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In this appendix I demonstrate that the terms
in equation 13
multiplying
the partial derivatives
with respect to the angles;
that is,
and
,are zero when evaluated at the point when
the events are correctly migrated at
zero subsurface offset.
We are interested in estimating the RMO function
measured for an incorrect velocity.
That RMO function can be seen as a perturbation around
the image obtained with the correct velocity.
After simple evaluation of partial derivatives
the term multiplying
in equation 13 can be written as the following:
 

 (34) 
that can be easily demonstrated to be equal to zero
after substitution of the relationship
between phase angles and group angles
presented in equation 33.
The term multiplying
is equal to
 
(35) 
which is obviously equal to zero when the subsurface offset is zero,
the point around which we are interested in expanding the RMO function.
C
Next: Derivatives of VTI slowness
Up: Biondi: RMO in anisotropic
Previous: Phase and group angles
Stanford Exploration Project
11/1/2005