Geophysical Prospecting, zyxwvutsrq 1994, 42, 755-776 zyxwvu Cost-effective 3D one-pass depth migration' A. Sollid' and B. Arntsen2 Abstract zyxwvuts A crucial point in the processing of 3D seismic data is the migration step, both because of its 3D nature and the computational cost involved. The efficiency and accuracy of 3D migration are determined by the wavefield extrapolation technique employed. Wavefield extrapolation based on second-order differential operators of variable-length is very efficient and accurate at the same time. Compared to migra- tion based on the McClellan transform and operator splitting, the use of variable- length second-order differential operators offers significant advantages. The 3D migration operator has an almost perfect circular symmetry. No positioning errors in the zyxwvuts 45" azimuth between the in-line and cross-line directions are evident. The method is, in practice, only limited by spatial aliasing and does not require expen- sive interpolation of data to reduce numerical artifacts. This reduces the computa- tional cost of 3D one-pass depth migration by a large factor. Introduction The 3D seismic method was first widely used in the late 1970s and early 1980s. Although an expensive method, the rewards in terms of increased drilling success rates have been very encouraging. A crucial point in processing of 3D seismic data is the migration step, both because of its 3D nature and the computational cost involved. Thus, it is desirable that the algorithms employed in the migration step are both accurate and effective. This paper describes an accurate and efficient method for 3D migration. The use of effective migration algorithms is even more important when 3D pre- stack migration is considered. Promising results have been achieved in the imaging of subsalt fault systems by using 3D prestack migration methods based on asymp- totic ray theory (Western and Ball 1992). Since ray theory cannot adequately describe all aspects of seismic wave propaga- tion, it is expected that a method based on the full wave equation will yield even better results than those obtained by ray theory. Development of 3D prestack migration methods based on the full wave equation is not straightforward due to the massive computational power required. Shot-record migration of a realistic Paper presented at the 55th EAEG meeting, Stavanger, June 1993. Received December 1993, revision accepted April 1994. Statoil Research Centre, Postuttak, 7005 Trondheim, Norway. zyxwv 755