Solving the 3D acoustic wave-equation on generalized structured meshes: A FDTD approach

Abstract

Summary The key computational kernel of most advanced 3D seismic imaging and inversion algorithms involves calculating solutions of the 3D acoustic wave equation, most commonly with finite-difference time-domain (FDTD) methods. While well suited for regularly sampled rectilinear computational domains, FDTD methods seemingly have limited applicability in scenarios involving irregular 3D domain boundary surfaces and mesh interiors best described by non-Cartesian geometry (e. g., surface topography). Using coordinate mapping relationships and differential geometry, I develop a FDTD approach for generating 3D acoustic wave-equation solutions appropriate for generalized (structured cuboid) computational meshes. Impulse response tests on a “semi-orthogonal” topographic coordinate system demonstrate the utility of this 3D FDTD approach for seismic imaging and inversion experiments in scenarios involving more general computational meshes.