Finite-difference modelling in two-dimensional anisotropic media using a flux-corrected transport technique

Abstract

The conventional finite-difference (FD) method often suffers from numerical dispersion when too few samples per wavelength are used or when models have large velocity contrast, or artefacts caused by source at grid points. In this paper, we present a fast finite-difference scheme that is based on the application of vectors and matrices in 2-D anisotropic media, and obtain the stability equations. Our method is based on a flux-corrected transport (FCT) technique, originating from hydrodynamics, which can be incorporated in the conventional finite-difference method to eliminate the numerical dispersion and source-generated noises. An n-times decoupled absorbing boundary condition is used in our study. Three-component seismograms in a transversely isotropic medium with a vertical symmetry axis (TIV) are generated for two models using the FCT finite-difference modelling. Compared with the results of the reflectivity method and the conventional FD method without the FCT technique and any absorbing boundary treatments, we conclude that our FCT based FD method can is very accurate and efficient in computing synthetic seismograms in general heterogeneous and anisotropic media.