3d Seismic-Wave Modeling With A Topographic Fluid-Solid Interface At The Sea Bottom By The Curvilinear-Grid Finite-Difference Method

The curvilinear-grid finite-difference method (FDM), which uses curvilinear coordinates to dis-cretize the nonplanar interface geometry, is extended to simulate acoustic and seismic-wave propagation across the fluid-solid interface at the sea bottom. The coupled acoustic velocity-pressure and elastic velocity-stress formulation that governs wave propagation in seawater and solid earth is expressed in curvilinear coordinates. The formulation is solved on a collo-cated grid by alternative applications of forward and backward MacCormack finite difference within a fourth-order Runge-Kutta temporal integral scheme. The shape of a fluid-solid interface is discretized by a curvilinear grid to enable a good fit with the topographic inter-face. This good fit can obtain a higher numerical accuracy than the staircase approximation in the conventional FDM. The challenge is to correctly implement the fluid-solid interface con-dition, which involves the continuity of tractions and the normal component of the particle velocity, and the discontinuity (slipping) of the tangent component of the particle velocity. The fluid-solid interface condition is derived for curvilinear coordinates and explicitly imple-mented by a domain-decomposition technique, which splits a grid point on the fluid-solid interface into one grid point for the fluid wavefield and another one for the solid wavefield. Although the conventional FDM that uses effective media parameters near the fluid-solid interface to implicitly approach the boundary condition conflicts with the fluid-solid interface condition. We verify the curvilinear-grid FDM by conducting numerical simulations on several different models and compare the proposed numerical solutions with independent solutions that are calculated by the Luco-Apsel-Chen generalized reflection/transmission method and spectral-element method. Besides, the effects of a nonplanar fluid-solid interface and fluid layer on wavefield propagation are also investigated in a realistic seafloor bottom model. The proposed algorithm is a promising tool for wavefield propagation in heterogeneous media with a nonplanar fluid-solid interface.