Solving the 3D Acoustic Wave-Equation on Generalized Structured Meshes: A FDTD Approach

Abstract

The key computational kernels of most advanced 3D exploration seismic imaging and inversion algorithms involve calculating solutions of the 3D acoustic wave equation, most commonly with a finite-difference time-domain (FDTD) methodology. While well suited for regularly sampled rectilinear computational domains, FDTD methods seemingly have limited applicability in scenarios involving irregular 3D domain boundaries and mesh interiors best described by non-Cartesian geometry (e.g., surface topography). Using coordinate mappings and differential geometry, I specify a FDTD approach for generating numerical solutions to the acoustic wave equation that is applicable to generalized 3D coordinate systems and (hexahedral) structured meshes. I validate the method on different computational meshes and demonstrate the viability of the modelling approach for 3D non-Cartesian imaging and inversion scenarios.