Seismic reflection surveys are frequently conducted over very complicated geological structure, but surveying often must be confined to existing crooked roads or tracks. Typically, data from such 2D crooked-line surveys are processed using standard common midpoint (CMP) stacking techniques to obtain a 2D time section which is then 2D migrated. In Part I, we show that a reflector dip component across the processing line can cause serious problems for standard CMP stacking. We also propose a supplementary processing step in which cross-dip is determined locally and cross-dip moveout (CDMO) is removed from data to form an optimum cross-dip stack. However, a crooked-line survey is really a swath 3D survey, and ideally we would like to obtain a 3D image of reflectivity surrounding the profile.Here we investigate the potential of 3D prestack Kirchhoff migration to directly image all observed reflections; i.e., we attempt to construct a 3D image volume of all reflectors viewed by the survey. Because reflectors that face away from the acquisition line cannot return much wave energy from available sources to available receivers, they cannot be imaged even if they lie directly beneath the survey profile. Tests that the cross-profile spread of trace midpoints usually is sufficient to provide a useful degree of cross-line positioning of reflection points. A very helpful image volume is thus obtained. Kirchhoff 3D prestack migration is computationally laborious. A much quicker but less complete method is to create the 3D migrated image volume from the 2D optimum cross-dip stack and the associated set of cross-dips. Robustness of migration methods to time errors in the prestack data traces such as poorly corrected statics is also an issue. Tests show that in difficult cases, particularly where only 2D processing is warranted, migration of trace absolute amplitude rather than standard phase data may lead to a superior result.
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