Determining finite difference weights for the acoustic wave equation by a new dispersion-relationship-preserving method

Numerical simulation of the acoustic wave equation is widely used to theoretically synthesize seismograms and constitutes the basis of reverse-time migration. With finite-difference methods, the discretization of temporal and spatial derivatives in wave equations introduces numerical grid dispersion. To reduce the grid dispersion effect, we propose to satisfy the dispersion relation for a number of uniformly distributed wavenumber points within a wavenumber range with the upper limit determined by the maximum source frequency, the grid spacing and the wave velocity. This new dispersion-relationship-preserving method relatively uniformly reduces the numerical dispersion over a large-frequency range. Dispersion analysis and seismic numerical simulations demonstrate the effectiveness of the proposed method.