INTRODUCTION

Computational cost is a main obstacle to the the widespread use 3-D prestack depth migration for full-volume imaging. Currently, 3-D prestack migration is almost exclusively performed by Kirchhoff methods because they effectively handle the irregular and sparse geometries of 3-D prestack data. However, the computational cost of full-volume imaging by Kirchhoff migration increases by a factor proportional to the cube of the depth extent of the image, making the imaging of deeper targets extremely expensive. In contrast, the cost of migration methods based on the downward continuation of the wavefield increases only with the square of depth. But 3-D prestack data cannot be efficiently downward-continued by standard methods because of their irregular and sparse sampling.

Here I present a procedure for full-volume prestack imaging of marine data sets that takes advantage of the limited azimuthal range of 3-D marine data to reduce significantly the computational cost. The procedure comprises two steps. The first step transforms the recorded data into effective common-azimuth data, where the common-azimuth is the direction of the acquisition sail line. The second step images the synthesized common-azimuth data set by prestack migration based on the downward continuation of the wavefield.

To transform marine data into effective common-azimuth data, I ``rotate'' the prestack data using a partial-prestack migration operator called azimuth moveout (AMO) Biondi et al. (1996a). The AMO operator is defined in the time-space domain, and it can be applied as an integral operator to 3-D marine data with geometry irregularities caused by cable feather and multi-streamer recording. The spatial aperture, and consequently the computational cost, of the AMO operator is approximately proportional to the azimuth rotation between the input offset vector and the output offset vector, and it is small when the azimuth rotation is small. Since the azimuths of most of the traces recorded during a marine acquisition are close to the nominal common azimuth, the cost of the AMO transformation is low.

Common-azimuth migration is based on a downward-continuation operator derived from the full 3-D prestack operator Biondi and Palacharla (1996). The method takes advantage of the narrow range of the source-receiver azimuth typical of marine data to propagate only a selected portion of the whole prestack wavefield. From an imaging perspective, the propagated portion of the wavefield is the main component of the wavefield.

In addition to being computationally efficient for full-volume imaging, common-azimuth migration has the advantage to be based on a recursive solution of the wave-equation, rather than on relying on the computation of asymptotic Green functions. Kirchhoff migration methods have been shown to have difficulties in accurately imaging reflectors below complex structures (); Albertin et al. (1996); Geoltrain and Brac (1993); Godfrey et al. (1993). Multi-pathing of wave propagating through complex velocity models is the main culprit for this loss of accuracy. The negative effects of multi-pathing can be ameliorated by performing the Kirchhoff summation over the most energetic arrivals, or even better, over multiple arrivals Nichols (1996). However, these improvements are seldom bullet-proof, while they add significantly to the computational cost and the implementation complexity of Kirchhoff migration.

The speed and robustness advantages of common-azimuth imaging compared with conventional Kirchhoff imaging are important in the context of velocity estimation, because velocity estimation often requires several imaging iterations. Furthermore, the availability of an efficient method for downward-continuing 3-D prestack data opens the possibility for the application to 3-D problems of velocity estimation methods based on the focusing of wavefield at depth MacKay and Abma (1992); Yilmaz and Chambers (1984).