Wave propagation across fluid-solid interfaces: a grid method approach

This paper presents a new numerical technique for modelling wave propagation in media with both fluid (acoustic) and solid (elastic) regions, as found for instance in a marine seismic case. The scheme can correctly satisfy the fluid-solid interface conditions and accurately models the arbitrary interface topography. This work is an extension of the grid method, which is able to model wave propagation in heterogeneous solid (elastic) media with arbitrary surface topography and irregular interfaces. The scheme is developed by formulating the problem in terms of displacements in elastic regions and pressure in acoustic regions with an explicit boundary between them. The fluid-solid interface conditions on this explicit boundary are implemented by introducing an integral approach to the fluid-solid interface conditions. The solution in terms of pressure in acoustic regions together with this integral approach means that no extra computational cost is needed to implement the fluid-solid interface conditions for a complex geometry, instead of resulting in additional computations as with the spectral-element, finite-element or finite-difference methods. In this paper an acoustic grid method is developed to solve the acoustic problem inside the fluid, and the (elastic) grid method, which is improved based on a parsimonious staggered-grid scheme, is used to solve the elastic problem inside the solid. The numerical dispersion and stability criteria for the acoustic grid method are discussed in detail. Comparison with an analytical solution demonstrates that the proposed scheme handles the fluid-solid interface conditions correctly. Examples of wave propagation in a mixed fluid/solid model with both weak and strong sinusoidal fluid-solid interfaces illustrate the suitability of the proposed scheme for modelling wave propagation across fluid-solid interfaces with complex geometries.