An anti‐dispersion wave equation for modeling and reverse‐time migration

Abstract

The acoustic wave equation has been widely used for the modeling and reverse-time migration of seismic data. The finite-difference method has long been the favored approach to solve this equation. To ensure quality results, accurate approximations are required for the spatial and time derivatives. This can be achieved numerically by using either very fine computation grids or very long finite-difference operators. Otherwise, the numerical error, called numerical dispersion, will be present in the data and contaminate the signals. However, either approach increases the computation cost dramatically. In this paper, we propose a new approach to address this problem by constructing a new wave equation, which we call the anti-dispersion wave equation. It involves introducing a dispersion attenuation term to the standard wave equation. When it is solved using finite difference, numerical dispersion in the original wave equation is attenuated significantly, leading to a much more accurate finite difference scheme with little additional computation cost.