For the v(z) medium case, I will use the reflector model shown in Figure 10, which includes reflectors with dips ranging from 0 to 90 degrees. In v(z) media, unlike in homogeneous media, dips up to and beyond 90 degrees can be recorded with a limited aperture due to the ray bending. However, since our equation is based on the equivalent medium assumption some of the restrictions of the homogeneous case will hold in the v(z) approximation as well.
Figure 11 shows four synthetic seismograms generated using the model in Figure 10 for offsets of (a) 0, (b) 1, (c) 2, and (d) 3 km.
Figure 12 shows prestack time migration of the synthetic data given in Figure 11 plotted in depth for offsets, from top to bottom, of zero, 1, 2, and 3 km, respectively. The migrated sections overall agree well with the model used to generate the synthetic seismograms. However, such an agreement in this v(z) example is less evident compared to what we obtained in the homogeneous medium case. This is some what expected since equivalent medium derivations are approximations. As dip increases slight under migration is apparent, however, these results are preliminary; improvements are expected in a follow up paper.