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A prestack image provides information on both velocity errors
and rockproperty characteristics. This paper obtains the
prestack image through waveequation methods. Several authors
have described this process in general, so it will not be
the main focus of this paper. However, this section
describes the basics of waveequation imaging, and outlines
the method we use to obtain subsurface offsetdomain
commonimage gathers.
Biondi (2003) shows the equivalence of waveequation
sourcereceiver migration with waveequation shotprofile
migration. The main contribution of this paper is independent
of the migration algorithm implemented, as long as the migration
algorithm is based on the wavefield downward continuation,
and the final prestack image is a function of the horizontal
subsurface offset. For the purposes of this paper,
we are using shotprofile migration as our
imaging algorithm.
The final prestack image is obtained with the following
imaging condition Sava and Fomel (2005):
 
(1) 
Here, is a vector describing
the locations of the image points, and is a vector describing the subsurface
offset. For 2D convertedwave seismic data, the component represents the horizontal coordinate,
is the depth coordinate of the image point relative to a reference
coordinate system, and is the horizontal subsurface offset Rickett and Sava (2002).
The summation over temporal
frequencies () extracts the image at zerotime.
The propagation of the receiver wavefield (U^{r}_{z}) and the
source wavefield (U^{s}_{z}) is done by
downward continuing the recorded data, and the given source wavelet,
each one respectively as:
 

 (2) 
where v_{p} is the Pwave velocity and
v_{s} is the Swave velocity.
The next section describes the main focus of this paper,
which is the transformation of subsurface offset into the
angle domain.
Next: Transformation to the angle
Up: Rosales et al.: PSADCIG
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Stanford Exploration Project
4/5/2006