Green's functions generated at a few frequencies can be interpolated to all frequencies of interest and used for modeling and migration. I have shown that Green's function calculated in a polar coordinate frame can be used to model and migrate overturned waves in a V(z) medium.
If the Green's functions contain the true amplitude information, i.e. they are not not just kinematic operators, the migration algorithm must be modified to account for the amplitude effects. The simplest scheme is to use a diagonal approximation to the true inverse operator. This scheme produced satisfactory results for the geometry used in my examples.