A nodal high-order discontinuous Galerkin method for elastic wave propagation in arbitrary heterogeneous media

We present an extension of the nodal discontinuous Galerkin method for elastic wave propagation to high interpolation orders and arbitrary heterogeneous media. The high-order lagrangian interpolation is based on a set of nodes with excellent interpolation properties in the standard triangular element. In order to take into account highly variable geological media, another set of suitable quadrature points is used where the physical and mechanical properties of the medium are defined. We implement the methodology in a 2-D discontinuous Galerkin solver. First, a convergence study confirms the hp-convergence of the method in a smoothly varying elastic medium. Then, we show the advantages of the present methodology, compared to the classical one with constant properties within the elements, in terms of the complexity of the mesh generation process by analysing the seismic amplification of a soft layer over an elastic half-space. Finally, to verify the proposed methodology in a more complex and realistic configuration, we compare the simulation results with the ones obtained by the spectral element method for a sedimentary basin with a realistic gradient velocity profile. Satisfactory results are obtained even for the case where the computational mesh does not honour the strong impedance contrast between the basin bottom and the bedrock.