Elastic wave propagation in fractured media using the discontinuous Galerkin method

Abstract

We have formulated and implemented a discontinuous Galerkin method (DGM) for elastic wave propagation that allows for discontinuities in the displacement field to simulate fractures or faults. 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 by including an additional term that is similar to the penalty term but uses the fracture compliance instead of an arbitrary penalty parameter. We have calibrated our results against an analytic solution of fracture-induced anisotropy for a set of elongated horizontal fractures, and we have evaluated numerical examples that simulate the reflection and transmission of waves at a fracture and at fracture interface waves. This method can further be used with models containing intersecting fractures and multiple fracture sets in 2D or 3D domains.