Determining finite difference weights for the acoustic wave equation by a new dispersion-relationship-preserving method
W. Liang, Y. Wang and C. Yang
Journal name: Geophysical Prospecting
Issue: Vol 63, No 1, January 2015 pp. 11 - 22
Info: Article, PDF ( 1.56Mb )
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.