Proposed is the method of designing the finite-difference schemes of the 2nd and 4th order in 2-D and 3-D regular rectangular grids, both inside geological blocks and at structural interfaces. Considered are only the point schemes, expressed in terms of the gridpoint values of the material and other model parameters and of the wavefield. The common, simple, and highly symmetric point schemes are applicable only in smooth parts of seismic models, inside geological blocks. To maintain the comparable accuracy at structural interfaces, special finite-difference schemes have to be derived. These special schemes are linear operators acting on the wavefield gridpoint values, and are dependent on the positions and slopes of the interfaces.
Finite differences of the 2nd and 4th order, 2-D and 3-D seismic modelling, structural interfaces, elasticity, anisotropy.
The image of the paper in GIF 150dpi (456 kB) is designed for an instant screen preview.
The paper is available in PostScript (148 kB) and GZIPped PostScript (44 kB).