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For the case of offset rayparameter gathers, we can rewrite the
DSR equation (22) as
 

 (26) 
In this case, the imaging Jacobian becomes
 

 (27) 
which can be rearranged as:
 
(28) 
For an arbitrary 2D reflection geometry (Figure 1),
we can write Equation (28) as
 
(29) 
For flat reflectors, defined by and ,
the Jacobian takes the simple form
 
(30) 
which is equivalent to the weighting factor introduced by
Wapenaar et al. (1999).
For the case of flat reflectors, we also have
 
(31) 
which explains the opposite behavior of the uncorrected migration
amplitudes for reflectionangle gathers (Figure 10)
and offset rayparameter gathers (Figure 11).
After we apply the Jacobian weights, we obtain the corrected
anglegathers shown in Figures 12 and 13.
As expected, the amplitudes are constant for the entire usable
angular range.
Next: Jacobian for Commonazimuth migration
Up: Transformation Jacobians
Previous: Anglegathers
Stanford Exploration Project
4/30/2001