We apply the AMO operator Biondi and Chemingui (1994a) to organize wide azimuth 3-D surveys as common-azimuth common offset cubes. This transformation preserves the amplitude information Chemingui and Biondi (1995) as well as structural dip by coherent partial stacking Biondi et al. (1996). We derived the amplitude-preserving function for the AMO operator based on the FK definition of DMO cascaded with its true asymptotic inverse.
For AVO analysis to be well defined, prestack migration is required to determine the location and extent of AVO anomalies. Migration aims at imaging the reflectivity function based on a one-way representation of seismic data. In this frame, migration can be formulated as an inversion problem (i.e, Sullivan and Cohen 1987;Bleistein 1987;Schleicher et al. 1993; ...). The derivation of the forward-modeling operator provides insight into the form of the inversion operator. In generating the seismic model, each trace is modeled as a weighted sum of image sources on a reflector. Therefore, the Kirchhoff migration of the seismic data involves a weighted sum of filtered surface-recorded traces where the weights are deduced from the inversion theory. In our implementation of the Kirchhoff prestack depth migration, the model is raytraced to evaluate the Green's function traveltimes associated with the source and receiver terms and to compute their corresponding WKBJ amplitudes Lumley (1989). Given the scope of this work, we only used a depth-dependent modeling/migration algorithms which will be easily generalized to the full 3-D case, pending the development of a robust 3-D raytracer.
Since both AMO and the migration algorithms were developed for a Kirchhoff style implementation, a great deal of care was taken to avoid the aliasing of the operators. A band-pass time filter, whose maximum frequency is determined by the local slope of the operator, was applied to avoid the aliasing of the operator along its steep traveltime slopes.