Tensorial elastodynamics for coupled acoustic/elastic anisotropic media: incorporating bathymetry

Abstract

SUMMARYCorrectly implementing the fluid/solid boundary conditions at the seafloor is important for accurate full-wavefield imaging and inversion of marine seismic data. Because bathymetric profiles are rarely flat, the associated undulations influence wave modes interacting with the seafloor and, therefore, the ensuing imaging and inversion results. The conventional method of using single-domain elastic finite-difference (FD) solutions assumes that the fluid/solid contact is welded, which leads to incorrect handling of the boundary conditions and introduces modelling errors. We present a mimetic finite-difference (MFD) approach to solve the equations of anisotropic elastodynamics in a non-orthogonal coordinate system conformal to the bathymetric interface. The vertically deformed coordinate mapping transforms the irregular Cartesian (physical) domain into a regularly sampled generalized computational domain. We partition the medium into the acoustic and elastic subdomains and explicitly satisfy the fluid/solid boundary conditions with a split-node approach involving high-order one-sided MFD operators that achieve uniform spatial accuracy throughout the computational domain. Fully staggered grids (FSGs) are used to solve the velocity–pressure and velocity–stress formulations of the acoustic and anisotropic elastic wave equations, respectively. Numerical examples demonstrate that the proposed MFD+FSG algorithm accurately simulates wavefields even for strongly undulating bathymetric surfaces overlying structurally complex anisotropic media, and produces no spurious numerical artefacts (e.g. staircasing) or unphysical wave modes often caused by improper handling of the strong-contrast bathymetric interface. The wavefields generated by the tensorial MFD scheme closely match those from the more computationally expensive spectral-element method used to validate our implementation. The developed MFD+FSG technique can be effectively employed as the modelling kernel in a variety of coupled acoustic/elastic imaging and inversion applications.