Enriched Galerkin finite element approximation for elastic wave propagation in fractured media

Abstract

Finite Element Methods (FEM) are becoming increasingly popular in modeling seismic wave propagation. These methods provide higher order accuracy, geometrical flexibility and adaptive gridding capabilities that are not easy to incorporate in traditional finite difference methods employed for generation of synthetic seismograms. Moreover, several studies have shown that Discontinuous Galerkin FEM (DGM) is a promising approach for modeling wave propagation in fractured media. Here we propose an Enriched Galerkin FEM (EGM) for elastic wave propagation. EGM uses the same bilinear form as DGM and the continuous Galerkin finite element spaces enriched by discontinuous piecewise constants or bilinear functions. EGM satisfies local equilibrium while reducing the degrees of freedom in DGM formulations. In this paper, we consider elastic wave propagation and derive optimal a priori error estimates for DGM and EGM. We present numerical examples in two spatial dimensions that confirm these theoretical results. In addition, we provide numerical comparisons with the Spectral element method. In previous work, DGM has been shown to be effective in modeling elastic wave propagation in fractured media using the linear slip model. We now extend these results to EGM with reduced computational costs over DGM.