oct. 18, 2005 gsa salt lake citypardee keynote symposium new paradigms for teaching structural...

GSA Salt Lake City Pardee Keynote Symposium Oct. 18, 2005

New Paradigms for Teaching Structural Geology in the 21st Century

David D. PollardStanford University

Pardee Keynote SymposiumResearch Opportunities, New Frontiers, and theQuestioning of Paradigms in Structural Geology

and Tectonics: SG&T 25th Anniversary


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


Icons of Structural Geology: Are they venerable or vulnerable ?

• Stereographic projection

• Mohr’s circle


Icons: Venerable or Vulnerable ?

• compass / clinometer

• topographic map


Icons: Venerable or Vulnerable ?

• descriptive geometry

• stress and strain analysis


Can we do better than the stereonet?

Chimney Rock, Utah: Maerten (2000)

Data: (d, d, r) for 47 stationsNormal faults, slip down dip


Stereonets ignore locations

Data: (x, y, z, d, d, r) for 47 stations obtainedusing GPS and a compass/clinometer (Maerten, 2000).


Spatial data reveals fault mechanics(Maerten, 2000)


Can we improve upon Mohr’s Circle?1999 Hector mine earthquake (Mw 7.1), southern California

(Treiman et al., 2002)


Deformation is not homogeneousDescending & 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.


Deformation is not homogeneousCampaign 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.


Spatial data reveals fault mechanicsInverting for slip on 3D fault surfaces (Maerten, Resor et al., 2005)


Can we surpass the compass?

(Bergbauer & Pollard, 2004)


Given the compass, one produces:



GPS enables one to describe and analyze the fold shape in 3D



Is the topo map adequate for the modern structural geologist?

(Hilley, Mynatt, et al., 2005)


Lidar provides (x, y, z) and spectacular resolution

(NCALM, NSF-CMG)


High resolution data enables a quantitative study of fold shape


Can we improve upon descriptive geometry?

(Bellahsen,Fiore, et al.,2005)


Differential geometry provides arc lengths and areas of folded surfaces

2 2

,

d d d d

x x y y z zu v s s s

I E u F u v G v

Eu u

Fu v

Gv v

s e e e

s s

s s

s s


Differential geometry provides measures of the shapes of folded surfaces

2 2

2

2

2

2

2

,

d d d d

x x y y z zu v s s s

II L u M u v N v

Lu

Mu v

Nv

s e e e

sN

sN

sN

(Forster et al., 1996)


There are four possible shapes at any point on a folded surface

n

2 21 1

1m 1 22

2

g 1 2

2

2

cos sin

1 2

2

II I

EN FM GL

EG F

LN M

EG F

Traditional structural analysis focusesonly on the cylindrical surface, g=0.



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).


Chapter 3: Characterizing structures using differential geometry

http://pangea.stanford.edu/projects/structural_geology/


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…


Conservation of linear & angular momentum

*jiii

j

Dvg

Dt x

, ij ji i j

A. L. Cauchy

These laws are independent of material properties.

Cauchy’s Laws of Motion


A constitutive law for ductile deformation

Navier-Stokes Equations

G. G. Stokes

2*i ii

i k k

Dv p vg

Dt x x x

jiij ij

j i

vvp

x x


A constitutive law for brittle deformation

Navier’s Equations of Motion

C.L.M.H. Navier

22 2*

2i i k

iik k k

uu uG G gX X X Xt

2ij ij kk ijG


Chapter 7: Conservation of mass and momentum



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


Thought-provoking questions

• Should we continue to emphasize stereonets and Mohr’s 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?


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?


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 studentsfor the challenges of the 21st century.


oct. 18, 2005 gsa salt lake citypardee keynote symposium new paradigms for teaching structural...

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