Assessment of the finite element solutions for 3D spontaneous rupture using GeoFEM

Numerical simulations of spontaneous shear rupture on a planar fault using a slip-weakening model in a three-dimensional uniform elastic medium were conducted using a parallel FE code, GeoFEM, which was originally developed for the solid-Earth simulations on the Earth Simulator. The aim was to evaluate the accuracy and applicability of GeoFEM to earthquake rupture. The present numerical results are compared with published results obtained using a finite-difference (FD) method and a boundary integral (BI) method for rupture times and time functions of slip, slip rate, and shear stress at two particular points on the fault plane. The effects of mesh size and damping on the attenuation of spurious oscillations were also examined in a range of simulations. The appropriate degree of damping depends on mesh size and must be introduced in order to obtain reliable numerical solutions; weak damping leads to significant oscillation and strong damping to artificially low rupture speeds and low slip rates. Our results indicate that mesh size should be sufficiently small to allow the inclusion of a few grids in the cohesive zone, as shown in other numerical methods. The solutions by GeoFEM that have the appropriate mesh size and damping are quite similar to those obtained using the FD and BI methods, the difference between them being generally less than 2% in terms of the rupture time and 5.2% in terms of the peak slip rate.