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We presented the convertedmode PS 3D commonazimuth
migration operator. The difference between
this operator and the singlemode PP
operator is the use of two different velocity fields.
Therefore, a more careful implementation is needed
to ensure the correct velocity model.
We demonstrate that the subsurface area covered by the
PS commonazimuth migration operator is different than that
covered by the PP commonazimuth
migration operator; therefore, only the area that the two surfaces
share can be used for rockproperties analysis based on the
two complementary images. This might have important impacts
on the reservoircharacterization process.
A
This section derives
the exact solution for the common azimuth prestack migration for a
reflecting point within an homogeneous Earth.
The total travel time is
 
(8) 
The following procedure shows how to go from
to :
 
(9) 
where represents the PtoS velocities ratio.
If we make the following definitions,
 

 
 (10) 
(9) becomes
 
(11) 
We square both sides to get a new equation with only one square root:
 
(12) 
Squaring again to eliminate the square root, and combining elements, we obtain
 
(13) 
This expression is a 4^{th} degree polynomial in ; which is:
 

 (14) 
This can also be writen as follows
 

 
 
 (15) 
This polynomial equation has 4 solutions, which take the following well known form:
 
(16) 
where
 

 
 
 (17) 
Next: REFERENCES
Up: Rosales and Biondi: PSCOMAZ
Previous: Impulse response
Stanford Exploration Project
5/3/2005