Review of seismic imaging: prestack
John C. Bancroft
The kinematics of prestack data considers an arbitrary offset between the source and receiver. The added dimension of the source-receiver offset defines a prestack volume where the location of source gathers, constant offset sections, common midpoint gathers, etc. are identified. Reflection energy from horizontal reflectors, dipping reflectors, or scatterpoints can be modelled to these gathers using the double square-root equation. A reversal of these modelling processes describes the various forms of prestack migration.
Conventional moveout correction and stacking of common midpoint gathers is based on the assumption of horizontal reflectors and hyperbolic moveout. The moveout correction of energy from dipping reflectors will not relocate the energy at the reflection point, even though the moveout is hyperbolic. In addition, prestack energy from a scatterpoint will not stack to the zero-offset hyperbola: i.e. diffractions don't stack. Prestack migrations are required to focus this energy.
Offset raypaths and prestack modelling techniques are reviewed to provide a foundation of the principles from which prestack migrations are derived. The objective is to acquaint the reader with the kinematics (traveltimes) of the prestack migration processes, and leave the discussion of amplitudes to the third article in this series.
With the intent to make this paper more readable, references have not been included. Instead, the interested reader should consult the references that are contained in my SEG course notes (Bancroft 2000).