Numerical Challenges in Earthquake Simulations

Jeremy Kozdon
Geophysics Department
Stanford University
Stanford, California, USA


Earthquakes pose a huge societal hazard in many parts of the world. The largest and most destructive events are extremely rare so computation is a critical partner to theory, experiments, and field work. As computing power has increased there has been a push to include more realistic physics in the models. Since earthquakes involve a complex coupling of many different physical processes at different spatial and temporal-scales this has lead to many new (and exciting!) numerical challenges.

Our group is tackling these problems through a variety of computational techniques. The workhorse code of group is based on summation-by-parts finite difference methods with interface and boundary conditions handled through the simultaneous approximation term method. Complex geometries are handled through the use of multiblock grids and coordinate transforms. We are currently extending this method to handle additional physics (such as coupling with volcanic conduit flow models) as well as implicit time integration for quasi-static elasticity so that 10,000 year histories of repeated earthquakes occurring in response to slow tectonic loading can be accommodated.

A big challenge in earthquake simulations is the multi-scale nature of the problem. When laboratory measured parameters are used the grid resolution required for accurate simulation is impractically small for fixed grid methods, thus in practice artificially enhanced parameters are used. To explore what is lost by not using laboratory parameters in field-scale simulations, we are developing an adaptive mesh refinement (AMR) code. The numerical method used in the AMR code is a multi-dimensional finite volume method with the Berger-Oliger adaptive time stepping routine.