In this section, we demonstrate that the problem of a complex overburden that involves only one layer boundary, such as an irregular water bottom, at which significant ray bending takes place can sometimes be addressed by prestack layer replacement followed by NMO correction, CMP stacking, and poststack time migration. In both cases, the approaches are based on the philosophy of revising velocity estimates and obtaining an improved unmigrated stacked section.
Consider the velocity-depth model in Figure 8.1-1a. Note that complex geometry of the boundary (horizon 2) between the overburden and the substratum and the significant velocity contrast across this boundary cause the severe ray bending. This in turn causes distortions and disruptions of the underlying target reflections. Without the velocity contrast (Figure 8.1-1b), the rays would not bend and there would be no need for depth migration. Figure 8.1-1 suggests that replacing the overburden velocity with the substratum velocity can be a viable alternative to using depth migration to remove the deleterious effects of a complex overburden, such as an irregular water-bottom topography, on the substrata. This technique is known as layer replacement.
A technique for layer replacement  based on wave-equation datuming ,  is presented here. Berryhill’s datuming technique involves extrapolating a known wavefield at a specified datum of arbitrary shape to another datum, also of arbitrary shape. Wave extrapolation is performed using the Kirchhoff integral solution to the scalar wave equation. It incorporates both the near-field and far-field terms (Section H.1). The velocity used in extrapolation is that of the medium confined between the input datum and the output datum.
- Yilmaz and Lucas, 1986, Yilmaz, O. and Lucas, D., 1986, Prestack layer replacement: Geophysics, 51, 1355–1369.
- Berryhill, 1979, Berryhill, J.R., 1979, Wave-equation datuming: Geophysics, 44, 1329–1333.
- Berryhill, 1984, Berryhill, J.R., 1984, Wave-equation datuming before stack: Presented at the 54th Ann. Internat. Mtg., Soc. Expl. Geophys.