Why Perform 3-D Prestack Time migration on the Prairies?

Hardware platforms have now achieved a level of sophistication which permits the use of full 3-D prestack time migration as a production-style processing tool. While most geophysicists are aware that performing 3-D prestack time migration on structured data sets offers certain advantages, particularly from the viewpoint of velocity analysis, many may be surprised to learn that prestack migration can sometimes produce superior image quality even in areas of flat-lying geology such as the Canadian plains. In some cases, the amount of improvement is large enough to justify the large cost associated with this computationally intensive processing step. However, in other situations the amount of improvement is negligible, so the added expense would be wasted. The purpose of this talk is to explain why 3-D prestack time migration sometimes produces better results in simple structural settings than the conventional processing flow consisting of NMO + DMO + stack + poststack time migration.

Efforts to explain why prestack • migration works well, some of the time, in areas exhibiting only mild structural variation have given rise to two schools of thought. The first of these assumes that prestack and poststack migration algorithms exhibit different signal-to-noise (SIN) enhancement characteristics, so that prestack migration preferentially improves image quality for noisy input data sets but offers little or no improvement for cleaner input volumes. The second maintains that prestack migration does a better job of handling some acquisition geometries than others.

Both possible explanations are explored through synthetic testing. First, a noisy synthetic input 3-D volume is used to study the effects of random noise on 3-D Kirchhoff prestack and poststack time migrations. Then, noise-free synthetic 3-D data volumes generated using real survey coordinates and uniform dipping planes are used to investigate the effects of irregular geometry on both types of migration. The tests indicate that there is very little difference in noise attenuation properties between the two algorithms, but that prestack migration does a better job of handling midpoint scatter than poststack migration. The improvement is due to the fact that traveltimes along the Kirchhoff prestack migration operator are computed using true source and receiver coordinates, whereas bin centre coordinates are used for the poststack operator. Therefore, a traveltime error is introduced in the poststack situation whenever source-receiver midpoints are significantly displaced from the bin centres.

In addition to performing a more accurate operator traveltime computation in the presence of midpoint scatter, prestack migration may offer another advantage over the conventional processing stream by providing a better dip moveout correction than traditional DMO algorithms, which can have their own problems in handling irregular geometry. Thus at first glance, it is unclear whether improved image quality observed after prestack migration of Canadian plains-style data sets arises because the prestack migration avoids the introduction of geometry- related DMO artifacts, or because it is doing a better job of handling the midpoint scatter. A semi-quantitative analysis shows that the size of the error introduced by midpoint scatter is larger than the DMO correction for the shallow dips typically present in the Canadian plains, and therefore that the improvement after prestack migration is due to midpoint scatter effects.

The results of this study help to shed light on the effect of 3-D acquisition on final image quality, as well as on the questions of when to expect significant differences between 3-D prestack and poststack time migration for data sets with little structure and which prestack migration algorithms are able to properly account for the effects of midpoint scatter.