Differences in Dynamic Modeling Techniques and Their Implications

1. Differences in Dynamic Modeling Techniques and Their Implications David Oglesby UC Riverside WGCEP Workshop March 16, 2005

2. Numerical Models with Complex Fault Geometry • Static • Segall and Pollard (offsets/stepovers) • Andrews (bends and branches) • Dynamic • Harris and Day, Kase and Kuge (offsets/stepovers) • Aochi, Fukuyama, Oglesby, Aagaard, Kame/Rice Group (bends and branches) • Duan, Shaw, Mora group (effect of prior EQs)

3. Purpose of Talk • We need a common set of assumptions for scenario models. • Fault geometry • Material model • Stress field • Friction law/parameters • By pointing out differences in assumptions by various groups, I hope to spur discussion on: • the potential effects of these assumptions. • which assumptions are most realistic/useful.

4. Basic Topics • Static Stress • Dynamic Stress/Frictional Formulation • Fault Geometry+Mesh/Grid

5. Static Stress: Depth-Dependence of Normal Stress • Lithostatic load and effective normal stress should increase with depth. • So static and dynamic frictional levels should also increase with depth. • But stress drop doesn’t appear to increase with depth. • How do we reconcile these two points?

6. Static Stress: Depth-Dependence of Normal Stress • Some models just go ahead and have depth-dependent stress drop.

7. Static Stress: Depth-Dependence of Normal Stress • Others just ignore depth-dependence of normal stress--stresses constant with depth.

8. Static Stress: Depth-Dependence of Normal Stress • Most Common: Depth-dependent effective normal stress near surface, then constant with depth. • Assume pore fluids are overpressured at depth, and follow lithostatic load.

9. Static Stress: Depth-Dependence of Normal Stress

10. Static Stress: Depth-Dependence of Normal Stress • Another way: Effective normal stress is depth-dependent, but yield stress doesn’t depend on effective normal stress.

11. A B C Static Stress: Amplitude and Direction of Shear Stress • Most common way: take regional tectonic stress field + overburden and resolve it onto faults of different orientation.

12. Static Stress: Amplitude and Direction of Shear Stress • Some segments more favorable for rupture than others

13. Static Stress: Amplitude and Direction of Shear Stress • Simpler technique: same shear and normal tractions on all segments

14. Static Stress: Amplitude and Direction of Shear Stress • Another technique: Get normal stress amplitude and shear stress direction from tectonic stress + overburden, but set shear stress to be just below failure stress. • Motivation: After many earthquakes, fault may be critically stressed • May give “worst-case” scenario.

15. Static Stress: Amplitude and Direction of Shear Stress • Another technique: use multi-cycle simulations to get stress field consistent with loading, relaxation, and previous earthquakes.

16. Static Stress: Amplitude and Direction of Shear Stress

17. Static Stress: Amplitude and Direction of Shear Stress • Effect of constant vs. tectonic stress

18. Static Stress: Amplitude and Direction of Shear Stress • Backwards branching • Extra-wide stepover jump

19. Dynamic Normal Stress and Friction • Typical friction formulation • Time-dependent normal stress could be important for non-trivial fault geometry. • Feedback between normal stress, friction, rupture propagation, radiation

20. Dynamic Normal Stress and Friction • Offset parallel Faults (Harris et al., 1991; Harris and Day, 1993)

21. Dynamic Normal Stress and Friction • Offset parallel Faults (Harris et al., 1991; Harris and Day, 1993)

22. Dynamic Normal Stress and Friction • Rupture paths in branched faults are a complex result of static and dynamic stress field.

23. Dynamic Normal Stress and Friction • Initial work by Aochi and others ignored dynamic normal stress increments for computational efficiency. • Argued it wasn’t very important. • Now they include it.

24. Dynamic Normal Stress and Friction • Another approach: yield stress not proportional to normal stress • Normal stress is time-dependent, but there is no effect on the friction. • Motivation: lithostatic load is so large that increments in normal stress are negligible. • This approach is needed if effective normal stress increases with depth, but stress drop doesn’t.

25. Dynamic Normal Stress and Friction • Another approach: yield stress not proportional to normal stress • Rupture path result of interaction between static and dynamic shear stress field. • Would remove asymmetry between releasing and restraining stepovers. • Could have a big effect in ability of rupture to jump from fault to fault (Cucamonga-SAF?)

26. Fault Geometry+Mesh/Grid • Uncertainty in actual fault geometry • Parameterization of segment junctions

29. Other issues • Friction law (rate/state vs. slip weakening) • Instantaneous or immediate effect of normal stress on friction? • Even if we agree on which parameters should be in the model, can we agree on what their values should be? • Differences in numerical modeling methods • SCEC is working on this!

30. Conclusions • Different approaches reduce our ability to compare results of different studies. • Scenario earthquake models will require a common set of assumptions. • So which do we pick? • How do we weight different choices? • Can observations or experiments provide constraints?