Time versus depth migration
We continue our discussion with the salt diapir model data. Figure 8.2-6 shows time and depth migrations of the zero-offset section associated with the salt diapir model shown in Figure 8.2-1. Ignore the dispersive noise in the vicinity of the top-salt event on the migrated sections; this is caused by the differencing approximations made to the differential operators in the implicit scheme used here. While the top-salt boundary is imaged accurately by both time and depth migration, note the overmigration exhibited by the base-salt and the deeper event in the time-migrated section. Depth migration, on the other hand, images these two reflectors, accurately, if the velocity-depth model input to depth migration is the true model as in the case of Figure 8.2-6. Although we used the true velocity-depth model, time migration produced the incorrect image of the base-salt boundary and the subsalt region. Time migration algorithms do not include the term that accounts for strong lateral velocity variations as manifested by the image rays shown in Figure 8.2-5. On the other hand, depth migration algorithms include this term and thus are able to correct for the lateral shift in image rays.
Figure 8.2-7 shows time and depth migrations of the CMP-stacked section associated with the salt diapir model shown in Figure 8.2-1. Again, the top-salt boundary is imaged accurately by both time and depth migration. As expected, however, time migration fails to produce a correct image of the base-salt boundary and the deeper reflector. Note that even depth migration fails to image these two reflectors with sufficient accuracy, although the velocity-depth model input to depth migration was the true model. Note, for instance, the subtle distortions on the base-salt event and the not-so-flat reflector in the depth-migrated section. This is a direct consequence of the fact that the CMP-stacked section is only a close representation of the zero-offset wavefield in the presence of strong lateral velocity variations associated with complex overburden structures. Since poststack migration algorithms are based on the zero-offset wavefield theory (migration principles), application of zero-offset migration to a CMP-stacked section would produce less-than-ideal results. To circumvent this deficiency in CMP stacking, and to correctly image the substratum that includes the base-salt boundary and the flat reflector, strictly, one needs to do prestack depth migration. Prestack depth migration is reviewed in the next section; however, for comparison, results of the zero-offset, poststack and prestack depth migrations are shown in Figure 8.2-8. Note that prestack depth migration produces an image that is free of the distortions observed on the image produced by poststack depth migration. Imaging accuracy is similar to that of the zero-offset section.
A way to minimize departure of a stacked section from a zero-offset section — that is, to minimize traveltime and amplitude distortions caused by nonhyper-bolic moveout during CMP stacking, is to use partial stacking. Figure 8.2-9 shows a portion of a full-fold CMP-stacked section that contains a salt diapir structure. (The CMP fold is 30.) Note the spurious horst-like structure at the base-salt boundary B. This data set is from the Red Sea where such structures are common. Hence, at first, this horst structure appears to be geologically plausable. Note, however, the horst block at the base-salt is replaced with a continuous event on the single-fold near-offset section. What may seem to be a horst block actually is no more than a manifestation of amplitude and traveltime distortions caused by the full-fold stacking that spans the entire offset range of the recorded data. The conclusion we can draw from this observation is that it is not necessarily the full-fold stack, but the near-offset section that better resembles a zero-offset section. Hence, it is the near-offset section, and not the full-fold section, that is an appropriate input to poststack depth migration. An immediate objection to this conclusion is that the near-offset section contains a significant amount of multiple energy that was naturally attenuated during CMP stacking by way of velocity discrimination between primaries and multiples. Also, note the loss of continuity of the base-salt event on the near-offset section; in contrast, CMP stacking improves the signal-to-noise ratio. A way to benefit from the power of CMP stacking to attenuate multiples and improve the signal-to-noise ratio while circumventing the nonhyperbolic moveout effect is to do partial stacking. By a simple series of tests, one can judge as to what portion of the cable — near offsets, mid-range offsets or far offsets, provides this optimum stack as input to poststack depth migration. It is important to note that, while poststack depth migration may require a stack based on a subset of offsets, prestack depth migration requires all offsets.
Figure 8.2-7 Time and depth migrations of the CMP-stacked section associated with the salt diapir model. Trace spacing is 25 m.
Figure 8.2-8 Depth migrations of the zero-offset, CMP-stacked, and prestack data associated with the salt diapir model using the correct velocity-depth model.
Figure 8.2-10 Depth migrations of the zero-offset, CMP-stacked, and prestack data associated with the salt diapir model using an incorrect velocity-depth model.
Figure 8.2-1 (Top) An earth model in depth with a salt diapir; (middle) CMP-stacked section derived from the modeled prestack data in Figure 8.2-3; (bottom) the modeled zero-offset section. The stacked and zero-offset sections are appropriately aligned in the lateral direction with respect to the earth model above. Trace spacings in the stacked and zero-offset sections are 25 m and 50 m, respectively. No amplitude scaling has been applied to the sections. The aspect ratio of the horizontal and vertical axes in the velocity-depth model is 1.
We must remind ourselves that an accurate image from depth migration is attainable only when the velocity-depth model is correctly defined, independent of the input data type — zero-offset, stack, or prestack. Figure 8.2-10 shows results of the zero-offset, post-and prestack depth migrations of the salt diapir model data using an incorrect velocity-depth model. An incorrect velocity-depth model causes a poor image produced by not just poststack depth migration, but also by zero-offset and prestack depth migration.
- 2-D poststack depth migration
- Image rays and lateral velocity variations
- Iterative depth migration
- Iteration with zero-offset data
- Iteration with CMP-stacked data
- Iteration with prestack data
- Iteration in practice