Geophysical Prospecting 37, 925-958,1989

An efficient full 3D wavefield extrapolation technique is presented. The method can be used for any type of subsurface structure and the degree of accuracy and dip-angle per-formance are user-defined. The extrapolation is performed in the spacefrequency domain as a space-dependent spatial convolution with recursive Kirchhoff extrapolation operators. To get a high level of efficiency the operators are optimized such that they have the smallest possible size for a specified accuracy and dip-angle performance. As both accuracy and maximum dip-angle are input parameters for the operator calculation, the method offers the possibility of a trade-off between these quantities and efficiency. The operators are calcu-lated in advance and stored in a table for a range of wavenumbers. Once they have been calculated they can be used many times. At the basis of the operator design is the well-known phase-shift operator. Although this operator is exact for homogeneous media only, it is assumed that it may be applied locally in case of inhomogeneities. Lateral velocity variations can then be handled by choosing the extrapolation operator according to the, local value of the velocity. Optionally the operators can be designed such that they act as spatially variant high-cut filters. This means that the evanescent field can be suppressed in one pas % with the extrapolation. The extrapolation method can be used both in prestack and post-stack applications. In this paper we use it in zero-offset migration. Tests on 2D and 3D synthetic and 2D real data show the excellent quality of the method. The full 3D result is much better then the result of two-pass migration, which has been applied to the same data. The implementation yields a code that is fully vectorizable, which makes the method very suitable for vector computers