Simulation of elastic wave propagation in fractured media with multi-scale finite elements

We apply the Generalized Multi-scale Finite Element Method (GMsFEM) to simulate seismic wave propagation in fractured media. Fractures are represented explicitly on a fine-scale triangular mesh, and they are incorporated using the linear-slip model. The motivation for applying GMsFEM is that it can reduce computational costs by utilizing basis functions computed from the fine-scale fracture model to simulate propagation on a coarse grid. We first apply the method to a simple model that has a uniform distribution of parallel fractures. At low frequencies, the results could be predicted using a homogeneous, effective medium, but at higher frequencies GMs- FEM results allow simulation of more complex, scattered wavefields generated by the fractures. The second, complex model has two fracture corridors in addition to a few sparsely distributed fractures. Simulations compare scattered wavefields for different acquisition geometries. GMsFEM allows a reduction of computation of about 90% compared to a conventional finite element result computed directly from the fine-scale grid.