DISCONTINUOUS GALERKIN METHOD FOR SOLVING 2D DISSIPATIVE SEISMIC WAVE EQUATIONS

Seismic dissipation widely exists in underground media. To develop a detailed understanding of wave propagation in dissipative media, in this study, we introduce a discontinuous Galerkin (DG) method for solving acoustic and elastic wave equations in D'Alembert media. This method uses the numerical flux-based DG formulations with the explicit 3rd-order total variation diminishing (TVD) time discretization. We first derive an empirical formula for numerical stability conditions, which shows that the relative error of the Courant-Friedrichs-Lewy (CFL) condition numbers between the actual the numerical cases does not exceed 3%. The analyses also show that both the dispersion and dissipation in D'Alembert media are frequency dependent, and have a strong correlation with the dissipation factor. Finally, we present some numerical experiments. The quantitative comparisons of the attenuation ratios of the waveforms show that they are close to the theoretical ones, verifying the findings of the analyses. In particular, for elastic waves, the relative errors between the numerical attenuation ratios and the theoretical ones do not exceed 4%. The simulation of dissipative elastic wave propagation in a model with surface topography indicates our method is capable of dealing with complex geometry.