Migration results

Figure 2 shows a typical in-line section through the velocity model, taken at the constant cross-line coordinate y=6,850 m. Figure 3 shows the corresponding common-azimuth migration results. Almost perfect images are obtained for the reflectors in the sediment above the salt, the top and the bottom of the salt. The flat `basement' is well imaged in some areas and not in others. The dipping reflectors in the subsalt are not easily distinguishable from the background noise, if they are present at all. The good results above the salt are to be expected from common-azimuth migration. Prestack time migration would have produced similarly good results. However, poststack migration after constant velocity DMO would have had trouble to image correctly the steep faults that terminate at the top of the salt because of NMO-velocity conflicts Biondi (1998a); Rietveld et al. (1997).

 

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Figure 2 Velocity model at constant cross-line coordinate y=6,850 m.

 

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Figure 3 Common-azimuth migration at constant cross-line coordinate y=6,850 m.

The focus of this paper is on the subsalt region, and on the comparison with Kirchhoff migration results. Figure 4 shows the in-line section taken through the velocity cube at constant cross-line coordinate y=9,820 m . This section is interesting because it crosses both sand lenses in the subsalt. Further, between the lenses there is an anticlinal structure broken by converging normal faults that has some chances to be visible in the images because it is flattish. Figure 5 shows the subsalt images obtained by Kirchoff migration (top) and common-azimuth migration (bottom). The common-azimuth image is superior to the Kirchhoff image in several ways. First, the common-azimuth image lacks the strong coherent artifacts that makes the Kirchhoff image difficult to interpret. These artifacts are caused by partially coherent stacking of multipathing events along wrong trajectories. They are typical of Kirchhoff subsalt images, and can be only partially removed by a ``smart'' selection of the Kirchhoff summation surfaces, such as the ones suggested by the most-energetic arrival or shortest-path criteria Nichols et al. (1998). Second, both lenses are interpretable from the common-azimuth image while in the Kirchhoff image they are either lost in the noise (top lens) or completely missing (bottom lens). Third, both the bottom of the salt and the basement are more continuous in the common-azimuth image. On the other hand, the large fault visible on the left part of the section at (1,800-4,000 m) is not perfectly imaged by common-azimuth migration. I will analyze this problem in more detail at the end of this section with the help of cross-line sections (Figure 9, Figure 10 and Figure 11).

 

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Figure 4 Velocity model at constant cross-line coordinate y=9,820 m.

 

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Figure 5 Kirchhoff migration (a) and common-azimuth migration (b) at constant cross-line coordinate y=9,820 m. Both sections are rendered using the same (98) percentile for clipping amplitudes.

Figure 6 shows the cross-line section taken through the velocity cube at constant in-line coordinate y=7,440 m. This cross-line section passes through the two subsalt lenses as the in-line section shown in Figure 4. Figure 7 shows the corresponding migrated images; Kirchhoff migration on the top and common-azimuth migration on the bottom. As before, the two lenses are clearly interpretable in the common-azimuth image, whereas they are not in the Kirchhoff image. However, in this case the central portion of the salt bottom is not perfectly imaged in either of the two images. This area is right below the deep canyons in the salt body visible in Figure 6. The steep flanks of the canyons, and the large velocity contrast between the salt body and the soft sediments filling the canyons, cause a severe distortion of the reflected wavefield. The bottom of the salt and the reflectors below, including the basement, are thus poorly illuminated. In the column below the canyons, the Kirchhoff image shows strong artifacts that could be easily interpreted as reflections. The common-azimuth image is much cleaner, although without interpretable coherent events. The poor reflectors' illumination below the canyons can be analyzed further by looking at the Common Image Gathers (CIG) displayed in Figure 8. The gather on the left corresponds to a cross-line location right below the canyons; the one on the right is further toward the right. In both gathers, the images of the reflectors above the salt and the top-of-salt are well imaged and are aligned nicely along the offset ray parameter axis. In the gather on the right, the bottom of the salt, the shallower lens, the deeper lens, and the basement are also coherent and well aligned horizontally. But in the gather on the left, there is very little coherent energy below the salt.

 

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Figure 6 Velocity model at constant in-line coordinate x=7,440 m.

 

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Figure 7 Kirchhoff migration (a) and common-azimuth migration (b) at constant in-line coordinate x=7,440 m. Both sections are rendered using the same (98) percentile for clipping amplitudes.

 

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Figure 8 Angle-domain Common Image Gathers obtained by common-azimuth migration. The locations of these CIGs are marked on the in-line axis of the common-azimuth image shown in Figure 7

Finally, I analyze the question of the poor imaging by common-azimuth migration of the fault shown in Figure 5. Figure 9 and Figure 10 show respectively the velocity model and the migrated images at constant in-line coordinate x=2,560 m. The fault under study is the fault on the right part of the sections. The deeper part of the fault is not illuminated by the data because of lack of spatial coverage, and thus is not imaged by either Kirchhoff migration or common-azimuth migration. The shallower part of the fault is well imaged by both migrations, but the middle part of the fault is well imaged by Kirchhoff migration and not by common-azimuth migration. The poor imaging seems to be correlated with the velocity inversion right above the fault visible in the velocity sections (Figure 4 and Figure 9). Both the geological dip and the local gradient of the velocity function are roughly oriented at an angle of 45 degrees with respect to the shooting direction. Therefore, they have a large component in the cross-line direction, creating the conditions under which the approximations inherent in common-azimuth migration are the worst Biondi and Palacharla (1996). On the other hand, the problem may be simply caused by the fact that I used too few reference velocities (three) when I downward continued the wavefield with an extended split-step method. This issue deserves more studies and to investigate it further. I am now developing a better common-azimuth continuation method based on Ristow's Fourier finite-difference methodology Ristow and Ruhl (1994).

Both Kirchhoff migration and common-azimuth migration have trouble to image the two deeper flattish reflectors at cross-line location of about 7,000 meters. The culprit seems to be again the sharp velocity contrast above the fault. However, the problem may be caused by the salt edge above the reflectors, not visible in these sections.

Figure 11 shows the CIG gathers taken at both problematic locations. The gather on the left shows some coherent energy for the poorly imaged reflections, though the energy is not perfectly aligned along the ray-parameter axis. The gather on the right shows no coherent energy corresponding to the poorly imaged fault, suggesting a worse imaging problem for this case.

 

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Figure 9 Velocity model at constant in-line coordinate x=2,560 m.

 

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Figure 10 Kirchhoff migration (a) and common-azimuth migration (b) at constant in-line coordinate x=2,560 m. Both sections are rendered using the same (98) percentile for clipping amplitudes.

 

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Figure 11 Angle-domain Common Image Gathers obtained by common-azimuth migration. The location of these CIGs are marked on the in-line axis of the common-azimuth image shown in Figure 10