A comparison of finite-difference and spectral-element methods for elastic wave propagation in media with a fluid-solid interface

Abstract

The numerical simulation of wave propagation in media with solid and fluid layers is essential for marine seismic exploration data analysis. The numerical methods for wave propagation that are applicable to this physical settings can be broadly classified as partitioned or monolithic: The partitioned methods use separate simulations in the fluid and solid regions and explicitly satisfy the interface conditions, whereas the monolithic methods use the same method in all the domain without any special treatment of the fluid-solid interface. Despite the accuracy of the partitioned methods, the monolithic methods are more common in practice because of their convenience. In this paper, we analyse the accuracy of several monolithic methods for wave propagation in the presence of a fluid-solid interface. The analysis is based on grid-dispersion criteria and numerical examples. The methods studied here include: the classical finite-difference method (FDM) based on the second-order displacement formulation of the elastic wave equation (DFDM), the staggered-grid finite difference method (SGFDM), the velocity-stress FDM with a standard grid (VSFDM) and the spectral-element method (SEM). We observe that among these, DFDM and the first-order SEM have a large amount of grid dispersion in the fluid region which renders them impractical for this application. On the other hand, SGFDM, VSFDM and SEM of order greater or equal to 2 yield accurate results for the body waves in the fluid and solid regions if a sufficient number of nodes per wavelength is used. All of the considered methods yield limited accuracy for the surface waves because the proper boundary conditions are not incorporated into the numerical scheme. Overall, we demonstrate both by analytic treatment and numerical experiments, that a first-order velocity-stress formulation can, in general, be used in dealing with fluid-solid interfaces without using staggered grids necessarily.