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Commonazimuth migration is the second component of the
commonazimuth imaging procedure.
Commonazimuth migration Biondi and Palacharla (1996) is based on a downwardcontinuation
operator derived from the full 3D prestack downwardcontinuation
operator.
Commonazimuth data sets are recursively evaluated
at increasing depth levels,
starting from the commonazimuth data set
recorded at the surface.
Commonazimuth data has zero crossline offset, and thus it is only fourdimensional.
Consequently, the commonazimuth
operator is also only four dimensional,
whereas the full 3D prestack downward continuation
operator is five dimensional.
This reduction in dimensionality of the continuation
operator results in a substantial reduction
of computational and storage requirements,
though at the cost of some potential loss in accuracy.
The full prestack downward continuation operator
is expressed in the frequencywavenumber domain
by the Double Square Root (DSR) dispersion relation
 

 (2) 
where is the temporal frequency, k_{x} and k_{y} are the
midpoint wavenumbers, and k_{hx} and k_{hy} are the offset wavenumbers;
and are respectively the propagation
velocities at the source and receiver location.
A stationaryphase approximation of the full DSR
yields the commonazimuth dispersion relation.
This new dispersion relation can be expressed as
the cascade of two 2D relations.
The first relation is that for 2D prestack downwardcontinuation
along the inline direction,
 
(3) 
and the second relation is the one for 2D zerooffset downward continuation
along the crossline axis,
 
(4) 
The commonazimuth downward continuation operator
is not as a general operator as the full DSR,
and consequently it introduces some approximations.
However, the components of the wavefield that contribute
significantly to the final image are correctly
extrapolated Biondi and Palacharla (1996).
Next: COMMONAZIMUTH IMAGING OF A
Up: Biondi: CommonAzimuth Imaging
Previous: AZIMUTHMOVEOUT TRANSFORMATION
Stanford Exploration Project
11/11/1997