The data set used for the tests was recorded in the southern sector of the North Sea. A typical in-line geological section of the area is shown in Figure . An in-line section showing the velocity model superimposed onto a wiggle plot of the migrated image is shown in Figure . The geological section indicates shallow velocity variations created by variable thickness in the low-velocity Tertiary sediments and in a high-velocity Cretaceous chalk layer. The reflections from the complex three-dimensional faulting in the Jurassic and Triassic formations just above the salt swell are affected by these shallow velocity variations. The exploration targets are the reflectors immediately below the salt. The correct positioning and the full focusing of the reflections from the target require prestack depth migration. McKay and Abma 1992 used a 2-D data set recorded above a similar geological setting to test their depth-focusing velocity analysis methodology; they provide a detailed description of the geological setting and its effects on depth imaging.
Although the geology in the area has predominant dips in the in-line direction, there are few interesting 3-D effects that require full 3-D migration to be properly taken into account. The fault blocks and the lithological boundaries in the Jurassic and Triassic layers are rotated with respect to the in-line direction, generating reflections with uneven azimuth. Both the top of the salt and the dolomite intrusions have complex reflector geometry that require 3-D migration. Further, because of the 3-D nature of the velocity model, full 3-D depth migration is needed to properly image the mildly dipping reflectors at the bottom of the salt layer.
The data were acquired using a flip-flop double-source and triple streamer acquisition configuration and affected by cable feather. Therefore, the original data geometry is not exactly common-azimuth and the data need to be transformed to a regularly sampled ``equivalent'' common-azimuth data set before migration. The transformed data set had the same sampling of the nominal sampling of the acquisition; that is, 9.75 m in the in-line direction, and 25 m in the cross-line direction. The offset axis was sampled with a 80 m interval; this coarse sampling introduced some aliasing along the offset axis, which seems to have caused only minor artifacts in the migration. I used this coarse sampling to reduce the migration computation time, and limit the size of the data set that needed to be handled. Tests with finer sampling of the offset axis are needed to determine more reliably the impact of offset aliasing on the results. To fully take into account the deviations of the source-receiver azimuth from the nominal common azimuth, AMO Biondi et al. (1996b) should be applied to compute the common-azimuth data. But, for this initial test I used a simple horizontal binning and interpolation procedure that placed the traces at the correct midpoint, and normalized the interpolated output by the bin fold. The coarse sampling of the output offset axis implied some offset mixing, thus I applied NMO before the binning-interpolation procedure, and applied inverse NMO afterward.
Both the stacking velocity function used for NMO and inverse NMO, and the interval velocity function used for migration were provided by Conoco. The interval velocity model was derived by a tomographic procedure that used a 3-D migrated volume to define lithological boundaries Hanson and Witney (1995). The velocity model can thus be used as an indirect check of the geometric correctness of the migrated images; that is, that common-azimuth migration correctly positions in depth the reflectors.
The velocity model was the same for both the 3-D and the multi-line 2-D migration. In both cases I used five reference velocities in the PSPI algorithm. Preliminary tests showed that, if only three reference velocities were used in the PSPI algorithm, migration would poorly focus the reflectors. Possibly, it would be beneficial to increase the number of reference velocities even further; more tests in this direction are needed. For downward continuation, the interval velocity was linearly interpolated to the dense sampling of the image (8 m depth, 9.75 m in-line, 25 m cross-line) from a sparser grid (40 m depth, 187.5 m in-line, 200 m cross-line). No smoothing was applied to the interpolated velocity.