The problems of reflection-point smearing, or dispersal, and changes in apparent stacking velocity introduced by reflector dip are well known for conventional (P-P) data. An expression for the converted-wave (P-SV) dispersal within a common-conversion-point (CCP) gather is derived here. It is found that the P-SV dispersal is asymmetric about zero dip, with greater dispersal for data acquired in the down-dip direction than in the up-dip direction. Calculations of P-SV apparent velocity vs. dip angle also show an asymmetry about zero-dip. Because of this, conventional P-P dip moveout (DMO) is not appropriate for converted-wave data.
The DMO concept is here extended to P-SV data by using geometrical optics to construct the P-SV zero-offset mapping function for the constant-velocity case. It is shown that, as in the P-P case, an exact solution to the time response curves for a P-SV DMO operator can be obtained. This solution contains within it the equation of the P-P DMO traveltime curves as a special case. The time-response curves for P-SV DMO operators generated using this equation show the operators to be asymmetric, with the location of maximum time on the curves corresponding to the position of the zero-dip conversion point. Application of P-SV DMO moves the data samples horizontally to the proper conversion points, performing a conversion-point rebinning of the data. This leads to a new method for computing the location of the zero-dip conversion point. Application of P-SV DMO to synthetic data using an integral-summation algorithm is found to greatly reduce the dispersal within CCP gathers. This gives a visible improvement in the amplitude and continuity of dipping horizons.
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