The standard imaging condition for prestack reverse time
migration is based on the crosscorrelation in time of the
source wavefield (*S*) with the receiver wavefield (*R*).
The equivalent of the stacked image
is the average over the sources (*s*)
of the zero lag of this
crosscorrelation,
that is:

(1) |

This imaging condition has the disadvantage of
not allowing a prestack analysis of the image for
either velocity updating or amplitude analysis.
The conventional way of overcoming this limitation
is to avoid the averaging over sources,
and thus to create CIGs where the horizontal axis
is related to a
*surface offset*;
that is, the distance between the source location and the image point.
This kind of CIG is known to be prone to artifacts even
when the migration velocity is correct because the non-specular
reflections do not destructively interfere.
Furthermore, in presence of migration velocity errors
and structural dips,
this kind of CIG does not provide useful
information for improving the velocity function.

Rickett and Sava (2001) proposed a method
for creating more useful angle-domain CIGs
with shot profile migration using downward continuation.
Their method can be easily extended to reverse time migration.
Equation (1)
can be generalized by crosscorrelating
the wavefields shifted with respect to each other.
The prestack image becomes function
of the horizontal relative shift,
that has the physical meaning
of a *subsurface offset* ().
It can be computed as

(2) |

Reverse time migration is more general
than downward continuation migration
because it allows events to propagate both upward and downward.
Therefore the ADCIG computed from reverse
time migration can be more general
than the ones computed from downward-continuation migration.
This more general imaging condition is actually needed
when the source and receiver wavefields
meet at the reflector when propagating along opposite
vertical direction.
This condition may occur either
when we image overturned events
or image prismatic reflections.
I analyze these situations in more details in
the following sections.
To create useful ADCIGs in these situations
we can introduce
a *vertical offset* *z*_{h} into
equation (2) and obtain

(3) |

6/7/2002