Generic Description of Earthquake Simulators

1. Generic Description of Earthquake Simulators Terry Tullis Jim Dieterich Keith Richards-Dinger Olaf Zielke John Rundle Steve Ward Fred Pollitz

2. Outline • What are Earthquake Simulators? • Inputs • Rheology • Fault Geometry and Slip Rates • Backslip Loading • Strengths • Outputs • Differences Between Simulators • Conclusions

3. What Are Earthquake Simulators? • Earthquake simulators are computer programs that use known physics to describe earthquake sequences • To generate long histories on many faults, simplifications are made to make computation feasible • The amount of detail computed within individual earthquakes depends on the simulator • None of those capable of generating long histories include elastodynamics, but some make approximations of it • Thus seismic waves are not computed in the many-fault simulators • The faults are typically approximated by many rectangular elements, although in the future triangles may be used to represent curved surfaces better

4. Inputs – Rheology • Faults – Some representation of friction is used on the faults • In most cases the surrounding medium is represented by a linear elastic half space • However, ViscoSim assumes viscoelastic behavior • In order to express the interactions between the faults, the simulators use boundary element methods to covert slip on each element to changes in stress on each element (Okada, 1992, or other dislocation representations)

5. Inputs – Geometry and Slip Rates • Relatively well-known inputs are fault geometry and slip rates • Our current version of an all-California model allcal2 (excluding Cascadia) is nearly the same as UCERF2 • This means that the fault geometry and the slip rates come from that fault and deformation model • In the future we are set up to use the UCERF3 model when it is available • We use so called “backslip” to load the faults. • Thus, the stress change felt on each element in each time step is the sum of the dislocation stresses from every element that slips and the backslip stresses

6. allcal2 Model It is essentially the UCERF2 Fault and Deformation Model ~3 km squares, down to ~12 km depth ~ 15,000 elements 0 10 20 30 40 Slip rate, mm/yr

7. allcal2 Model ~3 km squares, down to ~12 km depth It is essentially the UCERF2 Fault and Deformation Model ~ 15,000 elements Details of Southern CA Few rips and tears down dip, since using rectangles rather than triangles to fit curved surfaces 0 10 20 30 40 Slip rate, mm/yr

8. Inputs – Geometry and Slip Rates • Relatively well-known inputs are fault geometry and slip rates • Our current version of an all-California model allcal2 (excluding Cascadia) is nearly the same as UCERF2 • This means that the fault geometry and the slip rates come from that fault and deformation model • In the future we are set up to input the UCERF3 model when it is available • We use so called “backslip” to load the faults. • Thus, the stress change felt on each element in each time step is the sum of the dislocation stresses from every element that slips and the backslip stresses

9. Inputs – Backslip Loading • It is the the stress rate on all elements resulting from slipping each element backward at its prescribed slip rate • Thus the local stress builds up tending to move each element forward to counteract its own backslip stresses • When an element finally slips its locally induced stresses are relaxed by the slip. Stress due to its slip is transferred to the other elements via the dislocation stresses. • Thus there is no long-term build-up of stresses resulting from the slip on the faults • Other loading arrangements are under consideration, but backslip is the only one presently developed that • Prevents build-up of stresses due to complex fault geometry • Causes each fault to slip at its long-term rate on the average

10. Inputs – Fault Strengths (More Properly Stress Drops) • The various simulators use different constitutive descriptions for fault friction • However, for all simulators, each fault section requires some description of the fault strength • In the real world these presumably vary from point to point, but are unknown • For most faults we use relations such as area-magnitude scaling to estimate strengths that will cause earthquakes of typical size for each section or fault • In places where paleoseismic data provide recurrence intervals we “tune” the strengths to match those data (e.g. increase the strengths to lengthen intervals)

11. Outputs • Any desired statistical or other items can be output • We have created a variety of tools to create standard output plots so all the simulators can be compared • We have many more plots than we selected to show today • We may have already created others of interest and, if so, we can pull them up quickly during discussion

12. Differences Between Simulators • Representation of fault friction is one big difference • Another is whether/how elastodynamic effects are approximated • Differences between the simulators mean that somewhat different values of strength as a function of location are needed to “tune” each simulator with paleoseismic data • However, we start from common values based on scaling • These are used when no paleoseismic data are available • There are also other more detailed earthquake simulators that are not suited for generating long histories of earthquakes on many faults, but that make fewer approximations. Notable among these is one by Nadia Lapusta that treats elastodynamcis with rate and state friction.

13. Comparison of Current Simulator Features

14. Conclusions • All of the simulators use much of what is known about the physics of earthquakes and the California faults and slip rates. • Each simulator makes a variety of simplifications in order to allow calculation of long earthquake histories on many faults. • Representation of fault friction and whether or how to deal with approximations to elastodynamic behavior are among the differences between the simulators. • More information is needed about the faults, especially their strengths, than is known. Consequently estimates are made for strengths in those places where information is lacking. • The diversity of simulator assumptions and methods provides some idea of the influence that different assumptions have on the results.