Generalized multiscale finite elements for simulation of elastic-wave propagation in fractured media

Abstract

We applied the generalized multiscale 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 using basis functions computed from the fine-scale fracture model to simulate propagation on a coarse grid. First, we 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, GMsFEM allows simulation of more complex, scattered wavefields generated by the fractures without assuming a specific form of anisotropy. A second, more complex model has two fracture corridors in addition to a few sparsely distributed fractures. Simulations compare scattered wavefields for different acquisition geometries. The third test case represents a vertical section of subsurface structures and is designed to test the influence of fractures on the surface seismic. We compared the fine-scale solution with multiscale solution to demonstrate the accuracy and efficiency of computations. Given the simulation results of three different test cases, GMsFEM allows a reduction of computation time of approximately 80% compared with a conventional finite-element result computed directly from the fine-scale grid, and it can predict seismic signal variations useful for the interpretation of fracture distributions.