Discontinuous Galerkin finite-element method for elastic wave modeling including surface topography

As a powerful high order finite element numerical simulation method, Discontinuous Galerkin finite element method (DG-FEM) has been extensively studied by researchers worldwide. In this paper, we discretize the elastic wave equation based on the arbitrary high order discontinuous Galerkin finite element method in spatial domain, and then transform the final non-homogeneous linear system to a homogeneous one. Finally, combined with strong stability preserved Runge-Kutta integrator aiming at homogeneous system, DG-FEM is extended to arbitrary high order precision in time. A new PML absorbing boundary condition named CFS-NPML is also derived based on the idea of nearly PML (NPML) technology and complex-frequency-shifted(CFS) stretching coordinate transformation. An effective seismic wave numerical simulation method with topography is obtained by combining DG-FEM with the CFS-PML technology. The numerical results show that DG-FEM is characterized by high order accuracy. This method is available for the numerical simulation of elastic wave propagation in the models with arbitrary complicated topography and geologic structures. Meanwhile, CFS-NPML technology has a good absorbing effect on the artificial boundary reflections including the artificial reflections of surface wave.