3-D elastic modeling with surface topography by a chebychev spectral method

A 3-dimensional numerical modeling scheme which accounts for surface topography is presented. The method is based on spectral derivative operators. Spatial differencing in the horizontal directions is performed by the Fourier method, whereas vertical derivatives are carried out by a Chebyshev method which allows for the incorporation of boundary conditions. The implementation of surface topography is done by mapping a rectangular grid onto a curved grid. The study of near surface effects of seismic wave propagation in the presence of surface topography is important since non-ray effects such as diffractions and scattering at rough surfaces must be considered as wave phenomena. The modeling algorithm presented here can serve as a tool for understanding these phenomena. All wave types are included in the solution since the full wave field is computed. A 3D modeling example of a half space with a trench at the surface is given.