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 Biondi, B., 2001, Narrowazimuth migration: Analysis and tests in vertically layered media: SEP108, 105118.

 Biondi, B., 2003, Narrowazimuth migration of marine streamer data: SEP113, 107120.

 Tisserant, T., and Biondi, B., 2003, Wavefieldcontinuation angledomain commonimage gathers in 3D: SEP113, 211220.

 Vaillant, L., and Biondi, B., 2000, Accuracy of commonazimuth migration approximations: SEP103, 157168.

A
This appendix derives the expressions for
the weights to be applied to the
ADCIGs before averaging over azimuths.
These weights are based on the jacobian of the
transformation into angle domain.
The first step is therefore to
find the expressions for evaluating this jacobian.
The starting point for computing the jacobian
is the transformation into angle domain.
Tisserant and Biondi (2003) showed
that 3D ADCIGs can be computed according
to the following mappings:
 
(3) 
 (4) 
where the primes on the wavenumber indicate the rotation
of the coordinate axis by according
to the following relationships:
 
(6) 
 (7) 
and similarly
 
(8) 
 (9) 
We need to compute the partial derivatives of
the offset wavenumbers at constant aperture angle
.Therefore,
we start from rewriting the coplanarity condition
in equation (4)
in terms of reflections angles in the rotated coordinate system:
the aperture angle ,
the inline dip angle ,and the crossline dip angle .The following relationships link the wavenumber in the image
domain to these angles
 
(10) 
 
(11) 
and
 
(12) 
Then
equation (4)
becomes:
 
(13) 
and
equation (3)
becomes:
 
(14) 