We assume that a migration operator maps events from x-t space outside the evanescent zone to events in x-z space, and that this mapping is unitary, or white. To do this we need a unitary migration operator. The migration operator should look white outside the evanescent zone, but be zero within the evanescent zone. If we take an operator with position information only and calculate an operator that will whiten it as above, we should get a reasonable approximation to the correct migration operator. For this we can used a 2-D prediction-error filter. While we expect some problems in the evanescent zone, we hope all the energy on the input will be moved to the output with just the proper phase changes due to dips.
This approach to migration is different from other approaches in that we are ignoring much of the physics of the problem, or at least we are taking a different view of the physics. The unitary operator being developed may be considered to be somewhere between the conjugate operator and the inverse. (See Claerbout 1992, pages 99-145.) It might be possible to extend this approach to DMO and prestack migration.