3-D dynamic rupture simulations by a finite volume method

Dynamic rupture of a 3-D spontaneous crack of arbitrary shape is investigated using a finite volume (FV) approach. The full domain is decomposed in tetrahedra whereas the surface, on which the rupture takes place, is discretized with triangles that are faces of tetrahedra. First of all, the elastodynamic equations are described into a pseudo-conservative form for an easy application of the FV discretization. Explicit boundary conditions are given using criteria based on the conservation of discrete energy through the crack surface. Using a stress-threshold criterion, these conditions specify fluxes through those triangles that have suffered rupture. On these broken surfaces, stress follows a linear slip-weakening law, although other friction laws can be implemented. For The Problem Version 3 of the dynamic-rupture code verification exercise conducted by the SCEC/USGS, numerical solutions on a planar fault exhibit a very high convergence rate and are in good agreement with the reference one provided by a finite difference (FD) technique. For a non-planar fault of parabolic shape, numerical solutions agree satisfactorily well with those obtained with a semi-analytical boundary integral method in terms of shear stress amplitudes, stopping phases arrival times and stress overshoots. Differences between solutions are attributed to the low-order interpolation of the FV approach, whose results are particularly sensitive to the mesh regularity (structured/unstructured). We expect this method, which is well adapted for multiprocessor parallel computing, to be competitive with others for solving large scale dynamic ruptures scenarios of seismic sources in the near future.