Staggered grids for 3D pseudospectral modelling in anisotropic elastic media

Richard Andrew Bale

Pseudospectral modeling is an alternative to finite-difference that is based on Fourier spatial operators. It can be applied in 3D to anisotropic elastic media. The nature of noncausal artifacts, which arise during pseudospectral modelling, is reviewed. They are a result of Nyquist discontinuities in the periodic wavenumber spectrum. The well-known solution, using staggered grids, can be made exact for isotropy or for anisotropy with at least orthorhombic symmetry, but cannot be done exactly for general anisotropy. Further interpolation or shifting is required. The stress-strain relationship can be factorized into an orthorhombic type term, where the staggering is exact, and a residual term where the shifting operations are applied as diagonal matrices. Examples illustrate the benefit of using this scheme over the standard (non-staggered) grid approach.