Simulation of anisotropic wave propagation based upon a spectral element method

We introduce a numerical approach for modeling elastic wave propagation in 2-D and 3-D fully anisotropic media based upon a spectral element method. T he technique solves a weak formulation of the wave equation, which is discr etized using a high-order polynomial representation on a finite element mes h. For isotropic media, the spectral element method is known for its high d egree of accuracy, its ability to handle complex model geometries, and its low computational cost. We show that the method can be extended to fully an isotropic media. The mass matrix obtained is diagonal by construction, whic h leads to a very efficient fully explicit solver. We demonstrate the accur acy of the method by comparing it against a known analytical solution for a 2-D transversely isotropic test case, and by comparing its predictions aga inst those based upon a finite difference method for a 2-D heterogeneous, a nisotropic medium. We show its generality and its flexibility by modeling w ave propagation in a 3-D transversely isotropic medium with a symmetry axis tilted relative to the axes of the grid.