Velocity sensitivity

The difficulties of imaging below salt edges are compounded by the difficulty of generating an accurate velocity model in these areas. The majority of imaging techniques require an accurate velocity model in order to produce a well focused result. The geophysical regularization scheme in particular expects the events to be flat along the offset ray parameter axis - that is, that the correct velocity be used.

I applied the geophysical RIP scheme to the Sigsbee2A dataset, using different velocity models. The correct velocity model can be seen in Figure . The result of migration using the correct velocities is Figure . The result of 3 iterations of geophysical RIP using the correct velocities is in Figure .

 

geop.corvel
Figure 17 The result of 3 iterations of geophysical RIP inversion using the correct velocity model. Note the more consistent amplitudes of events as they pass beneath the salt in the CRP-depth panel and the lack of artifacts obscuring events beneath the salt (inside ovals). In the offset ray parameter-depth panel note the filling in of the holes in the events at the mid-range of offset ray parameters (inside ovals).

To test the sensitivity of the geophysical RIP, the first incorrect velocity model I tested simply scaled up the correct velocities by 67#67. 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.

 

mig.hivel
Figure 18 The result of downward-continuation migration using a velocity model 67#67 higher than the correct model. The events are all positioned deeper than they should be and there is moveout along the offset ray parameter axis. The ovals still indicate the loss of amplitudes under the salt edge and the poor imaging beneath the salt in the CRP-depth panel and holes in the events in the p_h panel.

Recall that the geophysical regularization 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 geophysical RIP using the high velocity model (Figure ). Note that once again the geophysical RIP 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 CIG panel. The inversion is still successfully filling in the holes along the events at the mid-range of offset ray parameters. At large p_h, where the moveout is more pronounced, the regularization 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 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 67#67.

 

geop.hivel
Figure 19 The result of 3 iterations of regularized inversion using the 67#67 scaled up velocity model. Despite the use of the incorrect velocity model, the image is quite comparable to the result using the correct velocity (Figure ). In the CRP-depth panel, the events extend farther under the salt and events under the salt can be seen (inside the ovals). In the p_h-depth panel, the holes in the events are filled in (inside the oval).

 

vel.smoothvel Figure 20 The smoothed velocity model. Note that the canyon in the top of the salt has disappeared.

 

mig.smoothvel
Figure 21 The result of downward-continuation migration using a severely smoothed velocity model. The events in the CRP-depth panel are properly imaged away from the salt but are mispositioned near the salt. The offset ray parameter-depth panel is completely uninformative. The ovals indicate the same absolute regions as the ovals in .

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 CIG panel appear to be mostly random.

 

geop.smoothvel
Figure 22 The result of 3 iterations of preconditioned inversion using the smoothed velocity model. The result is cleaner than the migration result, but not more believable. The ovals indicate the same absolute regions as the ovals in .

The result of 3 iterations of geophysical RIP 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 CIG panel are more horizontal, but they are not more believable than the events in the CIG 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.

The results of geophysical RIP with incorrect velocity models are encouraging. As long as the velocity model is not too inaccurate, the regularization operator behaves as it would for the correct velocity model and produces a better image than migration alone. In the case of a highly inaccurate model, the inversion itself prevents us from producing an image that would conflict with the known data. Overall, as long as the velocity model is reasonably close to correct, the assumption of zero moveout made by the geophysical regularization operator is acceptable.