Simulation of Seismic Wave Propagation due to Finite Source Rupture Models Using an Arbitrarily High Order Discontinuous Galerkin Method on Tetrahedral Meshes

The accurate simulation of seismic wave propagation in heterogeneous, anisotropic media with complicated, 3-dimensional geometry is still a very challenging task. As waveforms contain important information about the interior structure and properties of a material, it is necessary to develop numerical schemes that are capable of computing accurate seismograms even on distorted or rather coarse meshes. Unstructured, tetrahedral meshes can be fitted to difficult geometrical features of realisitic geological models. We present a new, numerical method that solves the 3-dimensional elastic wave equations on such tetrahedral meshes. The so-called Discontinuous Galerkin Method provides very high approximation orders in space and time, if combined with a new time integration scheme termed ADER. It uses Arbitrary high order DERivatives of the spatial basis functions to replace time derivatives appearing in the time Taylor-series expansion. As we solve the elastic wave equations in the velocity-stress-formulation, anisotropic material can be handled through modified Jacobian matrices, that include all 21 coefficients describing an elastic material in the most general case of a triclinic crystalline structure. The new method can treat spatial point sources at arbitrary locations inside the computational domain. As the point source positions are not restricted to mesh nodes, the scheme regards kinematic source models very elegantly. Finite source rupture models providing rupture planes of arbitrary orientation or size, including curvature and branching, can be handled, as each subfault is treated as a point source at an arbitrary position independent of the local mesh geometry. Test cases to validate the performance of the new method are shown and its strengths and weaknesses are discussed. Finally, we conclude with preliminary results in the case of visco-elastic materials.