Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods

Abstract

A numerical method suitable for wave propagation problems in complex geometries is developed for simulating dynamic earthquake ruptures with realistic friction laws. The numerical method couples an unstructured, node-centered finite volume method to a structured, high order finite difference method. In this work we our focus attention on 2-D antiplane shear problems. The finite volume method is used on unstructured triangular meshes to resolve earthquake ruptures propagating along a nonplanar fault. Outside the small region containing the geometrically complex fault, a high order finite difference method, having superior numerical accuracy, is used on a structured grid. The finite difference method is coupled weakly to the finite volume method along interfaces of collocated grid points. Both methods are on summation-by-parts form. The simultaneous approximation term method is used to weakly enforce the interface conditions. At fault interfaces, fault strength is expressed as a nonlinear function of sliding velocity (the jump in particle velocity across the fault) and a state variable capturing the history dependence of frictional resistance. Energy estimates are used to prove that both types of interface conditions are imposed in a stable manner. Stability and accuracy of the numerical implementation are verified through numerical experiments, and efficiency of the hybrid approach is confirmed through grid coarsening tests. Finally, the method is used to study earthquake rupture propagation along the margins of a volcanic plug.