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In Appendix A transpose operators to hyperbola and parabola stacking in
continuous domain are derived.
For hyperbola stacking it is
weighted parabola stacking in space, which is symbolically
denoted as , and for parabola stacking in
space it is weighted stacking in (t,x)space.
A dot product test was used to test these results (Table 1).
The following form of the
dot product test was used:
 
(13) 
where is , or whatever operator was used.
Table 1:
Dot product test for
various operators.
2cOperator in 
2cDot product 


time domain 
sloth domain 




110.5207 
110.5218 


106.6519 
106.6530 


107.6680 
108.4489 


110.5207 
111.3971 


105.1228 
105.8237 


110.5207 
108.4480 
From the table we can see that adjoint operators derived in the continuous
domain are much less precise (relative error about 0.7) than adjoint operators derived in the
discrete domain (relative error ).
Operators and in the last line of the table are not
adjoint to each other, but they were tested to support the theoretical
results from Appendix A (relative error about ).
Next: SAMPLING IN VELOCITY DOMAIN
Up: DATA INVERSION
Previous: Modifications of basic equations
Stanford Exploration Project
1/13/1998