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() introduces this
concept and provides all the basic details for
downward-continuation methods, including the survey-sinking 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
converted-wave data.
The concept of survey-sinking 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 survey-sinking to
converted-wave data the downward continuation of
the source wavefield is carried out with the P-waves
velocity, and the receiver wavefield
is downward-continued with the velocity for the S-wave.
Using the concept of survey-sinking 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 converted-wave 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
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|
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| (29) |
The final prestack image is extracted by summing all
the frequencies at each depth level.
| |
(30) |
Different downward-continuation 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 P-waves and the S-waves velocities, the energy should
collapse to zero subsurface-offset. 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 converted-wave data and
presents both a synthetic and a real data examples.
Next: About this document ...
Up: Wave-equation imaging
Previous: Wave-equation imaging
Stanford Exploration Project
12/14/2006