1. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium New Paradigms for Teaching Structural Geology in the 21 st 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 25 th Anniversary

2. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium 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. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Icons of Structural Geology: Are they venerable or vulnerable ? Stereographic projection Mohr’s circle

4. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Icons: Venerable or Vulnerable ? compass / clinometer topographic map

5. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Icons: Venerable or Vulnerable ? descriptive geometry stress and strain analysis

6. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Can we do better than the stereonet? Chimney Rock, Utah: Maerten (2000) Data: (  d,  d,  r ) for 47 stations Normal faults, slip down dip

7. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Stereonets ignore locations Data: (x, y, z,  d,  d,  r ) for 47 stations obtained using GPS and a compass/clinometer (Maerten, 2000).

8. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Spatial data reveals fault mechanics (Maerten, 2000)

9. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Can we improve upon Mohr’s Circle? 1999 Hector mine earthquake (M w 7.1), southern California (Treiman et al., 2002)

10. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Deformation is not homogeneous Descending & ascending radar interferograms (Jonsson et al., 2002): Color cycle = 10 cm displacement. Data size = 1.5 x 10 6. Pixel size = 80 x 80m. Number of Mohr’s circles to represent strain ~843 and ~452.

11. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium 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.

12. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Spatial data reveals fault mechanics Inverting for slip on 3D fault surfaces (Maerten, Resor et al., 2005)

13. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Can we surpass the compass? (Bergbauer & Pollard, 2004)

14. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Given the compass, one produces: (Bergbauer & Pollard, 2004)

15. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium GPS enables one to describe and analyze the fold shape in 3D (Bergbauer & Pollard, 2004)

16. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Is the topo map adequate for the modern structural geologist? (Hilley, Mynatt, et al., 2005)

17. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Lidar provides (x, y, z) and spectacular resolution (NCALM, NSF-CMG)

18. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium High resolution data enables a quantitative study of fold shape

19. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Can we improve upon descriptive geometry? (Bellahsen, Fiore, et al., 2005)

20. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Differential geometry provides arc lengths and areas of folded surfaces

21. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Differential geometry provides measures of the shapes of folded surfaces (Forster et al., 1996)

22. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium There are four possible shapes at any point on a folded surface Traditional structural analysis focuses only on the cylindrical surface,  g =0. (Bergbauer & Pollard, 2003)

23. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium 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. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Chapter 3: Characterizing structures using differential geometry http://pangea.stanford.edu/projects/structural_geology/

25. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium 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. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Conservation of linear & angular momentum A. L. Cauchy These laws are independent of material properties. Cauchy’s Laws of Motion

27. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium A constitutive law for ductile deformation Navier-Stokes Equations G. G. Stokes

28. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium A constitutive law for brittle deformation Navier’s Equations of Motion C.L.M.H. Navier

29. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium Chapter 7: Conservation of mass and momentum http://pangea.stanford.edu/projects/structural_geology/

30. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium 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

31. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium 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?

32. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium 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?

33. Oct. 18, 2005 GSA Salt Lake CityPardee Keynote Symposium 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 21 st century. http://pangea.stanford.edu/projects/structural_geology/