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Claerbout (1999) introduces this
concept and provides all the basic details for
downwardcontinuation methods, including the surveysinking concept.
The explanation of all of these details is
beyond the scope of this dissertation. I
present only the basic concepts and describe how they can be adapted to
convertedwave data.
The concept of surveysinking is basically a downward continuation of the
sources and the receivers. The shots and receivers
can be downward continued to different depths
during the process; however, they need to be at
the same depth for the final image to
be correct.
To apply surveysinking to
convertedwave data the downward continuation of
the source wavefield is carried out with the Pwaves
velocity, and the receiver wavefield
is downwardcontinued with the velocity for the Swave.
Using the concept of surveysinking the final
prestack is obtained by
taking the wavefield U at time equal zero (t=0),
 
(27) 
where s, g, z represent the source position,
the receiver position, and the reflector depth, respectively.
For the final image to be correct, the data should
migrate both to zero traveltime zero subsurface offset. This
point in the image space also represents the conversion point
for PS data. This
is achieved with the correct velocity model. For
the convertedwave case there will be two different
velocity models.
The sinking or downward continuation of the wavefield
at the surface (z=0) to a different depth level is described by
 
(28) 
This process is enabled by applying the Double Square Root (DSR)
equation. In 2D this is described as follows
 

 
 (29) 
The final prestack image is extracted by summing all
the frequencies at each depth level.
 
(30) 
Different downwardcontinuation migration algorithms differ
in the implementation of the DSR equation. This does not
impact the results presented in the following sections.
As mentioned before, in both
the Pwaves and the Swaves velocities, the energy should
collapse to zero subsurfaceoffset. However, we can
extract more information from our image  that is
velocity information  by transforming the
subsurface offset into angle information. Chapter 3
describes this process for convertedwave data and
presents both a synthetic and a real data examples.
Next: PS angledomain commonimage gathers
Up: Waveequation imaging
Previous: Waveequation imaging
Stanford Exploration Project
12/14/2006