A Computational Method for Earthquake Cycles in Anisotropic Media

Maricela Best Mckay, Brittany A. Erickson, & Jeremy E. Kozdon

Under Review June 2, 2019, SCEC Contribution #9205

We present a numerical method for the simulation of earthquake cycles on a 1D fault interface embedded in a 2D homogeneous, anisotropic elastic solid. The fault is governed by an experimentally motivated friction law known as rate-and-state friction which furnishes a set of ordinary differential equations which couple the interface to the surrounding volume. Time enters the problem through the evolution of the ODEs along the fault and provide boundary conditions for the volume, which is governed by quasi-static elasticity. We develop a time-stepping method which accounts for the interface/volume coupling, and requires solving an elliptic PDE for the volume response at each time step. The 2D volume is discretized with a second order accurate finite difference method satisfying the summation-by-parts property, with boundary and fault interface conditions enforced weakly. This framework leads to a provably stable semi-discretization. To mimic slow tectonic loading, the remote side-boundaries are displaced at a slow rate, which eventually leads to earthquake nucleation at the fault. Time stepping is based on an adaptive, fourth order Runge-Kutta method and captures the highly varying time-scales present. The method is verified with convergence tests for both the orthotropic and fully anisotropic cases. An initial parameter study reveals regions of parameter space where the systems experiences a bifurcation from period one to period two behavior. Additionally, we find that anisotropy influences the recurrence interval between earthquakes, as well as the emergence of aseismic transients and the nucleation zone size and depth of earthquakes.

Citation
Best Mckay, M., Erickson, B. A., & Kozdon, J. E. (2019). A Computational Method for Earthquake Cycles in Anisotropic Media. Geophysical Journal International, (under review).