MODELING DYNAMIC RUPTURE IN A 3D EARTHQUAKE FAULT MODEL

We propose a fourth-order staggered-grid finite-difference method to s tudy dynamic faulting in three dimensions. The method uses an implemen tation of the boundary conditions on the fault that allows the use of general friction models including slip weakening and rate dependence. Because the staggered-grid method defines stresses and particle veloci ties at different grid points, we preserve symmetry by implementing a two-grid-row ''thick'' fault zone. Slip is computed between points loc ated at the borders of the fault zone, while the two components of she ar traction on the fault are forced to be symmetric inside the fault z one. We study the properties of the numerical method comparing our sim ulations with well-known properties of seismic ruptures in 3D. Among t he properties that are well modeled by our method are full elastic-wav e interactions, frictional instability, rupture initiation from a fini te initial patch, spontaneous rupture growth at subsonic and supersoni c speeds, as well as healing by either stopping phases or rate-depende nt friction. We use this method for simulating spontaneous rupture pro pagation along an arbitrarily loaded planar fault starting from a loca lized asperity on circular and rectangular faults. The shape of the ru pture front is close to elliptical and is systematically elongated in the inplane direction of traction drop. This elongation is due to the presence of a strong shear stress peak that moves ahead of the rupture in the in-plane direction. At high initial stresses the rupture front becomes unstable and jumps to super-shear speeds in the direction of in-plane shear. Another interesting effect is the development of relat ively narrow rupture fronts due to the presence of rate-weakening fric tion. The solutions for the ''thick fault'' boundary conditions scale with the slip-weakening distance (D-0) and are stable and reproducible for D-0 greater than about 4 in terms of 2T(u)/mu x Delta x. Finally, a comparison of scalar and vector boundary conditions for the frictio n shows that slip is dominant along the direction of the prestress, wi th the largest deviations in slip-rate direction occurring near the ru pture front and the edges of the fault.