The role of roughness in earthquake source physics

Abstract

Faults are rough at all scales and can be described as self-affine fractals. This deviation from planarity results in geometric asperities and a locally heterogeneous stress field, which affect the nucleation and propagation of shear rupture. I study this effect numerically at the scale of small earthquakes, in which realistic geometry and friction law parameters can be incorporated in the model. The numerical approach developed in this thesis includes three main features. First, to enable slip that is large relative to the size of the elements near the fault, as well to capture accurately of the variation of normal stress during slip, I implement slip-weakening and rate and state friction laws into the Mortar Finite Element Method, in which non-matching meshes are allowed across the fault and the contacts are continuously updated. Second, the mesh near the fault is refined using hanging nodes to enable accurate representation of the fault geometry. Finally, to model the whole seismic cycle, including a completely spontaneous nucleation process, the method uses variable time stepping with quasi-static and fully dynamic implicit schemes. The developed methodology is used to study the response of rough faults governed by rate and state friction to slow tectonic loading, where, in each simulation, the earthquake sequence includes at least two seismic cycles. With increasing roughness, there is a transition from seismic to aseismic slip behavior, in which the load on the fault is released by more slip events but with lower slip rate, seismic moment, and average static stress drop. We analyze the nucleation process in the fast slip events and show that the roughness introduces local barriers that complicate the nucleation process and result in asymmetric expansions of the rupture, non-monotonic increases in the slip rates on the fault, and the generation of multiple slip pulses. In general, the nucleation length increases with increasing roughness amplitude. However, there are large differences between first slip events in the sequences, where the initial conditions are homogenous, and later events, where the initial stress field and friction conditions are determined by the rupture growth and arrest in previous slip events.