Recent interest in the extraction of fine detail from field seismograms has stimulated the search for numerical modeling procedures which can produce synthetic seismograms for complex subsurface geometries and for arbitrary source‐receiver separations. Among the various techniques available for this purpose, the replacement of the two‐dimensional wave equation by a suitable finite‐difference representation offers distinct advantages. This approach is simple and may be readily implemented. It automatically accounts for the proper relative amplitudes of the various arrivals and includes the contributions of converted waves, Rayleigh waves, diffractions from faulted zones, and head waves. Two computational schemes have been examined. For the so‐called “homogeneous formulation,” the standard boundary conditions between media of different elastic properties must be satisfied explicitly. In the case of the alternate “heterogeneous formulation”, these elastic properties may be specified at each grid point of a finite‐difference mesh, and the boundary conditions are satisfied implicitly. The proper simulation of the source requires special treatment for both cases. Synthetic seismograms computed for several models of exploration interest serve to illustrate how the technique may help the interpreter. The examples also illustrate various implementational aspects of the finite‐difference approach, which involve such phenomena as grid dispersion, artificial reflections from the edge of the model, and choice of spatial and temporal sampling increments.

No abstract

Recent interest in finite-difference modeling of the wave equation has raised questions regarding the degree of match between finite-difference solutions and solutions obtained by the more classical analytical approaches. This problem is studied by means of a comparison of seismograms computed for receivers located in the vicinity of a WI-degree wedge embedded in an infinite two-dimensional acoustic medium. The calculations were carried out both by the finite-difference method and by a more conventional eigenfunction expansion technique. The results indicate the solutions arc in good agreement provided that the grid interval for the finite-difference method is sufficiently small. If the grid is too coarse, the signals computed by the finite-difference method become strongly dispersed, and agreement between the

No abstract

No abstract