GEOS 304 Lab 5: Strain Analysis
Fall 2002
Name:____________________
The purpose of this lab is to become more comfortable with interpreting and quantifying strain
using a variety of methods applied to real-world examples. A proper assessment of strain is
often an essential component of a complete geological interpretation and the following
techniques will be powerful additions to your structural geology toolbox.
1. Interpreting strain using changes in lines.
The photograph on the next page shows a granitic gneiss outcrop containing several aplite
dikes (white). Because the aplite is much more competent (i.e. stronger) than the gneiss, it
tends not to deform internally and is therefore a useful strain marker. Note that the gneiss is
much less competent than the aplite, and had to flow into the spaces between separated dike
segments as well as into and out of the fold hinges. During deformation, some dikes were
folded while others were stretched into boudins because the dikes had different initial
orientations relative to the stress responsible for deformation. What are boudins, you ask?
The term comes from the French word for sausage (think of a long string of linked sausages)
and refers to once-continuous segments of a marker (bed or fossil). Boudins result from
stretching a competent layer that is surrounded by an incompetent matrix. In the case of very
high differences in competency, the competent layer first responds to stretching by jointing
(perpendicular to the stretch direction). Continuing extension just widens the spaces between
segments while the incompetent matrix flows into the gaps. Usually the competency contrast
is not so extreme and the competent layer undergoes some internal deformation in the
process of stretching. The diagram below shows the progressive development of boudinage
with strain increasing towards the right.
From Davis and Reynolds, 1996. Structural Geology of Rocks and Regions. John Wiley & Sons, Inc., New
York. p. 402.
A. Using the photograph on the next page, estimate both the directions of maximum stretch
(S1) and minimum stretch (S3) using the structures developed in the dikes. Plot these
lines on the photo.
B. Using the stretched dikes, estimate the magnitude of S1. Your answer will be an
approximation, as it will be hard to tell just how much internal deformation there is in the
dikes - use your best estimate.
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Picture from Ramsay & Huber, 1983. The Techniques of Modern Structural Geology, Volume 1: Strain
Analysis. Academic Press, New York. p. 102.
C. Using the folded dikes, estimate the magnitude of S3.
D. Even without actually calculating strain magnitudes, we often sketch strain ellipses to get
an idea of how different outcrops or regions may relate to each other. Knowing both
rough magnitudes and directions of strain, sketch in a strain ellipse on the photograph.
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E. Plot your results on a Mohr strain diagram.
F. A smaller dike in the center of the page has an orientation of about 45 degrees (measured
clockwise) from S3 . Use the Mohr strain diagram to estimate the stretch this dike has
undergone. Extra credit: Is this value consistent with the amount of folding you see in
the dike? If not, come up with 3 or 4 possible explanations for the discrepancy i.e. what
are some reasons why strain might deviate from ideal 2-D Mohr behavior in real rocks.
2.
Interpreting strain from angular changes
Many other types of fossils lend themselves to the type of analysis you just did in the above
problem. The figure on the next page shows three deformed crinoids of the species
Pentacrinus. Not only is this a bombproof indicator that the rock is Jurassic, but these
critters can also be used to quantify strain. Undeformed crinoids show a perfectly regular
pentagonal symmetry with the rays oriented at 72 degrees to each other. Each crinoid
therefore has five directions along which angular shear can be measured.
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Picture from Ramsay & Huber, 1983. The Techniques of Modern Structural Geology, Volume 1: Strain
Analysis. Academic Press, New York. p. 135.
A. On the center crinoid sketch in two lines that were originally perpendicular. (To find these
lines it may help to first draw a few undeformed stars and contemplate their geometry)
B. Assuming the rock was deformed homogeneously, do you expect that angular shear will be
roughly the same in all five directions? Why or why not?
C. Working with a partner, measure the angular shear in the five possible directions on the
center crinoid. Was your hypothesis in part B correct? If not, explain your findings. If
necessary, consult page 71 in your textbook for clues.
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3. More Mohr fun - interpreting strain from changes in lines
Belemnites are linear Jurassic-Cretaceous critters related to modern squids and octopi.
Deformed examples are quite common in the Alps where they make excellent strain markers
since they tend to deform by separating into segments that maintain their shape while the
gaps between them widen. In this example, the gaps between segments are filled with
fibrous quartz or calcite (lined pattern on the figure). Armed with the length of the belemnite
before (l0) and after (lf) deformation plus the angle between each belemnite and S1 one can
compute the extension e and the values of the principal stretches, S1 and S3. Hint: There are
two ways to solve for S1, and S3. You can use the equations for the Mohr circle and solve
algebraically (two equations and two unknowns) however it is quicker to use a Mohr strain
diagram and solve graphically (use the graph paper on the next page if you like). Make sure
you show your arithmetic (expect about a page) or explain how you obtained your results
with the Mohr diagram.
Long Belemnite
Short Belemnite
Original length (lo)
Final length (lf)
Stretch
Angle (d)between fossil and S1
S1
S3
Picture from Ramsay & Huber, 1983. The Techniques of Modern Structural Geology, Volume 1: Strain Analysis.
Academic Press, New York. p. 94.
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Interpreting strain across a shear zone
It is often the case that ore bodies are cut by large faults (local examples include the San
Manuel and Sierrita porphyry copper bodies). A Tucsonan named Dave Lowell has found
more copper than anyone in history by using his knowledge of structural geology to track
down the missing pieces of faulted ore bodies. Imagine you are hot on the trail of a BIG gold
vein. You follow it for kilometers with dollar signs in your eyes, and suddenly…whamo….a
shear zone. It would be nice to know where your motherlode lies on the other side of this
shear zone! Well your prayers have been answered. It just so happens that this shear zone
cuts a granite. Using the Fry Method (from last week) on feldspar grains, you have mapped
out many S1 orientations within the shear zone. These measurements are plotted on the shear
zone map below. With their help, you can figure out the net offset on the shear zone.
Unimaginable riches will soon be yours if you get it right...
Non-sheared granite
S1 azimuths in
sheared granite
Non-sheared granite
N
1.0 km
A. Using the S1 directions as a guide, divide the shear zone into five shear domains, i.e.
regions of roughly parallel S1 orientations. The boundaries of each domain should be
parallel to the shear zone walls. Show these domains on the map, then determine the
distance from the southern boundary of the shear zone to the southern boundary of the
domain (measured perpendicular to the shear zone wall). Next, determine the width of
each domain. Use the chart on the next page for your answers.
B. For each of the above domains, determine the angle 1 between the average S1
orientation and the orientation of the shear zone boundaries.
C. For each of the domains, compute the shear strain (). Shear strain is related to the
orientation of S1 (in simple shear) by the formula 2/ = tan21.
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Shear
Domain
Distance from southern
boundary of shear zone
to southern boundary of
domain
Width of
domain
Angle (1)
between (S1)
and shear zone
wall
Shear strain
1
2
3
4
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D. How much has the vein been offset? It is easiest to calculate the offset in each domain
separately, then add the values together to get a grand total. To help answer this
question, think about the formula for shear strain i.e. consider what your numerical
values of shear strain physically mean. (see pages 64 and 65 in your textbook).
E. Just as importantly, which way has the vein been offset? In other words, is the shear zone
right-lateral or left-lateral? How do you know?
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4. Qualitative strain interpretation
In structural geology, we are often confronted with multiple types of structures within a
single region and sometimes even within a single outcrop. Without actually calculating
strain magnitudes, we can use strain ellipses as a qualitative tool to understand how the
different structures might relate to each other. For example, if different structures produce
the same finite strain ellipse, we might reasonably suspect that they are products of the same
sort of strain. If the strain ellipses are not similar then the structures may still be products of
the same generation of strain but we need to think more carefully about how they could be
related. The figure below shows three folds. Each is drawn with a different type of
associated structure.
Picture from Ramsay & Huber, 1987. The Techniques of Modern Structural Geology, Volume 2: Folds and
Fractures. Academic Press, New York. p. 458.
Fold A: This is typical of a marly (clay-rich) limestone. The straight lines represent pressure
solution cleavage. They are planes along which material has been dissolved and
transported out of the system. In outcrop, they are typically marked by relatively
high concentrations of insoluble clay residue. S3 is always perpendicular to the
cleavage.
Fold B: This is more typical of a sandstone or phyllite. The openings are tensile joints
(cracks) such as you saw last week in lab. S1 is always perpendicular to the joint
surface.
Fold C: This might also be a sandstone or phyllite. The structures are small faults and they
are a little trickier to interpret. Using the upper and lower surfaces of the fold as
guides, think about whether the faults serve to shorten or extend that edge of the
layer. If they are extensional, then S1 is parallel to the edge of the layer. If they
serve to shorten the layer, then S3 is parallel to the edge.
A. Using the criteria above, sketch a few strain ellipses in the top, middle, and bottom of each
fold. (You should have about 9 ellipses for each of the three folds).
B. Each of these folds accommodates the same strain (i.e. the folds have the same shapes), yet
the structures in each of the folds are not consistently oriented from fold to fold or even within
each of the folds. Using the ellipses you've drawn, explain in general terms how this can be. It
may help to start first with the variation in the orientation of structures within the folds. Use a
separate sheet of paper or the backside of this sheet.
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