒ pꞒ ꞒO on River ds Hu ig s nd a hl pꞒ ꞒO nsville Annsville S-D pꞒf pꞒf NY CT ꞒO Pompton 41° N fa ul t m Triassic - Jurassic Ra ꞒO o ap Newark basin Peapack apac Long Island 0 10 kilometers 20 351 activity are also located along the fault, strongly suggesting that the Ramapo may once again be undergoing reactivation as a thrust. If so, it may be one of the best-documented examples of both inversion and tectonic inheritance, with a history spanning more than 350 m.y. The Ramapo fault has been interpreted to have weakened the crust to provide a conduit system for mafic intrusions (Figure 5–20). The phenomenon of fault inversion leads to both interesting and useful consequences. Inverted faults are important for accumulation of hydrocarbons in the North Sea (Hardman and Booth, 1991) and elsewhere. Formation contacts that were displaced during growth normal faulting must pass through null points of zero displacement upon being inverted as thrusts. If the youngest contact was not displaced before inversion, it is a null point before inversion begins but is moved from the null condition as initial movement occurs (Figure 14E–3a). The next lower contact moves toward and through the null condition as displacement continues, then the next lower contact moves as the 74° W ꞒO | 352 | ESSAY Fractures and Faults continued null points migrate down dip along the fault (Williams et al., 1989). Except for the growth aspects, the opposite occurs if a thrust is inverted as a normal fault (Figure 14E–3b). Mitra (1993), using both experimental models and natural FIGURE 14E–3 Consequences of inversion of (a) a normal fault by thrusting, and (b) a thrust fault by normal faulting. (From Williams, G. D., Powell, C. M., and Cooper, M. A., Geometry and kinematics of inversion tectonics, in Cooper, M. A., and Williams, G. D., eds., Inversion tectonics: Oxford, England, Blackwell Scientific Publications, Geological Society of London Special Publication 44, 1989. Used by permission.) examples, has suggested that contractional reactivation of earlier extensional structures occurs by fault-propagation folding, by inversion of planar faults, and by fault-bend folding by inversion of listric faults. C Null point 3 2 3 N Syn-rift sequence 2 1 E E 1 C Null point C E N 3 2 1 E Null point 3 2 C N 1 Null point migrates between these stages E C N 3 2 1 Extensional heave 3 2 E 1 Null point C N (a) (b) References Cited McClay, K. R., and Buchanan, P. G., 1992, Thrust faults in inverted extensional Bailey, C. M., Giorgis, S., and Coiner, L. V., 2002, Tectonic inversion and base- basins, in McClay, K. R., ed., Thrust tectonics: London, Chapman and Hall, p. 93–104. ment buttressing: An example from the central Appalachian Blue Ridge McGeary, S., 1987, Nontypical BIRPS on the margin of the North Sea: The SHET province: Journal of Structural Geology, v. 24, p. 925–936. survey: Geophysical Journal of the Royal Astronomical Society, v. 89, p. 231–238. Butler, R. W. H., 1989, The influence of preexisting basin structure on thrust Mitra, S., 1993, Geometry and kinematic evolution of inversion system evolution in the western Alps, in Cooper, M. A., and Williams, G. D., structures: American Association of Petroleum Geologists Bulletin, v. 77, eds., Inversion tectonics: Oxford, England, Blackwell Scientific Publications, p. 1159–1191. Geological Society of London Special Publication 44, p. 105–122. Ratcliffe, N. M., 1971, The Ramapo fault system in New York and adjacent Gibbs, A. D., 1983, Balanced cross-sections from seismic sections in areas of northern New Jersey: A case of tectonic heredity: Geological Society of extensional tectonics: Journal of Structural Geology, v. 5, p. 153–160. America Bulletin, v. 82, p. 125–142. Hardman, R. P. F., and Booth, J. E., 1991, The significance of normal faults in Williams, G. D., Powell, C. M., and Cooper, M. A., 1989, Geometry and kine- the exploration and production of North Sea hydrocarbons, in Roberts, A. M., matics of inversion tectonics, in Cooper, M. A., and Williams, G. D., eds., Inver- Yielding, G., and Freeman, B., eds., The geometry of normal faults: London, sion tectonics: Oxford, England, Blackwell Scientific Publications, Geological Geological Society of London, Special Publication 56, p. 1–13. Society of London Special Publication 44, p. 3–16. Normal Faults | 353 Chapter Highlights • Normal faults are dip-slip faults in which the hanging wall moves down relative to the footwall. • Normal faults accommodate crustal extension and basin formation, and commonly lead to the formation of horsts, graben, and half-graben. • Metamorphic core complexes are regions in which dramatic crustal extension has brought mid- to deep-level crustal rocks to the surface along a sequence of low-angle extensional ductile mylonite zones with normal displacement and brittle normal faults. • Listric normal faults are concave up normal or thrust faults that are common in a variety of tectonic settings. They can be important hydrocarbon traps. • Continental rifts and mid-ocean ridges are dominated by normal faults and their associated structures, including transforms. Questions 1. Why are normal faults also called gravity faults? 2. Why do normal faults splay and form antithetic and synthetic faults? 3. How do reverse drag folds form? Why are they commonly associated with growth faults? 4. How do normal faults terminate? 5. If a listric normal fault zone flattens downward into a detachment in shale, and a listric normal fault forms in the upper crust and flattens into a detachment in the ductilebrittle transition zone, how would you expect them to differ in appearance and in fault rocks (if any)? 6. How would you attempt to document the timing of motion on a growth fault? 7. Copy the geologic cross section of the Corsair fault complex in Figure 14–15b, then, using a piece of tracing paper, trace the main fault and restore all faults to an undeformed state. What can you conclude about (1) the growth rate through time and (2) the mechanical process of movement along the fault? Can movement on the fault be accounted for by rotation of a block, or must a component of simple shear (parallel to the fault surface or parallel to bedding) be involved, or both? See the article by Xiao and Suppe in the American Association of Petroleum Geologists Bulletin (1992, v. 76, p. 509–529), and the abstract by Groshong (1993, AAPG New Orleans Annual Meeting Abstracts, p. 111). 8. What kinds of evidence would help you to decide whether or not a particular fault has been reactivated with a sense of motion different from its original motion sense? 9. What kinds of data would you need to determine if rifting occurred by a symmetrical or asymmetrical mechanism in an area such as the East African Rift or the continental margins around the present Atlantic Ocean? Further Reading Brun, J.-P., and Choukroune, P., 1983, Normal faulting, block tilting and décollement in a stretched crust: Tectonics, v. 2, p. 345–356. Outlines a series of models for crustal thinning—ductile, ductilebrittle transition, and mechanical boundaries, such as shear zones, brittle faulting, and magma intrusion. All relate to the normal faulting process. Cloos, E., 1968, Experimental analysis of Gulf Coast fracture patterns: American Association of Petroleum Geologists Bulletin, v. 52, p. 420–444. Models the normal fault system of the Gulf Coast by subjecting clay blocks to extensional deformation. The listric geometry was successfully modeled, as was the major regional pattern of down-to-basin faults. Cooper, M. A., and Williams, G. D., eds., 1989, Inversion tectonics: Oxford, England, Blackwell Scientific Publications, Geological Society of London Special Publication 44, p. 105–122. Contains a spectrum of papers that discuss various aspects of the theoretical, experimental, and field setting of fault inversion. Coward, M. P., Dewey, J. F., and Hancock, P. L., eds., 1987, Continental extensional tectonics: Oxford, England, Blackwell Scientific Publications, Geological Society of London Special Publication 28, 637 p. An extensive array of papers dealing with extensional processes, geometry, and mechanics that presents numerous examples from a variety of settings. Gans, P. B., 1987, An open-system, two-layer crustal stretching model for the eastern Great Basin: Tectonics, v. 6, p. 1–12. Employs data from structural reconstructions of exposed ranges along with considerations of kinds and volumes of magma that have been erupted in the northern Great Basin to estimate the amount of crustal thinning and extension here. 354 | Fractures and Faults Jackson, M. P. A., and Vendeville, B. C., 1994, Regional extension as a geologic trigger for diapirism: Geological Society of America Bulletin, v. 106, p. 57–93. Most of the traditional ideas about the nature and origin of diapirs focus on the diapirs as nontectonic features and not on tectonic processes that may form them (see Chapter 2). This paper provides documentation that regional extension serves not only to trigger diapirs but provides the means to localize and track their evolution. Keen, C. E., Stockmal, G. S., Welsink, H., Quinlan, G., and Mudford, B., 1987, Deep crustal structure and evolution of the rifted margin northeast of Newfoundland: Results from LITHOPROBE East: Canadian Journal of Earth Sciences, v. 24, p. 1537–1549. Discusses the crustal structure of part of the present-day Atlantic extensional margin and attempts to evaluate the applicability of both symmetrical and asymmetric spreading models. Roberts, A. M., Yielding, G., and Freeman, B., eds., 1991, The geometry of normal faults: London, Geological Society of London, Special Publication 56, p. 1–13. A compendium of papers summarizing the mechanics and applications to hydrocarbon accumulation related to normal faulting with examples from different parts of the world. Wernicke, B., 1985, Uniform-sense normal simple shear of the continental lithosphere: Canadian Journal of Earth Sciences, v. 22, p. 108–125. Examines models of pure and simple shear for crustal extension in the Basin and Range and elsewhere. Wernicke concluded that simple shear oriented in a single direction is the most common mechanism for crustal extension. PART 4 Folds and Folding OUTLINE 356 15 Anatomy of Folds 16 Fold Mechanics 381 17 Complex Folds 408 15 Anatomy of Folds Folds in layered rock commonly are nearly perfect geometric features. . . . Partly because of their geometric beauty, folds have attracted the attention of g eologists almost from the time of the birth of geological science. ARVID M. JOHNSON AND STEPHENSON D. ELLEN, 1974, Tectonophysics 356 Folds are wave-like structures that result from deformation of bedding, foliation, or other originally planar surfaces in rocks (Figure 15–1). They occur on all scales, ranging from those visible only under a microscope to those hundreds of kilometers long. Folds form in all deformational environments in the Earth’s crust, from near-surface brittle conditions to lower-crust ductile conditions, and under pure, simple, and general shear conditions. They range from very broad and gently curved surfaces to tightly compressed and attenuated structures. They occur singly as isolated folds and in extensive fold trains of different sizes. Rocks may be affected by a single folding event or by multiple events leading to overprinted fold generations (Chapter 17). Folds were the first structures recognized as hydrocarbon traps, leading to the anticlinal theory of petroleum accumulation, and the development of a major new industry near the end of the nineteenth century. Folds also play an important role in concentrating valuable minerals. For example, the widely known saddle-reef deposits, first identified in Australia, contain minable concentrations of sulfide minerals localized in fold hinges. In this chapter, we introduce folds, describe their properties, and discuss some of the classifications devised to help us to understand folds and communicate about them. Chapter 16 will present current views on the mechanics of folding, and Chapter 17 will discuss complex fold systems. It is important at this point to reintroduce the concept of scale: structures small enough to require magnification to be seen are microscopic. Those whose sizes range from hand specimen to outcrop scale are mesoscopic, and those at map scale are macroscopic. Most observations and measurements that provide information about orientations of various fold elements (limbs, axes, and axial surfaces), and allow inferences about the folding process, are made on the mesoscopic scale, yet microscopic- and map-scale studies also yield useful results. Conclusions regarding the orientation and shapes of folds are commonly drawn from a variety of scales. Recall Pumpelly’s rule (Chapter 2), which states that small-scale structures generally mimic larger-scale structures formed at the same time, a statement of self-similar or “fractal” behavior in today’s science. If Pumpelly’s Anatomy of Folds | 357 FIGURE 15–1 Disharmonic folds in shale and thin limestone beds of the Poultney Formation (Lower Ordovician) near Whitehall, New York. Note the difference in shape and thickness of the shale (dark) versus limestone (light) layers from the limbs to the hinges of the folds. (RDH photo.) Small (parasitic) folds have same shape as equivalent parts of major folds Descriptive Anatomy of Folds Fold Anatomy 0 1 meter FIGURE 15–2 Pumpelly’s rule relating small- and large-scale folds. rule holds true, mesoscopic folds should have the same style and orientation as macroscopic folds (Figure 15–2), enabling study of small folds to enhance our understanding of large folds and the structural history of an area. Consider the simple upright anticline-syncline pair in Figure 15–3a. These folds have a crest at the highest point (elevation) on a cross section of the fold, and a trough at the lowest point. The straighter or least-curved segments are the limbs and connect the parts of the fold exhibiting the greatest curvature—the hinge or hinge zone. The hinge line is the line joining points of greatest curvature on a folded surface or mid-line of arc of greatest curvature, the hinge zone. If several hinge lines are connected on successive folded layers of the same fold, they form the axial surface (axial plane, if the surface is planar). The line along which a folded surface changes dip is called the crest or trough line. In folds that have non-vertical axial surfaces, hinge and crest lines do not coincide. Fold hinges may be horizontal, or inclined to the horizontal and are said to plunge (Figure 15–3b); folds with nonhorizontal hinges are plunging folds. Ideal or cylindrically shaped folds have 358 | Folds and Folding Axial surface (plane) Crest β≠0 Hinge Axis Hinge Limb Plunging β=0 Inflection point Axis Trough (a) Wavelength Amplitude Nonplunging (b) Interlimb angle (c) E1 Inflection points FIGURE 15–3 (a) Anatomy of a fold. (b) Plunging and nonplunging folds. β is the angle of plunge and the angle between the horizontal and the hinge line, measured in the vertical plane. (c) Relationships between wavelength and amplitude of folds. E2 Traces of enveloping surfaces E1 and E2 (a) (b) FIGURE 15–4 (a) Vergence (direction of overturning observed in direction of plunge) of large (first-order) and small (second-order parasitic) folds (sense of overturning, or vergence, indicated by arrows) and relationships to an enveloping surface E1—by connecting inflection points—or E2—by connecting a tangent to the crests or troughs of second-order folds. (b) Slip lines illustrated by lines such as fibers or slickensides on a layer surface that indicate the direction of motion of one layer past another. a fold axis, which is the line that when moved parallel to itself generates the folded surface (Figure 15–4a). In a strict sense only cylindrical folds have fold axes, but the fold axis is a useful concept for visualizing the three dimensional shape of folded surfaces. An inflection point is a point separating concave curvature in one direction from concave curvature in the opposite direction, identified on a cross section of a fold (Figure 15–3a). The distance between the Anatomy of Folds hinges of adjacent folds is the wavelength. Half the distance from the crest to the trough of a fold, measured parallel to the axial plane, is the fold amplitude (Figure 15–3c). The direction in which the axial surface is inclined (opposite its dip direction) is called the vergence of a fold (Figure 15–4a). This property applies to asymmetrical folds that have one limb that dips more steeply and is shorter than the other. Vergence is not a property of symmetrical folds, but small folds may be asymmetric on the limbs of a larger symmetrical fold. A related property of folds is slip lines, which are generally another indication of vergence. Slip lines are produced by relative motion of originally adjacent reference points on either side of a slip surface (e.g., bedding) during folding or other deformation (but also occur with non-verging folds). They may occur on real movement surfaces and produce slickensides, fibers, or other visible motion indicators (Figure 15–4b), or they may be imaginary lines deduced from vergence. Determination of vergence is useful in working out the overall direction of tectonic transport of structures in an area, in addition to helping to fix an observer’s location on a large fold. The largest-scale folds in an area or region are firstorder folds; smaller folds on the flanks of large folds are second-order folds. Folds of successively higher order are also possible. It may be feasible to relate the geometry SAS 359 of small- to large-scale folds by using an enveloping surface (Figure 15–4a), which is a smoothly varying surface tangent to the crests or troughs of small folds that fold an already folded surface, where crests and troughs are measured perpendicular to the smooth surface joining the inflection points. Enveloping surfaces are useful for studying folds at outcrop scale and in cross section where many small folds occur on limbs of larger folds, but the geometry of the larger folds is not clear. While deciphering a fold, a geologist must keep in mind the relationship between the axial surface orientation and variations in the plunge of the fold axis (Figure 15–5). The fold axis lies within the axial surface, but its orientation may vary within the surface. The trend of the fold axis may differ considerably from the strike of the axial surface; for instance, the trend of the fold axis in a non-plunging fold and the strike of the axial surface are the same, but the trend and strike of the respective structures are different for a plunging fold with an inclined axial surface (Figure 15–5). Kinds of Folds In this section, we will consider simple folds, and you will see that many of the descriptive terms are closely interrelated as opposites or as synonyms. SAS TA TA | Pitch SAS SAS Pitch PAS TA TA Plunge FA AS (a) (b) SAS SAS SAS Pitch Pitch Pitch SAS TA Plunge TA TA (c) Pitch Plunge TA (d) FIGURE 15–5 Axial-surface orientation and constraints on the orientation of the fold axis at zero (a), intermediate (b and c), and steep plunge (d). Note that the plunge of the fold can be read directly from the fabric diagram, with the plunge angle being the value read along the line from the primitive circle to the fold axis. The pitch is obtained by reading the angle along the great circle from the primitive circle to the fold axis. PAS—pole to axial surface indicated by an x in all of the fabric diagrams. AS—axial surface. FA—fold axis. TA—trend of axis. SAS—strike of axial surface. Note that the strike of the axial surface and trend of the axis remain constant. 360 | Folds and Folding Later fold hinge O Ꞓ Synform Syncline S Anticline Ages of rocks known Ages of rocks unknown Earlier fold hinge S S O (c) O Ꞓ O Ꞓ Antiformal syncline S S O Ꞓ Ꞓ Anticline (doubly plunging) Syncline (doubly plunging) (d) Ꞓ S O S O (e) Dome Overturned limb FIGURE 15–7 Cross section of synformal anticline as a product of multiple folding. Note axial surfaces of both earlier and later folds. p–C, –C, and O indicate Precambrian, Cambrian, and Ordovician rocks, respectively. Synformal anticline S O Ꞓ Axial surface of earlier fold Erosion surface (b) O Axial surface of later fold Antiform (a) Ꞓ Synformal anticline Upright limb Basin FIGURE 15–6 (a) Anticline and syncline (cross section). (b) Antiform and synform (cross section). (c) Antiformal syncline and synformal anticline (cross section). (d) Doubly plunging anticline and syncline (map view). (e) Dome and basin (map view). –C, O, and S indicate Cambrian, Ordovician, and Silurian rocks, respectively. Dashed line in (a), (b), and (c) represents the Earth’s surface. The term anticline applies to folds that are concave toward older rocks in the structure, in other words, layers dip away from the hinge; an anticline contains older rocks in the center (Figure 15–6a). A fold that is concave downward and layers dip away from the hinge is called an antiform; the rocks may not be older in the middle, or the age of the rocks may be unknown. In the opposite sense, a syncline is a structure wherein layering is concave toward the younger rocks—layers dip toward the hinge—and as a result, younger rocks occur in the central part of the structure (Figure 15–6a). Similarly, a structure where layering is concave up and dips toward the hinge is a synform (Figure 15–6b). A dome is a special kind of antiform wherein layering dips in all directions away from a central point in three dimensions. A basin is a unique synform in which layering dips inward toward a central point in three dimensions (Figure 15–6e). Where the sequence can be worked out such that the ages of the rocks are determinable, it may be possible to categorize antiforms and synforms as antiformal synclines or synformal anticlines, depending on the relative ages of rocks found in the centers of the structures (Figure 15–6e). An antiformal syncline (downward-facing syncline) is a structure in which layering dips away from the axis, but the rocks in the center are younger. In contrast, a synformal anticline (upward-facing anticline) is a structure wherein layering dips inward as in a syncline, but the rocks in the center of the structure are older rather than younger (see Chapter 2 Essay). These structures may be produced during multiple episodes of folding (Figure 15–7; Chapter 17). A monocline is a type of fold characterized by only one tilted limb adjacent to more flat lying segments (Figure 15–8). Monoclines commonly form from the vertical offset of the layers above the tip of a steeply dipping blind fault. Rocks that dip uniformly in one direction may be described as a homocline, whereas a structural terrace is a local flattening of a uniform regional dip (Figure 15–8). Fault-bend and fault-propagation folds that form in association with thrust faults were described in Chapter 12. Recall that fault-bend folds are generally open parallel folds, but fault-propagation folds may be tighter parallel folds. As noted earlier, a fold is cylindrical (properly cylindroidal, or cylinder-like) if the fold can be generated by moving a line—the fold axis—parallel to itself. Generally, cylindrical folds are those in which the hinges are everywhere parallel on small and large folds (Figure 15–10a). Noncylindrical folds (Figure 15–10b) contain hinges that are not parallel on successive folds, or which hinges in successive folds of the same group may converge toward a point rather than Anatomy of Folds | 361 Fold and fault thrust gone Th rus t fa ult (a) (a) (b) FIGURE 15–9 Fault–propagation fold along the deformed zone accompanying the C umberland P lateau overthrust on the northwestern limb of the Sequatchie anticline, eastern T ennessee. Note that the fault continues only as far as the thrust propagated, hence the name fault-propagation fold. (RDH photo.) (c) (d) (a) FIGURE 15–8 (a) Raplee monocline near Mexican Hat, Utah. Note flat-lying strata in background and foreground with dipping limb between. (CMB photo.) (b) Monocline in cross section, (c) ho

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