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From equation (3) we established a relation between the
propagation angles for the downgoing and upgoing planewaves,
and , respectively.
Now, from Figure it is easy to see that the
propagation angles are related to: 1) the incidence angle of
the downgoing plane wave into the reflector ();
2) the reflection angle of the upgoing plane wave ();
and the structural dip (). The relation among all the angles is
 
(11) 
Combining equation (3) and (11), we can see the
direct relation between the angles that we compute with relations (7)
and/or (10) and the real structural dip, the incidence angle, and
the reflection angle. That is:
 

 (12) 
It is easy to note that the opening angle is the reflection angle and is the
geological dip when
, which is only valid for the singlemode case.
With these equations and Snell's law, we can convert the fullaperture angle ()obtained with equation (7) or (10) into the incidence angle () or
the reflection angle ():
 

 (13) 
Appendix A presents a full derivation of the same equations but with the perspective of the
Kirchhoff approach. The reader is encourage to follow that demonstration.
Next: Numerical analysis
Up: Kinematic equations
Previous: A Fourier domain look
Stanford Exploration Project
5/3/2005