A hybrid-Galerkin finite-element method for seismic wave propagation in fractured media

Abstract

The discontinuous Galerkin Finite Element Method (DGM) is a promising approach for modeling wave propagation in fractured media. It allows for discontinuities in the displacement field to simulate fractures or faults in a model. The approach is based on the interior-penalty formulation of DGM, and the fractures are simulated using the linear-slip model, which is incorporated into the weak formulation. On the other hand, the Spectral Element Method (SEM) can be used to simulate elastic wave propagation in non-fractured media. SEM uses continuous basis functions which do not allow for discontinuities in the displacement field. Since the inception of DGM for seismic wave propagation in fractured media there has existed a question of whether DGM can be made computationally efficient. Here we propose a Hybrid Galerkin FEM (HGM) for elastic wave propagation in fractured media. HGM combines SEM and DGM to model seismic wave propagation in fractured media at reduced computational costs. We use DGM in areas containing fractures and SEM in regions where there are no fractures. The coupling between the domains at the interfaces is satisfied in the weak form through interface conditions. The degree of reduction in computation time greatly depends on the density of fractures in the medium. In this paper, we formulate and implement HGM for seismic wave propagation in fractured media. Using realistic numerical examples, we show that our proposed HGM outperforms a stand-alone DGM with reduced computation cost and memory requirement while maintaining the same level of accuracy.