Multiscale modeling of acoustic wave propagation in 2D heterogeneous media using local spectral basis functions

Abstract

Seismic wave equation modeling is an essential part of all full wavefield based seismic imaging, inversion and data analysis methods. Solving seismic wave equation on highly heterogeneous media is computationally expensive and reduced-order models can be used to speed-up the computations by reducing the degrees of freedom. In this abstract we present a reduced order model that consists of an application of the multiscale finite element method to solving the acoustic wave equation using spectral multiscale basis functions (Enriched MsFEM). Generally, the continuous multiscale basis functions are constructed by solving local spectral problems first and a careful selection of partition of unity functions. We then choose the eigenvectors that correspond to small, asymptotically vanishing eigenvalues to form our approximation spaces. This method efficiently captures the effects of fine scale features of the domain on wave propagation without solving the problem on the fine mesh. The computation of basis functions on different coarse grid blocks is totally independent, which makes this method easy to parallelize. Compared to discontinuous multiscale methods, the proposed continuous methods have advantages in capturing subgrid effects more accurately; however, the mass matrix resulting in continuous multiscale methods is no longer block-diagonal. Our numerical experiments demonstrate that the method shows higher accuracy compared to traditional MsFEM and can reduce computation time and memory costs.