A Weighted Runge-Kutta Discontinuous Galerkin Method for 3D Acoustic and Elastic Wave-Field Modeling (Communications in Computational Physics, 2020)
Numerically solving 3D seismic wave equations is a key requirement forforward modeling and inversion. Here, we propose a weighted Runge-Kutta discontinuous Galerkin (WRKDG) method for 3D acoustic and elastic wave-field modeling. For this method, the second-order seismic wave equations in 3D heterogeneous anisotropic media are transformed into a first-order hyperbolic system, andthen we use a discontinuous Galerkin (DG) solver based on numerical-flux formulations for spatial discretization. The time discretization is based on an implicit diagonal Runge-Kutta (RK) method and an explicit iterative technique, which avoidssolving a large-scale system of linear equations. In the iterative process, we introducea weighting factor. We investigate the numerical stability criteria of the 3D method indetail for linear and quadratic spatial basis functions. We also present a 3D analysis ofnumerical dispersion for the full discrete approximation of acoustic equation, whichdemonstrates that the WRKDG method can efficiently suppress numerical dispersionon coarse grids. Numerical results for several different 3D models including homogeneous and heterogeneous media with isotropic and anisotropic cases show that the 3DWRKDG method can effectively suppress numerical dispersion and provide accuratewave-field information on coarse mesh.
Keywords: Numerical modeling; anisotropy; discontinuous Galerkin method; numerical dispersion; stability.