The velocity model we used for the migration was obtained by reflection tomography using the S.M.A.R.T method Ehinger and Lailly (1995); Jacobs et al. (1992). We smoothed their result before running the common-azimuth migration. Our smoothing scheme preserved the exact shape of the salt body to avoid high velocity spreading into the surrounding model, which would degrade imaging.
Figure 6 shows common-image gathers along our main in-line section, illustrating details of the salt boundaries. When searching for these boundaries on the left-hand side, the event marked ``R'' seems relatively coherent compared to the ratio of noise that can be observed inside the salt. It may reasonably correspond to the salt flank we hope to image on the left-hand side. The event could as well be an internal multiple created by reflections on Tertiary/chalk or chalk/salt interfaces around event ``I''. Additionally, Ogilvie and Purnell 1996 show how converted waves can also create spurious events sufficiently high in amplitude to confound interpretation.
If ``R'' is effectively the salt flank, its location after migration remains inaccurate, since we would expect it to be immediately against the reflectors bending upwards in the chalk. This event possibly comes from a wavefield seriously distorted while traveling through the salt body and recorded at large Cmp-X locations. In contrast, the salt boundary closer to the top is better migrated since the waves have not propagated through the dome and have instead been recorded at small Cmp-X locations. Panel (a) illustrates this hypothesis, showing flat gathers for the top of the salt edge and, below, reflectors bending upwards with angle around reflector ``R''.
Furthermore, panels (b) and (c) intersect an area where the continuity of the salt top is broken. At this particular location, the zero-offset migration, being less sensitive to velocity variations, yields more continuous imaging (Figure 7). The common-image gathers show reflectors bending upwards, indicating a too low velocity. Similarly, on the right-hand side, the salt flank shows a too low velocity (panel (d)).
We can see from the analysis of common-image gathers that the velocity model obviously needs further improvements. Figure 4 shows the salt boundaries in the migrated section superimposed on the velocity model we used for imaging. Performing accurate imaging, especially deeper in the model, requires a more precise relocation of the major reflectors, such as the salt edges, with respect to the velocity model.
For this purpose, the information provided by the common-image gathers can be reinvested in a residual migration process to improve the focusing of the migrated sections. The next step, which is less straightforward, is to update the velocity model from the perturbation between the starting and the improved images Biondi and Sava (1999). This remains an open research subject.
Last, we compare the result of 3-D prestack common-azimuth migration with the 3-D prestack preserved-amplitude depth migration (PAPsDM) result, courtesy of the Ecole des Mines de Paris Xu et al. (1999). Figure 8 shows both results, which are derived from the same velocity model. However, their implementation of the ray+Born formalism Thierry et al. (1999a,b) for elaborating the PAPsDM algorithm yields an image in impedance perturbation rather than in reflectivity (as in the case of 3-D prestack common-azimuth migration). In order to make the migrated images more comparable, we differentiated their result along the depth axis. Although this conserves the shapes of the reflectors, the conversion to reflectivity implies (in theory) differenting perpendicularly to the reflectors, which is not straightforward.
Both sections (a) and (b) in figure 8 display many similarities. The sides of the salt body seem accurately imaged in both cases, especially on the left-hand side where the chalk layer bends upwards. However, common-azimuth migration produces a result significantly more accurate for the top of salt and for the complex lithologic interfaces in that area. Moreover, the reflector marked ``S'', which may correspond to the salt boundary, is not visible in the PAPsDM image. The PAPsDM migrated section could probably be improved by using a larger offset range in the cross-line direction (700m here). Interestingly enough, handling multiple arrivals does not yield a significantly better image, since the result of 3-D PAPsDM with, respectively, first, strongest, and multiple arrival are similar at 97% (Gilles Lambaré, personal communication).