1. Data Assimilation and the Development of the Virtual_California Model Paul B. Rundle Harvey Mudd College, Claremont, CA Presented at the GEM/ACES Workshop, Maui, Hawaii July 30, 2001

2. References P. B. Rundle, J.B. Rundle, K.F. Tiampo, J. Sa Martins, S. McGinnis and W. Klein, Nonlinear network dynamics on earthquake fault systems, Phys. Rev. Lett., in press (2001). J.B. Rundle, P. B. Rundle, W. Klein, J. Sa Martins, K.F. Tiampo, A. Donnellan and L.H. Kellogg, GEM plate boundary simulations for the plate boundary observatory: Understanding the physics of earthquakes on complex fault systems, PAGEOPH, in press (2001). P. B. Rundle, J.B. Rundle, J. Sa Martins, K.F. Tiampo, S. McGinnis, W. Klein, Triggering dynamics on earthquake fault systems, pp. 305-317, Proc. 3 rd Conf. Tect. Problems San Andreas Fault System, Stanford University (2000). P. B. Rundle, J.B. Rundle, J. Sa Martins, K.F. Tiampo, S. McGinnis, W. Klein, Network dynamics of Earthquake Fault Systems, Trans. Am. Geophys. Un. EOS, 81 (48) Fall Meeting Suppl. (2000)

3. Topology of Virtual_California 1999 3D View

4. Topology of Virtual_California 2000 3D View

5. Topology of Virtual_California 2001

6. Earthquakes Used to Set Friction Values Only events larger than M > 5.8 were used.

7. Static Data Assimilation, Step 1: Assign Seismic Moments of Earthquakes to Faults j th earthquake i th fault r ij -3, the distance between the j th earthquake and the i th fault segment, is the rate at which stress amplitude falls off with distance from a dislocation. It is used as a probability density function that localizes the moment release on nearby faults. Seismic moments of paleo, historic, and instrumentally recorded large events are assigned to all faults in the model by a probability density function. Epicenters of historic earthquakes in Southern California since 1812

8. Static Data Assimilation, Step 2: Determination of Static-Kinetic Friction Coefficients Definitions: M o (t j ) -- Seismic moment of j th earthquake m i -- Average seismic moment resolved onto i th fault  -- Shear modulus  s  -- Average Slip  -- Static stress drop A -- Area of fault f - Fault shape factor (order ~ 1)  - Average normal stress (assume gravity)  s - Static friction coefficient  k - Kinetic friction coefficient Definition of Seismic Moment Slip-area for compact crack Difference between static & kinetic friction coefficients Assume: f ~ 1;  ~ 5 x 10 6 Pa;  ~ 3 x 10 10 Pa

9. Static Data Assimilation, Step 2: Computed Static-Kinetic Friction Coefficients At right is the result of the calculation of  S -  K for the Virtual_California 1999 model. This difference in friction coefficients determines the nominal values of slip on the various fault segments.

10. Static Data Assimilation, Step 2: Computed Static-Kinetic Friction Coefficients Above is  S -  K for the Virtual_California 2000 model.

11. Baseline values for parameters  are determined for each fault segment. It can easily be shown that: 2  = So  is an observable quantity. Deng and Sykes (1997) tabulate the average fraction of stable interseismic, aseismic slip for many faults in California. Average stable aseismic slip Total slip Static Data Assimilation, Step 3: Aseismic Slip Factor   determines fraction of total slip that is stable aseismic slip. FF RR  > 0 FF RR  = 0 Time Stress Stress,  Data from T Tullis, PNAS, 1996