Tensorial elastodynamics for isotropic media

Abstract

Numerical solutions of 3D isotropic elastodynamics form the key computational kernel for many isotropic elastic reverse time migration and full-waveform inversion applications. However, real-life scenarios often require computing solutions for computational domains characterized by non-Cartesian geometry (e.g., free-surface topography). One solution strategy is to compute the elastodynamic response on vertically deformed meshes designed to incorporate irregular topology. Using a tensorial formulation, we have developed and validated a novel system of semianalytic equations governing 3D elastodynamics in a stress-velocity formulation for a family of vertically deformed meshes defined by Bézier interpolation functions between two (or more) nonintersecting surfaces. The analytic coordinate definition also leads to a corresponding analytic free-surface boundary condition (FSBC) as well as expressions for wavefield injection and extraction. Theoretical examples illustrate the utility of the tensorial approach in generating analytic equations of 3D elastodynamics and the corresponding FSBCs for scenarios involving free-surface topography. Numerical examples developed using a fully staggered grid with a mimetic finite-difference formulation demonstrate the ability to model the expected full-wavefield behavior, including complex free-surface interactions.