Explicit coupling of acoustic and elastic wave propagation in finite difference simulations

TL;DR

This paper introduces a stable and accurate finite-difference coupling method for simulating acoustic and elastic wave propagation across interfaces, enabling detailed seismic exploration in complex geological regions.

Contribution

It presents a novel explicit coupling mechanism using summation-by-parts operators and penalty terms to simulate acoustic-elastic wave interactions in 2D models.

Findings

Stable and accurate coupled wave simulations achieved.

Energy conservation maintained in discretization.

Applicable to seismic exploration in complex geological settings.

Abstract

We present a mechanism to explicitly couple the finite-difference discretizations of 2D acoustic and isotropic elastic wave systems that are separated by straight interfaces. Such coupled simulations allow the application of the elastic model to geological regions that are of special interest for seismic exploration studies (e.g., the areas surrounding salt bodies), while with the computationally more tractable acoustic model still being applied in the background regions. Specifically, the acoustic wave system is expressed in terms of velocity and pressure while the elastic wave system is expressed in terms of velocity and stress. Both systems are posed in first-order forms and discretized on staggered grids. Special variants of the standard finite-difference operators, namely, operators that possess the summation-by-parts property, are used for the approximation of spatial derivatives. Penalty terms, which are also referred to as the simultaneous approximation terms, are designed to weakly impose the elastic-acoustic interface conditions in the finite-difference discretizations and couple the elastic and acoustic wave simulations together. With the presented mechanism, we are able to perform the coupled elastic-acoustic wave simulations stably and accurately. Moreover, it is shown that the energy-conserving property in the continuous systems can be preserved in the discretization with carefully designed penalty terms.