My analysis is based on the conceptual generalization
of integral (Kirchhoff) migration to the computation
of sub-surface offset gathers.
Integral migration is defined by the summation
surfaces over which the data are integrated
to compute the image at every point in the image space.
The shapes of these summation surfaces are usually computed
as the sum of the time delays from the image point in the subsurface to the source and receiver locations at the surface.
The basic idea underlying the generalization I introduce in this paper,
is that we can compute the summation surfaces by evaluating
the time delays starting not from the same point
in the subsurface for both the source and receiver rays,
but starting from two points horizontally
shifted by with respect to the image point.
The summation of data along these surfaces
produces a prestack image as a function of
the subsurface offset that is kinematically equivalent
to the image created by wavefield-continuation
migrations such as source-receiver downward continuation,
or shot-profile migration in conjunction to the
generalized imaging condition discussed by
Rickett and Sava (2002).
Therefore, the kinematic analysis that follows,
and its conclusions, are
independent from the migration method applied to compute the
prestack images.
An interesting observation is that the ADCIGs computed
using this generalization of integral migration should be immune
from the artifacts that affect angle gathers computed by
conventional integral migration and discussed
by Stolk and Symes (2003).