Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner

TL;DR

This paper introduces a hybrid numerical approach combining finite element and finite difference methods for elastic wave simulations with energy conservation, effectively handling complex topography in seismic modeling.

Contribution

The paper presents a novel energy-conserving interface treatment that smoothly joins finite element and finite difference discretizations for elastic wave equations.

Findings

The hybrid method accurately models seismic waves over complex topography.

The interface treatment ensures energy conservation across the combined methods.

Numerical examples validate the effectiveness of the proposed approach.

Abstract

We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain to account for the topography, and combined with the more efficient finite difference method that is applied to the deep region of the simulation domain. We demonstrate that these two discretization methods, albeit starting from different formulations of the elastic wave equation, can be joined together smoothly via weakly imposed interface conditions. Discrete energy analysis is employed to derive the proper interface treatment, leading to an overall discretization that is energy-conserving. Numerical examples are presented to demonstrate the efficacy of the proposed interface treatment.