Grid-characteristic method combined with discontinuous Galerkin method for simulation of wave propagation through linear elastic media in the three-dimensional case

The grid-characteristic method on regular structured meshes is combined with a discontinuous Galerkin method on tetrahedral meshes to solve the direct problem of three-dimensional elastic wave propagation through a geological medium consisting of four linear elastic layers with different parameters and arbitrary curved boundaries. The numerical methods are matched using a special algorithm taking into account the features of the transition from unstructured tetrahedral to regular structured meshes in three-dimensional space. A comparative convergence analysis of the combined method and the grid-characteristic method on curvilinear structured meshes is performed depending on the step sizes in spatial directions. The wave field of the velocity magnitude is obtained for a perturbation propagating from the source.