Numerical Simulation of Acoustic Wave Propagation in Layered Media With a Generalized Multiscale Finite Element Method

Numerical modeling of acoustic wave propagation often faces significant difficulties in application to models with fine scale heterogeneity. In some cases averaging techniques allow a reduction of the complexity of the models. However, the range of applicability of the effective medium theories is often quite narrow. For example, even for the relatively simple case of a binary, layered medium, analytical upscaling can be used only for wavelengths that are large with respect to the thickness of strata (Backus, 1962; Schoenberg and Muir, 1989). We present results using a new multiscale finite element method designed to reduce the computational complexity of wave simulation. It uses multiscale basis functions capturing the information about fine scale heterogeneities. These basis functions are then used on a coarse grid to accelerate computations. We apply the method to layered media to compare the accuracy of the mulitscale result to effective medium solutions for the same models. The results show the breakdown in effective medium results as layer thickness increases, while the multiscale method produces accurate results. The multiscale method has strong potential for modeling problems that need to consider complex, fine-scale heterogeneity when upscaling is inaccurate or suitable averaging methods are unknown.