In seismic frequency-domain finite-difference modeling, the numerical accuracy depends on how mass and partial differ-ential terms are discretized in the acoustic/elastic wave equa-tion. For the mass term(s), a combination of consistent and lumped mass methods is widely accepted. For the partial differ-ential terms, there exist many discretization technologies, such as the average-derivative method (ADM) and the rotated mixed-grid method (RMM). In comparison with the ADM, which focuses on the media interior, the RMM is excellent at handling the media interior and free-surface boundary simul-taneously. However, the existing RMMs are based on the orthogonal coordinate transformation and suffer from the re-striction of cube-grid sampling. Affine coordinate systems do not restrict the axes to be orthogonal. By introducing the 3D affine coordinate transformations to the RMM, we have devel-oped an affine mixed-grid method and generated an optimal 27-point scheme for the 3D elastic wave equation. Our scheme removes the sampling restriction of cubic mesh, thus working for general cuboid mesh. In addition, it provides consistent ex-pressions in the whole computational domain, thus improving the accuracies of the internal and free-surface grid points si-multaneously. Dispersion analysis and numerical examples demonstrate that our scheme provides acceptable accuracy with five points per minimal S-wavelength for the internal and free-surface points with arbitrary spatial grid intervals.
展开▼
