Three‐dimensional table‐driven migration

Abstract

A full 3-D wave field extrapolation technique is presented. It can be used for any type of subsurface structure, both with lateral and vertical velocity variations. The extrapolation is performed recursively in the spacefrequency (x-y-~) domain with precalculated recursive Kirchhoff extrapolation operators, that have been stored in a table. At the basis of the operator computation is the well-known phase-shift operator. Although this operator is exact for homogeneous layers only, it is assumed that it may be applied locally in case of lateral inhomogeneties. Lateral velocity variations can then be handled by choosing the extrapolation operator according to the local value of the wavenumber, w/c. The operators can be designed such that they act as spatially variant high-cut filters. This option means that the evanescent field can be suppressed simultaneously with the extrapolation. The extrapolation method can be used both in prestack and poststack applications. We used it in zero-offset migration. Tests on synthetic and real data show the high quality of the method. The implementation yields a code that is vectorizable, which makes the method very suitable for vector computers.