Causes and reduction of numerical artefacts in pseudo-spectral wavefield extrapolation

Artefacts and local instabilities are common in numerical solutions of seismic wave equations. Although many of these are already known, most are not well documented in an accessible form. One form of artefacts is a consequence of partial derivative operators that are non-local and are associated with the interaction between the propagating wavefield and the medium at discontinuities in material properties. When pseudo-spectral solutions are used, heterogeneous wave equations may be accurately solved in a wide dynamic range using even-based Fourier transforms on a staggered grid. Regardless of the implementation of a spatial differentiator, use of homogeneous wave equations or of standard (non-staggered) grids gives less accurate results. Synthetic examples include heterogeneous acoustic, elastic and poroelastic (Blot) equations.