Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

TL;DR

This paper introduces GMsFEM, a multiscale finite-element approach that efficiently models elastic wave propagation in complex, heterogeneous, and anisotropic media, significantly reducing computational costs while maintaining accuracy.

Contribution

The paper develops a novel GMsFEM framework that constructs multiscale basis functions from local problems, enabling efficient and accurate seismic wave simulations in complex media.

Findings

Effective modeling of elastic waves in anisotropic media

Significant reduction in degrees of freedom compared to traditional methods

Low error levels achieved in heterogeneous models

Abstract

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.