Slipping on a frictional fault plane in three dimensions: a numerical simulation of a scalar analogue

Abstract

Summary In this paper we Sci up and simulate numerically a scalar analogue for a rupturing seismic fault plane in a three-dimensional space. The scalar analogue bears the same relation to the full vector elastic system as an SH (anti-plane strain) system bears to a P-SV (plane strain) system in two dimensions. The fault plane is embedded in a whole space of homogeneous material and behaves like a frictional surface. We allow zones of rupture to propagate out at the wave speed in various ways within the fault plane. In some cases the region of slip propagates around unbreakable obstacles within the fault. The resulting far-field pulse shapes and spectra are computed. Mathematically we Sci up an integral equation for the displacement on the fault. As in earlier work which addressed the two-dimensional problem the integral equation has a non-integrable kernel, but a discretized version of this function may be found numerically from the discrete version of the wave operator and a stable explicit numerical scheme is obtained.