Finite difference modelling of the full acoustic wave equation in Matlab

Hugh D. Geiger and Pat F. Daley

ABSTRACT

Two subroutines have been added to the Matlab AFD (acoustic finite difference) package to permit acoustic wavefield modeling in variable density and variable velocity media. A centered finite difference scheme using a 5 point approximation has been chosen to closely approximate the full acoustic wave equation modeling used to generate the original Marmousi data set. Sampling of the wavefield in both time and space is an important consideration for accuracy, stability, and efficiency. A minimum of 10 spatial samples per wavelength and preferably 20 are required to eliminate phase and group velocity dispersion (commonly referred to as grid dispersion), while "Bording's conjecture" can be applied to determine the time sampling interval required for stability. Given these considerations, we show that the original Marmousi dataset likely contains significant grid dispersion.

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