During the past decade, the use of AVO (amplitude variation with offset) analysis in petroleum exploration has become increasingly common. Even though the goal of AVO analysis is to observe the anomalous angle-dependent reflectivity behavior of a reflector, the name amplitude variation with offset was chosen because most of the amplitude analysis is done in the common midpoint domain.
To analyze the properties of the reflector correctly, we need to know the angle-dependent reflectivity, which is often called AVA (amplitude variation with angle). When a target reflector is close to horizontal, and velocity does not change much in the lateral direction, angle-dependent reflectivity can be obtained by measuring amplitudes along the offset, followed by ray tracing for each event to determine the corresponding incidence angle to the reflector. If a target reflector has a complex structure and strong lateral velocity variation, however, AVO may not be the same as AVA because the amplitude can be affected not only by the angle-dependent reflectivity, but also by wave focusing or defocusing caused by propagation through complex velocities or structures. Resnick et al. (1987) discuss the fact that dips introduce serious problems for AVO analysis. They conclude that performing prestack migration on the data before doing AVO analysis is a necessity.
Most present day seismic migration schemes determine only the reflection coefficient of the zero offset or averaged reflectivity over a range of reflection angles for each depth point in the subsurface. This is mainly because of a simplified imaging condition. Recently, de Bruin et al. 1990 proposed an imaging technique that produces angle-dependent reflectivity. Unfortunately, this scheme is not easy to apply when the reflector is not flat, which commonly happens in the real world.
In chapter 5, I compare the imaging conditions of three different prestack migrations in terms of angle-dependent reflectivity recovery. The imaging conditions compared are shot profile migration with the conventional imaging condition, de Bruin's imaging condition, and plane-wave synthesis imaging. The conventional imaging condition can be applied to any reflector geometry and to arbitrary velocity, but it recovers only a diagonal component of the reflectivity matrix that contains angle-dependent reflectivity information. De Bruin's imaging condition recovers a full reflectivity matrix but has difficulty in implementing for arbitrary reflector geometry and under variable velocity. Plane-wave synthesis imaging takes advantage of both conventional and de Bruin's imaging conditions. Thus, plane-wave synthesis imaging can be applied to any arbitrary structure and implicitly uses the same imaging condition as that of de Bruin.