Therefore, I construct a structural model from the migrated image and limit the optimization to the events in the data that correspond to the major structural boundaries. This significantly reduces the amount of data in the optimization, and allows me to do prestack migrations at little cost in different iterations in the migration. Kirchhoff migration is well-suited for migrating limited amounts of data to certain target regions. The targets here are windows around the boundaries: if the model is updated, a simple event migration determines the position of the updated boundaries, and Kirchhoff imaging only has to be done for gates around the updated depth positions of the boundaries.
The constantly changing positions of the windows in the prestack depth-migrated data can be problematic in the optimization. A possible solution is to do zero-offset modeling of the migrated constant-offset sections; the depth axis then gets converted to a pseudo-depth axis, and the zero-offset section stays constant. The converted data is the same as DMO-corrected data, where the DMO correction is calculated for a arbitrary velocity medium (Popovici and Biondi, 1989).
This conversion also has some advantages for the optimization itself: the backprojection operator does not have to take movements of the zero-offset section into account, but instead concentrates on the non-zero-offset behavior of the reflections events - the part that provides the most velocity information. I discussed this matter in more detail in my previous report (Van Trier, 1989a). Figure and show the result of zero-offset modeling the migrated constant-offset sections; the plots show a constant offset and constant surface location slices through the converted data, respectively. A disadvantage of this data representation is that time sections are harder to interpret for complex structure. It is hard to decide which data representation is the most convenient in velocity analysis without actually applying the velocity inversion; I will investigate this in the near future.