The assumption that the earth is made up of plane-parallel, homogeneous, elastic layers, which can exhibit transverse isotropy and moderate constant-Q attenuation, leads to an effective method of modeling the response from a point source into a long spread of seismometer stations. Most of the computations are carried out in the complex frequency and complex horizontal wavenumber domains. Minimum sampling criteria are based on an algorithm that suppresses time and distance aliasing at the expense of the large dynamic range available on the digital computer. Other artifacts can be identified and are removed by additional wavenumber filtering. Computational effort is almost independent of the number of detectors and their nature. The structure and symmetry properties of the propagator matrices describing the response are the same for isotropic and transversely isotropic layers. Synthetic seismic panels for a regional model of a west Texas well site exhibit strong, shot-generated surface waves. A very simple model, based on a south Texas well site, shows the effects of transverse isotropy and the reverberatory nature of converted signals generated by a surface P-wave.

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