2-DIMENSIONAL MODEL OF A FAULT

We present the results of simulations of a two-dimensional mechanical model of a fault, which is a generalization of the one-dimensional model studied previously [Carlson and Langer, Phys. Rev. A 40, 6470 (1989)]. We incorporate both the lateral fault axis and the fault depth, and consider both cases of spatially homogeneous and depth-dependent velocity-weakening friction. Our main result is that in both cases for small- to moderate-sized events, the Gutenberg-Richter scaling exponent b is unity for a wide range of parameters, as observed in the one-dimensional model, and consistent with measurements for real earthquakes. In addition, in the depth-dependent friction model, we study the activity patterns as a function of depth. We observe that smaller events tend to be triggered near the surface, while on relatively shallow faults larger events tend to achieve their first appreciable velocities at depth, in agreement with certain trends observed in seismological studies of the hypocenter distributions of small and large earthquakes.