Staggered Finite-Difference Schemes to Model Acoustic Wave Propagation in a Three-Dimensional Fluid-Solid Configuration

In this work, some strategies and methods, based on finite-difference schemes, are introduced to model the propagation of acoustic waves in a three-dimensional fluid-solid configuration. Specifically, we have considered a heterogeneous propagation medium placed inside a 3D rectangular volume. A plane interface separates the volume into two regions: the first region is a fluid and the second one is an elastic solid. To describe the three-dimensional wave propagation problem, we use the isotropic elastic wave equation. Such equation is expressed in terms of displacement-stress and of velocity-stress, separately. Both formulations are discretized via staggered finite difference operators. We present two implicit approaches to model the heterogeneity at the interface. One of them defines a heterogeneous transition solid zone placed between both regions. The other one is the traditional strategy. Horizontal and inclined interfaces are considered in this study. The two strategies indicated above are applied for the case of the horizontal interface. To treat the inclined interface, only the traditional strategy is applied. We have developed a family of codes, based on finite differences schemes, to solve the discrete expressions for the two strategies and both formulations of the elastodynamic equations. Snapshots of the medium show the evolution of the wavefronts in time. The snapshots are obtained for three orthogonal planes. We analyze these images, as well as the respective seismograms. At the snapshots, the response of the interface can be clearly identified. This response was positively augmented when we use the transition heterogeneous zone to model the horizontal interface. For both plane interfaces, similar features associated to the reflected and transmitted wave fields were identified for the two formulations and all the strategies. This fact confirms the coherency of the strategies used to model the fluid-solid interface. The finite difference approach we have used seems to properly describe the wave propagation for the studied fluid-solid medium.