New Paradigms for Teaching Structural Geology in the 21st Century

1
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 SGT 25th
Anniversary
2
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

3
Icons of Structural Geology Are they venerable
or vulnerable ?

• Stereographic projection
• Mohrs circle

4
Icons Venerable or Vulnerable ?

• compass / clinometer
• topographic map

5
Icons Venerable or Vulnerable ?

• descriptive geometry
• stress and strain analysis

6
Can we do better than the stereonet?
Chimney Rock, Utah Maerten (2000)
Data (ad, fd, qr) for 47 stations Normal faults,
slip down dip
7
Stereonets ignore locations
Data (x, y, z, ad, fd, qr) for 47 stations
obtained using GPS and a compass/clinometer
(Maerten, 2000).
8
Spatial data reveals fault mechanics
(Maerten, 2000)
9
Can we improve upon Mohrs Circle?
1999 Hector mine earthquake (Mw 7.1), southern
California
(Treiman et al., 2002)
10
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 Mohrs
circles to represent strain 843 and 452.
11
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 Mohrs circles to
represent strain 50.
12
Spatial data reveals fault mechanics
Inverting for slip on 3D fault surfaces (Maerten,
Resor et al., 2005)
13
Can we surpass the compass?
(Bergbauer Pollard, 2004)
14
Given the compass, one produces
(Bergbauer Pollard, 2004)
15
GPS enables one to describe and analyze the fold
shape in 3D
(Bergbauer Pollard, 2004)
16
Is the topo map adequate for the modern
structural geologist?
(Hilley, Mynatt, et al., 2005)
17
Lidar provides (x, y, z) and spectacular
resolution
(NCALM, NSF-CMG)
18
High resolution data enables a quantitative study
of fold shape
19
Can we improve upon descriptive geometry?
(Bellahsen, Fiore, et al., 2005)
20
Differential geometry provides arc lengths and
areas of folded surfaces
21
Differential geometry provides measures of the
shapes of folded surfaces
(Forster et al., 1996)
22
There are four possible shapes at any point on a
folded surface
Traditional structural analysis focuses only on
the cylindrical surface, kg0.
(Bergbauer Pollard, 2003)
23
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).
24
Chapter 3 Characterizing structures using
differential geometry
http//pangea.stanford.edu/projects/structural_geo
logy/
25
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
26
Conservation of linear angular momentum
Cauchys Laws of Motion
A. L. Cauchy
These laws are independent of material properties.
27
A constitutive law for ductile deformation
Navier-Stokes Equations
G. G. Stokes
28
A constitutive law for brittle deformation
Naviers Equations of Motion
C.L.M.H. Navier
29
Chapter 7 Conservation of mass and momentum
http//pangea.stanford.edu/projects/structural_geo
logy/
30
The logical thread leading to an understanding of
tectonic processes and their structural products

• Conservation laws of mass momentum
• Cauchys 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

31
Thought-provoking questions

• Should we continue to emphasize stereonets and
  Mohrs circles or teach students how to
  investigate non-homogeneous 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?

32
Thought-provoking questions

• How can we expect students to understand the 3D
  geometry of geological structures without the
  fundamental concepts of differential geometry?
• Isnt it about time for geologists to adopt a
  complete mechanics for the investigation of
  tectonic processes and their structural products?

33

• 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.

http//pangea.stanford.edu/projects/structural_geo
logy/