1. Simulating Solid-Earth Processes Associated With Viscous and Viscoelastic Deformation Shijie Zhong Dept. of Physics University of Colorado Boulder, Colorado EarthScope CSIT Workshop Snowbird, UT, 2002

2. Outline 1)Introduction.  Why is simulating viscous and viscoelastic deformation relevant to the EarthScope?  Definition of Geodynamic Modeling 2) Current status in geodynamic modeling.  Where are we now in terms of modeling capability?  How do we get where we are? 3) Future developments.

3. Two questions asked in the EarthScope 1) How do continents form and evolve? large time scales (>10 5 years) -- viscous flow. Mantle convection and mantle-lithosphere interaction.

4. Dynamic Evolution of Continents Doin, Fleitout & Christensen, 1997Shapiro, Hager & Jordan, 1999

5. 2) Why do earthquakes and volcanic eruptions occur? small time scales -- viscoelastic flow. Post-seismic stress and strain evolution, GPS and InSAR observations.

6. Modeling Post-seismic Surface Deformation – Viscoelastic Effects Pollitz et al., 2001

7. Modeling Post-seismic Stress Evolution – Viscoelastic Effects Freed & Lin, 2002

8. Definition of Geodynamic Modeling 1) Mantle convection Physical basis: Conservation of MASS, ENERGY, and MOMENTUM + VISCOUS rheological equation. Objectives: Understand the long-term heat and mass transfer in the mantle and its consequences to surface observables.

9. 2) Viscoelastic deformation Physical basis: Conservation of MASS and MOMENTUM + VISCOELASTIC rheological equation. Objectives: Understand short-term evolution of surface deformation and lithospheric stress in response to certain forces (e.g., an earthquake).

10. Why Numerical (Finite Element) Method?  A set of nonlinear equations. Heterogeneous and nonlinear rheology. Deformable mesh, critical for viscoelastic stress analysis. Tectonic faults, … but spectral methods [Glatzmaier et al., 1990; Gable et al., 1991; Zhang and Christensen, 1993] and finite volume methods [Tackley, 1996; Ratcliff et al., 1997] work well for viscous flow problems.

11. Outline 1) Introduction.  Why is simulating viscous and viscoelastic deformation relevant to the EarthScope?  Definition of Geodynamic modeling. 2) Current status in geodynamic modeling.  Where are we now in terms of modeling capability?  How do we get where we are? 3) Future developments.

12. 2-D F. E. models Tecton for viscoelastic stress analysis [Melosh & Raefsky, 1981]. ConMan for mantle convection [King, Raefsky & Hager, 1990]. Director solver for matrix equations – robust but  memory usage ~ N 3/2,  # of flops ~ N 3,  difficult for parallel computing.

13. 3-D F.E. models Citcom for mantle convection [e.g., Moresi & Gurnis, 1996; Moresi & Solomatov, 1995]. Iterative solver (multi-grid) for matrix equations  memory usage ~ N,  # of flops ~ N,  suitable for parallel computing.

14. Execution Time vs Grid Size N for Multi-grid Solvers in Citcom FMG: Zhong et al. 2000 MG: Moresi and Solomatov, 1995 t ~ N -1

15. Recent Developments to Citcom 1)tectonic faults [Zhong & Gurnis, 1996]. 2)parallel computing [Zhong, Gurnis, & Moresi, 1998]. 3)spherical geometry [Zhong et al., 2000, Billen & Gurnis, 2002]. 4)viscoelastic rheology [Zhong, 2001].

16. Inclusion of Faults in Viscous Flow Models Zhong and Gurnis, 1996

17. Dividing the Earth for Parallel Computing Zhong et al., 2000

18. Benchmarks on an Parallel Supercomputer Zhong et al., 1998 Intel Paragon with 512 processors at Caltech’s CACR

19. Accuracy of CitcomS

20. Thermal Convection with Temperature- dependent Viscosity and Plates Zhong et al., 2000

21. Vertical Motion of Hawaiian Islands and Plate-plume Interaction Zhong & Watts, 2002

22. Modeling the Farallon Subduction Billen and Gurnis, 2002

23. Modeling the Farallon subduction Billen and Gurnis, 2002

24. Recent Developments to Citcom -- Viscoelastic Analysis Motivation: Post-glacial rebound problem.  Most previous studies use a linearized theory that ignores lateral structures.

25. Global Elastic Thickness Variations North America Modified from Watts [1999]

26. The Need for More Efficient Modeling for Post-seismic Viscoelastic Deformation Pollitz et al., 2001 Freed & Lin, 2002

27. 3D Spherical Models of Viscoelastic Deformation with Citcom Zhong, 2001

28. Effect of Mantle Viscosity Anomalies on Viscoelastic Stress Evolution Zhong, Paulson, & Wahr, 2002 Colatitude ( o )

29. Parallel Computing with Beowulf- Cluster Computers Clusters of commodity processors connected by commodity networks. Price-performance ratio: ~ $500/Gflops for best price systems (Aug. 2001). The first Beowulf cluster (16 nodes) was built in 1994 at the GSFC for the Earth and space sciences project (ESS).

30. The First Beowulf-cluster Computer (GSFC) Donald Becker, 1994

31. A Beowulf-Cluster Computer for CU’s Geodynamics 50 Processors (Pentium-III 1 GHz) 50 Gbytes Memory. 100 Mbits/sec Ethernet Cards. 100 Gflops theoretical peak speed.

32. So here we have: An Apparatus for Geodynamic Modeling -- Citcoms Viscoelastic and viscous rheology (nonlinear). 3D Cartesian and spherical geometry. Multi-physics in a single code. Robust and accurate. Parallel computing.

33. What’s next? -- Driving Forces for Future Developments in Geodynamic Modeling Resolving multiple scale (both temporal and spatial) physics in mantle convection and lithospheric deformation. Better and faster modeling to understand the EarthScope observations.

34. Multiple-Scale Thermal Structure from Mantle Convection Dubuffet, Yuen & Murphy, 2001 1025x1025x257 grid points

35. Multiple-scale Structure in Thermo-chemical Convection Van Keken et al., 1997 Zhong & Hager, 2002

36. San Andreas Faults System From USGS Website

37. Multiple Scale in Time Background stress in lithosphere from long-term tectonic processes. Largely ignored in post-seismic stress analyses. What is its role to the rheology?

38. Computer Memory Requirement Mantle convection with uniform 20-km resolution:  1 Tbytes RAM for global models (190 million elements).  120 Gbytes RAM for regional models like N.A. Viscoelastic deformation of lithosphere for a region of 400 km by 400 km with uniform 2-km resolution: 12 Gbytes RAM.

39. Future Developments in Geodynamic Modeling Technologies Incorporation of multi-scale physics (from global to regional and from large time scale to small time scale). Incorporation of faults in modeling of viscoelastic deformation of lithosphere. Adaptive mesh refinement and its parallel computing and multi-grid scheme.

40. Adaptive Mesh Refinement Wissink & Hornung, 2000

41. Future Developments in Geodynamic Modeling Technologies  More powerful PC clusters (faster networking with Gigabit ethernet and Myrinet, and faster processors).  Grid computing for resource sharing.