Cost effective prestack depth imaging of marine data
Authors: Biondi B. 
Published: October 2008

Abstract
Common-azimuth imaging can significantly reduce the cost of full-volume 3-D prestack depth imaging of marine data sets. The common-azimuth imaging procedure comprises of two steps: first, transformation of the prestack data to common azimuth data by azimuth moveout (AMO); second, imaging the transformed data by common-azimuth migration. Both these steps are computationally efficient. AMO is a partial migration operator and thus it has narrow spatial aperture. Common-azimuth migration is based on downward continuation of the wavefield; therefore, its computational cost increases only as the square of the image depth. In contrast, the cost of conventional Kirchhoff migration is proportional to the cube of the image depth. Because it is a wavefield-continuation method, common-azimuth migration does not require the computation of asymptotic Green functions. Therefore, common-azimuth imaging is likely to overcome some of the accuracy problems encountered by Kirchhoff migration in the presence of complex wave-propagation phenomena. The proposed common-azimuth imaging procedure successfully depth imaged a marine data set recorded in the North Sea. These positive results suggest the application of common-azimuth imaging to velocity estimation based on wavefield focusing.

Introduction
Computational cost is a main obstacle to the widespread use 3D 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 of 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 moveout3 (AMO). 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 multistreamer 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 operator2.