Elimination of numerical dispersion in finite‐difference modeling and migration by flux‐corrected transport

Abstract

Finite‐difference acoustic‐wave modeling and reverse‐time depth migration based on the full wave equation are general approaches that can take into account arbitrary variations in velocity and density and can handle turning waves as well. However, conventional finite‐difference methods for solving the acoustic‐ or elastic‐wave equation suffer from numerical dispersion when too few samples per wavelength are used. The flux‐corrected transport (FCT) algorithm, adapted from hydrodynamics, reduces the numerical dispersion in finite‐difference wavefield continuation. The flux‐correction procedure endeavors to incorporate diffusion into the wavefield continuation process only where needed to suppress the numerical dispersion. Incorporating the flux‐correction procedure in conventional finite‐difference modeling or reverse‐time migration can provide finite‐difference solutions with no numerical dispersion even for impulsive sources. The FCT correction, which can be applied to finite‐difference approximations of any order in space and time, is an efficient alternative to use for finite‐difference approximations of increasing order. Through demonstrations of modeling and migration on both synthetic and field data, we show the benefits of the FCT algorithm, as well as its inability to fully recover resolution lost when the spatial sampling becomes too coarse.