There is one aspect of using non-stationary PEFs that I have glossed over to this point: the requirement that we have field with similar statistics to estimate the PEF from. Viewed one way this is a significant weakness to the approach, viewed another it can be seen as a useful feature. One of the largest problems in seismic imaging is how to put the geologist's conception of geology into the geophysicst's inversion problem. The non-stationary PEF can be estimated from the geologist's model. Therefore, our regularization operator directly incorporates the geologist's conception of the velocity structure into the velocity estimation.
For this simple model, we will use as our conception of geology a vertically warped version of our initial velocity estimate. We measure how much a migrated reflector positions varies from our initial flat estimate. Figure 13 shows our initial estimate.
Figure 13 Warped velocity model used to estimate non-stationary filters from.