Figure 1 The correct velocity model.
The result of 3 iterations of conjugate-gradient preconditioned least-squares inversion using the correct velocity model can be seen in Figure . Note that the artifacts have been largely cleaned up. It is now possible to reliably pick out events beneath the salt (see inside the oval). In the CRP-depth panel, the amplitude of the events is maintained farther beneath the salt (particularly within the oval). The holes in the ph-depth panel (inside the oval) are being filled in.
To test the sensitivity of the preconditioned inversion, the first incorrect velocity model I tested simply increased the correct velocities by . As expected, the migration result using this velocity model (Figure ) shows the events positioned deeper than they should be and moveout along the offset ray parameter axis. The ovals on this figure are placed in the same absolute positions as the the ovals in Figures and , not relative to the events themselves.
Recall that the preconditioning operator acts horizontally along the offset ray parameter axis. It is this sensitivity that we are interested in observing in the result of 3 iterations of preconditioned inversion using the high velocity model (Figure ). Note that once again the preconditioned inversion has cleaned up many of the artifacts. In the CRP-depth panel, the events extend farther under the salt, in a similar way to the inversion result using the correct velocity (Figure ). The more interesting result is the ph-depth panel. The inversion is still successfully filling in the holes along the events at the mid-range of offset ray parameters. At large ph, where the moveout is more pronounced, the preconditioning has made some attempt to change the dips to be more horizontal, but the moveout is still visible. This means that this result is most likely not safe to use for velocity analysis, but this preconditioned inversion technique was never intended as a velocity tool. Overall, this result indicates that this technique can produce a better image than migration alone, even when the velocity model is incorrect by up to .
Figure 6 The smoothed velocity model. Note that the canyon in the top of the salt has disappeared.
A more extreme velocity model I tested was a severely smoothed one (Figure ). This model has been smoothed so much that the canyon in the top of the salt has disappeared. As expected, the migration result from this model isn't very good (Figure ). The depth positioning of events is fairly good away from the salt, but becomes poor near the salt. The salt top and bottom are very poorly imaged. The events in the ph-depth panel appear to be mostly random. Once again, the ovals indicate the same absolute regions as the ovals in Figures and .
The result of 3 iterations of preconditioned inversion using this smoothed velocity model can be seen in Figure . Although many of the artifacts have been cleaned up, overall the image is not any better than the migration result. The events in the ph-depth panel are more horizontal, but they are not more believable than the events in the ph-depth of the migration result. This is a reassuring result, as it indicates that the regularization was not able to artificially introduce events where the data indicated otherwise.