DIFFRACTION RESPONSE FOR NONZERO SEPARATION OF SOURCE AND RECEIVER

Through an appropriate extension of the Kirchhoff retarded potential method this paper develops a theory of diffraction amplitudes formulated for nonzero separation of source and receiver. 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.