Introduction

The amount of computations required by 3-D prestack depth migration is so high that its turn-around time and processing cost often discourage its usage, or, in the most of the cases, prevent from performing as many migration iterations as needed to estimate a satisfactory migration velocity model. Since the cost of migration is approximately proportional to the amount of data to be migrated, a simple and effective method to decrease the computational cost is to reduce the amount of input data. The most obvious way to accomplish this data reduction is to migrate only a subset of the available traces. To minimize the effects of data aliasing caused by the data subsampling, the input traces can be selected according to a quasi-random selection criterion Zhou and Schuster (1995). This method can be attractive in high signal-to-noise areas when all the data offsets are stacked during migration. However, when the signal-to-noise ratio is low, and/or when a prestack analysis of migration results is desired, either for velocity estimation or for AVO purposes, the trade-offs of neglecting available data traces should be carefully evaluated.

An alternative method for reducing the amount of data prior to migration is partial stacking of the input traces that have similar offsets and azimuths Hanson and Witney (1995). This method is more robust with respect to noise, either coherent or uncoherent, because it uses all the available traces to improve the signal-to-noise ratio. The more coherent the reflections are before partial stacking, the more the desired signal will be enhanced in the results. Normal moveout (NMO) increases coherency of reflections over offsets by a first-order correction of their traveltime. However, a simple trace-to-trace transformation such as NMO is insufficient when reflections have conflicting dips or in presence of diffractions. In these cases, it is necessary to apply to the data a partial prestack migration operator that moves energy across midpoints. In previous reports Biondi and Chemingui (1994); Chemingui and Biondi (1995); Fomel and Biondi (1995a,b) we introduced a new operator, called azimuth moveout (AMO), that transforms common-azimuth common-offset data to equivalent data at different azimuth and/or offset. AMO can be considered a generalization of dip moveout (DMO), in the sense that it transforms prestack data into equivalent data with an arbitrary offset and azimuth; in contrast DMO is only capable of transforming non zero-offset data to zero-offset data.

In this paper we present the result of applying AMO prior to partial stacking to a marine data set recorded in the North Sea. We compare the results of partial stacking after NMO and AMO with the results of partial stacking after simple NMO. The data set is a valuable test case for AMO because it shows numerous fault diffractions and because it requires 3-D prestack depth migration Hanson and Witney (1995) to be properly imaged. Reflections are affected by shallow velocity variations created by variable thickness in the low-velocity Tertiary sediments and in a high velocity Cretaceous Chalk layer.

To produce the results presented in this paper we used an implementation of integral AMO process based on the analysis developed in previous reports Biondi and Chemingui (1994); Chemingui and Biondi (1995); Fomel and Biondi (1995a,b). In particular, we applied the results on the operator aperture and anti-aliasing techniques presented by Fomel and Biondi . The main technical aspects of our implementation of the AMO integral operator are summarized in Appendix A.