New Paradigms for Teaching Structural
Geology in the 21st Century
David D. Pollard
Stanford University
Pardee Keynote Symposium
Research Opportunities, New Frontiers, and the
Questioning of Paradigms in Structural Geology
and Tectonics: SG&T 25th Anniversary
GSA Salt Lake City
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Oct. 18, 2005
Acknowledgements
• Stanford students: Laurent Maerten,
Frantz Maerten, Phil Resor, Stephan
Bergbauer, Tricia Fiore, Ian Mynatt
• Colleagues: Ray Fletcher, George Hilley
• NSF Tectonics Program, NSF
Collaborations in Mathematical
Geosciences Program
• Symposium organizers
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Icons of Structural Geology: Are
they venerable or vulnerable ?
• Stereographic
projection
• Mohr’s circle
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Icons: Venerable or Vulnerable ?
• compass /
clinometer
• topographic map
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Icons: Venerable or Vulnerable ?
• descriptive
geometry
• stress and strain
analysis
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Can we do better than the
stereonet?
Chimney Rock, Utah: Maerten (2000)
Data: (ad, fd, qr) for 47 stations
Normal faults, slip down dip
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Stereonets ignore locations
Data: (x, y, z, ad, fd, qr) for 47 stations obtained
using GPS and a compass/clinometer (Maerten, 2000).
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Spatial data reveals fault mechanics
(Maerten, 2000)
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Can we improve upon Mohr’s
Circle?
1999 Hector mine earthquake (Mw 7.1), southern California
(Treiman et al., 2002)
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Deformation is not homogeneous
Descending & ascending radar interferograms (Jonsson et al., 2002):
Color cycle = 10 cm displacement. Data size = 1.5 x 106. Pixel size = 80 x 80m.
Number of Mohr’s circles to represent strain ~843 and ~452.
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Deformation is not homogeneous
Campaign GPS displacement vectors (Agnew et al., 2002)
Greatest displacement = 2.2 m 3 km east of fault. Data size = 55.
Number of Mohr’s circles to represent strain ~ 50.
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Spatial data reveals fault mechanics
Inverting for slip on 3D fault surfaces (Maerten, Resor et al., 2005)
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Can we surpass the compass?
(Bergbauer & Pollard, 2004)
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Given the compass, one produces:
(Bergbauer & Pollard, 2004)
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GPS enables one to describe and
analyze the fold shape in 3D
(Bergbauer & Pollard, 2004)
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Is the topo map adequate for the
modern structural geologist?
(Hilley, Mynatt, et al., 2005)
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(NCALM, NSF-CMG)
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Lidar provides (x, y, z) and
spectacular resolution
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High resolution data enables a
quantitative study of fold shape
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Can we improve upon descriptive
geometry?
(Bellahsen,
Fiore, et al.,
2005)
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Differential geometry provides arc
lengths and areas of folded surfaces
s  u, v   s x e x  s y e y  s z e z
I  Edu 2  Fdudv  Gdv 2
s s
E

u u
s s
F

u v
s s
G 
v v
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Differential geometry provides measures
of the shapes of folded surfaces
s  u, v   s x e x  s y e y  s z e z
II  Ldu 2  Mdudv  Ndv 2
 2s
L  N 2
u
 2s
M  N
uv
 2s
N  N 2
v
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(Forster et al., 1996)
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There are four possible shapes at
any point on a folded surface
 n  II I
 1 cos 2 a   1 sin 2 a
m 
1
2
 1   2 
1 EN  2 FM  GL

2
EG  F 2
 g  1 2
LN  M 2

EG  F 2
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Traditional structural analysis focuses
only on the cylindrical surface, g=0.
(Bergbauer & Pollard, 2003)
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The folded surface from Sheep Mt. is
made up of all possible shapes
Differential geometry
enables one to actually
describe the surface, not
simply approximate it as
cylindrical (Mynatt,
Bergbauer, et al., 2006).
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Chapter 3:
Characterizing
structures using
differential
geometry
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http://pangea.stanford.edu/projects/structural_geology/
Oct. 18, 2005
Can we go beyond stress and strain
analysis?
• commonly taught as
independent topics
• not linked through
constitutive laws
• not put in a fundamental
context of conservation of
mass and momentum
Newton points the way…
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Conservation of linear & angular
momentum
Cauchy’s Laws of Motion
Dvi  ji
*


  gi
Dt
x j
 ij   ji , i  j
A. L. Cauchy
These laws are independent of material properties.
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A constitutive law for ductile
deformation
Navier-Stokes Equations
 vi v j 
 ij   p ij   

 x j xi 


Dvi
p
 2vi



  gi*
Dt
xi
xk xk
G. G. Stokes
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A constitutive law for brittle
deformation
Navier’s Equations of Motion
 ij  2G ij   kk ij
2
2ui
2ui

  u
k   g*
 2 G
 G   
i
X k X k 
t
 X X
i k
C.L.M.H. Navier
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Chapter 7:
Conservation
of mass and
momentum
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http://pangea.stanford.edu/projects/structural_geology/
Oct. 18, 2005
The logical thread leading to an
understanding of tectonic processes
and their structural products
•
•
•
•
•
•
•
Conservation laws of mass & momentum
Cauchy’s equations of motion
Selection of constitutive laws
Specialized equations of motion
Selection of initial and boundary conditions
Solutions to boundary value problems
Comparisons of results to geological data
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Thought-provoking questions
• Should we continue to emphasize
stereonets and Mohr’s circles or teach
students how to investigate nonhomogeneous fabrics/structures and
stress/strain fields using calculus?
• Should we continue to emphasize the
compass and topographic map or teach
students about GPS, Lidar, and other
modern technologies?
GSA Salt Lake City
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Thought-provoking questions
• How can we expect students to
understand the 3D geometry of geological
structures without the fundamental
concepts of differential geometry?
• Isn’t it about time for geologists to adopt a
complete mechanics for the investigation
of tectonic processes and their structural
products?
GSA Salt Lake City
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Teachers who adopt the techniques and
technology described here, and who add
differential geometry and a complete
mechanics to their curriculum will discover a
fascinating new perspective on structural
geology that prepares their students
for the challenges of the 21st century.
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http://pangea.stanford.edu/projects/structural_geology/
Oct. 18, 2005