An anti‐dispersion wave equation based on the predictor‐corrector method for seismic modeling and reverse time migration

Abstract

Wave equation solutions based on finite-differences is a standard technique and has been widely used for seismic forward modeling and reverse-time migration. However, the time step for the explicit method is restricted by the stability condition and to obtain good results both the spatial and time derivatives need to be computed with accurate operators. This can be achieved using higher order finite-difference schemes or very fine computational grids. However, both approaches increase the computational cost. On the other hand, numerical dispersion normally appears in the finite-difference results and can contaminate the signals of interest. Numerical dispersion noise is a very well known problem in finite-difference methods and several algorithms have being proposed to obtain seismic modeling sections and migration results free from this noise. In this paper, we propose to use the finite-difference technique together with a predictor-corrector method to obtain an efficient algorithm for seismic modeling and reverse time migration. First, we derive a new wave equation which we call the anti-dispersion wave equation. Then, we present some numerical results to demonstrate that the finite difference scheme based on this new anti-dispersion wave equation can be used as a new tool for seismic modeling and migration, producing little numerical dispersion compared with the original wave equation but requiring slightly more computational cost.