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.

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

Love wave propagation is studied by investigating numerical modeling results for several examples of geologic interest. The modal characteristics of the results are clarified by the use of narrow band‐pass filters and two‐dimensional Fourier transforms in range and time. Such processing makes it possible to study changes in phase and group velocity for the various modes and to locate points of reflection. This permits one to gain insight into changes in the physical properties of the surface channel supporting the waves.

Layered geological formations with large seismic velocity contrasts can effectively create channel waves in cross‐borehole seismic data. The existence of channel waves for such waveguides can be confirmed by ray tracing, wave equation modeling, and modal analysis. Channel wave arrivals are identified in cross‐borehole data recorded at Conoco’s Newkirk test facility. For these data, where velocity contrasts are about 2 to 1, tomography based on first arrival traveltimes, is limited due to problems with extreme ray bending and seismic shadow zones. However, it may be possible to extract geological information using channel wave information. The seismometer differencing method appears to be a promising approach for detecting waveguide boundaries by use of cross‐borehole data.

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