In a first experiment, we migrated the data using a true-amplitude Kirchhoff algorithm without accounting for fold variations. Figure 5 shows the results of the direct migration. The reflectivity map has a poor resolution and suffers amplitude distortions scattered along the entire flat reflector. Figure 6 shows the results of the normalized migration; the image is now smoother, it shows more continuity and better resolution than the unconditioned migration result. The equalization for fold coverage during migration eliminated most of the amplitude distortions along the horizontal reflector and helped image the location of the anomalies.
Next, we applied the AMO transformation to regularize the geometry and reconstruct the data as a zero-azimuth cube with 8000 ft effective offset and constant mid-point spacing of 80 ft. The CA/CO cube is then migrated using the 3D prestack depth migration algorithm. Figures 7 and 8 show the results of this processing sequence. Figure 7 is generated with an AMO algorithm that does not account for the variations in the fold coverage. This is the previous result presented in Chemingui and Biondi (1996b) regenerated and displayed at better resolution. We compare this result to the new image obtained by including the normalization procedure in the integral AMO algorithm. The output of the AMO transformation is a regularly gridded single-fold CA/CO cube well suited for prestack migration. Figure 8 shows that the normalization procedure improved the quality of the reflectivity map and eliminated the foot imprint of the geometry.
The results of the normalized migration and normalized AMO are very similar. The advantage of applying the correction procedure during the AMO transformation is the resulting reduction in the the size of the prestack volume and the regularization of the data into CA/CO cubes for prestack migration. This allows for more reliable amplitude analysis as a function of offset and azimuth.
Figure 9 shows the difference in the reflectivity maps between the unconditioned migration and the normalized migration, whereas Figure 10 shows the difference between the migrated images of the unconditioned AMO and the normalized AMO. The residual maps are very similar and show direct correlation with the fold distribution as displayed on the fold diagram (Figure 3).
We conclude that the normalization of the Kirchhoff operator in its discrete summation implementation helps eliminate the effects of fold variations. It is important to note that this approximate solution for equalization cannot compensate for missing traces or varying spatial distribution of traces within CMP bins. The latter aspect was not a major concern since most redundant traces shared the same spatial coordinates. This is related to the fact that, in land acquisition, Button-Patch geometry in this case, the receiver locations are fixed and geophones are only deployed after the recording of an entire patch.