On Godunov-type finite volume methods for seismic wave propagation

TL;DR

This paper evaluates Godunov-type finite volume methods for seismic wave simulation, finding they reduce dispersion in idealized models but are less effective than finite differences in realistic scenarios due to higher costs and lower accuracy.

Contribution

It provides a comparative analysis of finite volume and finite difference methods for seismic waves, highlighting the conditions under which FV methods are advantageous.

Findings

FV methods reduce dispersion in abrupt velocity models.

FV methods are less accurate and more costly in realistic seismic models.

Finite differences outperform FV in practical seismic simulations.

Abstract

The computational complexity of simulating seismic waves demands continual exploration of more efficient numerical methods. While Finite Volume methods are widely acclaimed for tackling general nonlinear hyperbolic (wave) problems, their application in realistic seismic wave simulation remains uncommon, with rare investigations in the literature. Furthermore, seismic wavefields are influenced by sharp subsurface interfaces frequently encountered in realistic models, which could, in principle, be adequately solved with Finite Volume methods. In this study, we delved into two Finite Volume (FV) methods to assess their efficacy and competitiveness in seismic wave simulations, compared to traditional Finite Difference schemes. We investigated Gudunov-type FV methods: an upwind method called wave propagation algorithm (WPA), and a Central-Upwind type method (CUp). Our numerical analysis uncovered that these finite volume methods could provide less dispersion (albeit increased dissipation) compared to finite differences for seismic problems characterized by velocity profiles with abrupt transitions in the velocity. However, when applied to more realistic seismic models, finite volume methods yielded unfavorable outcomes compared to finite difference methods, the latter offering lower computational costs and higher accuracy. This highlights that despite the potential advantages of finite volume methods, such as their conservative nature and aptitude for accurately capturing shock waves in specific contexts, our results indicate that they are only advantageous for seismic simulations when unrealistic abrupt transitions are present in the velocity models in the velocity models.