Prestack Migration And Applications
In areas of complex geological structures, the CMP (common midpoint) stacking process fails since the assumption that CMP equals CRP (common reflection point) is rendered invalid. The scattering of reflection points for CMP traces will occur whenever dipping beds are not flat. Figure 5-1 shows an example of this for a collection of CMP traces.
Therefore, for areas of complex structure, the incompatibility of CMP stacking and depth migration, dictate that the migration process be performed before stacking. The stacking can be done within the migration process itself. This process certainly does not obviate the need for accurate velocity estimation. In fact, we shall see that the success of the prestack migration process is closely coupled to velocity estimation, and that velocity analysis is the major problem.
The concept of prestack migration is most readily explained using the concept of aplanatic surfaces. This kinematic description probably relates more to Kirchhoff migration which is a ray tracing or wavefront mapping approach to depth migration. In relating prestack migration to reverse-time finite-difference methods, we use some of the first examples which were developed for VSP (vertical seismic profiling) migration by Chang and McMechan (1986) and by Whitmore and Lines (1986). Both of these methods relate to the imaging condition of Claerbout (1971). In essence, we will see that prestack migration involves two steps - the downward continuation of wavefields to the reflector and the application of an imaging condition.
In considering the downward continuation step, we use the concept of an aplanatic surface. For a given source and receiver, an aplanatic surface is defined as the locus of possible reflector surface points for a given reflection traveltime (ref. Sheriff, 1991). (This definition of an aplanatic surface assumes that we have knowledge of the medium’s seismic velocity variation.)
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Seismic Modeling and Imaging with the Complete Wave Equation
“Seismic modeling and imaging of the earth's subsurface are complex and difficult computational tasks. The authors present general numerical methods based on the complete wave equation for solving these important seismic exploration problems.”