The impulse response tests of our algorithm, along with the comparisons with original 17-point McClellan filter have been shown in SEP77. Here we show the results on a real dataset described below. The migration code was run on the CM-5 at SEP.
The data are a 3-D dip-moveout corrected post-stack volume acquired over a salt intrusion in the Gulf of Mexico, donated by Halliburton Geophysical Services to SEP. The dataset is the same as that used by David Lumley 1993. The data used in testing the migration algorithm comprise a smaller portion of the complete dataset. We used a surface grid of 128x128 traces, with a decimated inline spacing of 50 meters and an original crossline spacing of 50 meters , representing a surface area of 6.4 km inline by 6.4 km crossline. The traces were further decimated to 8 milliseconds, since the data did not contain any signal beyond 60 Hertz. Since our present implementation of the migration algorithm requires the same spacing along the inline and crossline traces, the data along the inline directions were subsampled, giving a 50 meter spacing along the crossline. Figure 2 shows an inline section sliced at Y=4000 meters (20th slice) from the input stacked data volume. We migrated the data with a simple velocity function varying only with depth because SEP was given only the post-stack dataset and the available picked stacking velocities yielded an unreliable interval velocity model. Consequently we do not expect to properly focus reflections below the upper salt boundary, and possibly also the diffractions at the top of the salt are not perfectly focused.
We used a depth extrapolation step dz=10 m and 300 depth steps for the migrations carried out using the different McClellan filters. The migrations were performed with the 9-point filter, the 17-point filter and the 9-9 averaged filter.
Figure 3 shows the inline slice taken from the migrated volume at the same position as the section in Figure 2. The diffractions seen in the input inline slice are now collapsed.
Figure 4 shows the crossline slices taken at X=10,800 meters. The slices are taken from the migrations performed using the nine-point filter (top) and the 9-9 averaged filter (bottom). The top of the salt can be seen at y=7000 meters and z=1380 meters.
Figure 5 shows the top of the salt body. The slices are taken from the migrations performed using the nine-point filter (top) and the 9-9 averaged filter (bottom), at z=1380 meters. The differences are small.
Figure 6 shows the depth slices taken at z=1600 meters from the migrations performed using the nine-point filter (top) and the 9-9 averaged filter (bottom). The differences are small. Figure 7 shows the difference of the sections shown in Figure 6. The peak amplitude in the difference section is 0.3 times of that in the original sections.
The lack of visible differences in the migrations performed by the 9-point and 9-9 averaged filters is most likely caused by the limited dip and frequency range in the dataset. Other causes can be an inaccurate velocity function that has prevented us from correctly imaging the diffraction at the top of the salt, and possibly the data size that reduced the migration aperture needed for imaging steeper dips.