This method can be used to pick salt boundaries that are discontinuous. An updated velocity model can then be created and used to remigrate the data.
Additionally, if the salt boundary changes only slightly, then the eigenvector solution to equation (2) from the previous segmentation can be used as an initial solution to the current segmentation.
The top panel of Figure 4 is a synthetic 2D section that has been migrated with a preliminary velocity model. The results of applying the segmentation method can be seen in the bottom. In general it does a good job picking the salt boundary, however at cmp locations -750 and -1950 it has some difficulty.
The top panel of Figure 5 contains the eigenvector with the second smallest eigenvalue from equation (2) that was partitioned to get the result in Figure 4. Below is a contour plot of this eigenvector. Notice that the spreading contours correspond to areas where the picking had some difficulty.
The top of Figure 6 is the same synthetic data used in Figure 4 except migrated with an updated velocity. Again, notice that the partitioning result in the bottom successfully picks the salt boundary except in a couple of places. The corresponding eigenvector is presented in Figure 7. Notice its similarity to the eigenvector from Figure 5. Initializing subsequent segmentation processes with previous eigenvectors should speed convergence.