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The following was submitted from Peter Hubral and Thilo Müller from The Geophysical Institute, Karlsruhe University, Hertzstr. 16, 76187 Karlsruhe, Germany.

Discussion on "In the Foothills, Prestack Depth Migration IS Interpretive Processing" by Samuel H. Gray and Gary MacLean

We read with interest the above article and welcome in particular the images constructed with the Foothills synthetic data set. It is the three parts of Figure 1, in particular, that have attracted our attention and on which we want to comment. Figure 1A shows the (bad) result of the NMO/DMO/stack followed by post stack depth migration and Figure 1C shows the (good) prestack depth migration.

For the construction of both figures the correct interval velocity function was used. Why do both figures differ in quality, where does the "high noise level" on Figure 1A come from?

The authors attribute it "in part to the lack of random noise on the original shot records". For us there is another more obvious reason that explains the high noise level in Figure 1A, it is the failure of the NMO/DMO/stack to simulate a proper zero-offset stack section because of the constant-velocity assumption involved in the NOM/DMO process. The desired task of the NMO/DMO/stack is to collect all primary reflections in a multi-coverage seismic data set from a common-reflection point on the reflector and stack these together to provide a simulated zero-offset reflection. Thus, the operation NMO/DMO/stack aims at providing what one may also call a common-reflection-point stack.

Unfortunately, the NMO/DMO/stack procedure is theoretically only designed for the constant-velocity case. The strict decomposition of the transformation of a common-offset section into a zero-offset section with NMO and DMO is therefore also only possible in the constant-velocity case. NMO/DMO works, however, reasonably well for not too strongly inhomogeneous velocity media, but must inherently fail for such complex velocities as obviously exist in the foothills. A good indication of the insufficiency of NMO/DMO/stack in the given example is the fact that the planar target reflector at the bottom does not appear planar in Figure 1A.

We claim (and we believe to have good theoretical reasons for this) that if in Figure 1, with all its structural complexities with the actual background velocity would have been constant (and the NMO/DMO/stack would be as accurately implemented as it could be in this case) both Figures 1A and 1B would have been (almost) identical. This would prove that lack of random noise, etc. is not really the cause that explains the lack of resolution of Figure 1A. It would also prove (but in the Foothills this would be of little help) that there exists a particular case (i.e. the constant-velocity case) for which the NMOIDMO/stack followed by poststack depth migration as well as the pres tack depth migration must with respect to the primary reflections and for noise-free data lead to identical results. Hence, one cannot claim that prestack depth migration is inherently better. It is only better in inhomogeneous velocity media.

We hope that our above arguments have not distracted from the main message, which this interesting paper wants to convey. The convincing message is that direct pres tack depth migration is conceptually simple and more accurate than any other industrial chain of processes, provided the (laterally inhomogeneous) velocity field is available. Moreover, prestack depth migration can now be implemented in form of interpretative processing that involves updating the velocity model.

There are two final questions that remain to be answered:

Quo vadis, seismic reflection imaging? Is prestack depth migration by interpretative processing possibly approaching THE ultimate solution to seismic reflection imaging?

If geophysicists concerned with improving seismic reflection imaging technology will convey the message to the interpreters and managers that this is the case, they should sooner or later prepare themselves for losing their jobs.

Response to Comments

By Samuel Gray and Gary MacLean

We thank Prof. Hubral and Mr. Mueller for their interest in our paper, and for their very provocative comment. Indeed, our statement about the failure of the NMO/DMO/stack/migration flow for our example did not mention the obvious failure of the CMP stacking progress in areas where the velocity is complicated and rapidly-varying. We agree that, if the velocity for this example had been constant, and all the geologic complexity had been expressed in density contrasts, the poststack migration would have produced a result comparable with the prestack time and depth migrations (which would be identical). So the major reason for the poor poststack migrated image is the rapid, though realistic, velocity variations across the model.

However, on field data, the stack never looks as good as the stack we showed, but the (poststack) migration often looks somewhat better than the migrated image that we showed. Why are we often able to obtain a good, interpretable, structural image when theory tells us that velocity variations will render our standard flow useless? We contend that field data tend to forgive processing errors more than synthetic data do, and that "routine" steps - applied to field data but not to synthetic data - that are not always consistent with the wave equation, such as trace balancing and statics, allow a skillful processor to recover from errors that arise inevitably from an incomplete knowledge of velocities. (Is it also possible, though, that these processing steps also cause a certain amount of velocity uncertainty?)

We re-emphasize that the standard processing flow yields stacking and imaging velocities that are non-physical. The end result of this flow might be a "cosmetically" superior image but one that is potentially less correct in a structural sense. Also, we repeat our contention that the actual seismic interpretation occurs by migrating before stack to build an image in depth.

Once again, we are grateful for the comments on our paper. We wish we could answer the final two questions that Prof. Hubral and Mr. Mueller pose. We can only state that we believe there are still a few issues in imaging technology left to be addressed.



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