Abstract

An existing theory based on the Kirchhoff retarded potential method makes distinctive predictions relating the amplitude characteristics of diffraction patterns to the geometry of subsurface reflectors. The application of this theory to seismic stacked sections would offer the geophysicist useful information to be included in subsurface interpretations. However, a possible barrier to such applications arises from the fact that the theory as originally put forth applies only to data recorded with zero source-receiver separation, whereas stacked sections are produced by averaging data recorded over a wide range of shot-geophone distances.To deal properly with seismic data as actually recorded, it is desirable to have a theory of diffraction amplitudes formulated for nonzero separation of source and receiver. This paper develops such a theory through an appropriate extension of the Kirchhoff approach. By expressing the problem in a special coordinate system, the Kirchhoff integral solution of the acoustic wave equation is reduced to a time-domain convolution of the source wavelet with an operator recognized as the impulse response of the subsurface geometry under consideration. Impulse responses are computed explicitly for an infinite reflecting plane and for diffracting edges perpendicular and parallel to the source-receiver axis.The nonzero-separation theory is compared to the zero-separation theory through numerical evaluation of the relevant formulas, and the latter is shown to be a special case of the former, as it should be. More importantly, the unexpected conclusion emerges that diffraction amplitudes at nonzero source-receiver separation are controlled almost exclusively by the location of the source-receiver midpoint. Since the data summed together in stacking all share a common shot-geophone midpoint, the diffraction amplitudes on the stacked trace should behave in good approximation to the zero-separation theory. Theoretical support is thus obtained for applying the zero-separation theory to stacked seismic data.

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