Accurate Pseudo-Spectral Acoustic Wave Modelling with Time Dispersion Elimination

Abstract

We propose an accurate method for modeling acoustic wave propagation. The spatial derivatives are calculated using Fourier transform to reduce spatial numerical dispersion. The standard staggered grid is adopted to suppress the non-causal ringing artifacts as in the traditional pseudo-spectral method. Moreover, to eliminate time dispersion arising from the discretization of the time derivative, an additional time-dispersion elimination term is introduced. As a result, the present method not only retains the advantages of the conventional pseudo-spectral method such as coarser spatial sampling or higher spatial derivative approximation accuracy, but also achieves higher temporal derivative approximation accuracy due to the adoption of the additional time-dispersion elimination term. Numerical examples demonstrate that the temporal dispersion elimination process can be contaminated by spatial numerical dispersion. Thus, the temporal and spatial numerical dispersions should be handled simultaneously, as proposed in this paper, to achieve accurate acoustic simulation.

Keywords

• acoustic modelling
• seismic imaging
• pseudo-spectral method
• time dispersion elimination