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Weighting operator

To construct a weighting operator for this dataset, we must choose a reference model. Claerbout and Nichols (1994) suggested that the best reference model would be the perfect image, but we never have a perfect image, especially in areas of poor illumination. Rickett (2001) suggested two alternative reference models. One reference model was composed of random noise. This left a ``footprint'' of the random number field on the weighting function and produced different weighting functions for different random number fields. The final suggested reference model was that of flat layers, essentially the flat layer calibration done by Black and Schleicher (1989). This model produces a weighting function that is noise-free and well-behaved. The flat layer reference model doesn't rely on the data. It does depend on the velocity model and the survey geometry, which are the primary causes of poor illumination with which we are concerned. I choose to use the flat layer reference model for these reasons.

The flat layer model I constructed can be seen in the top right panel of Figure [*]. It has the same dimensions as the migration result from the previous subsection, but is composed entirely of flat layers. I modeled the data that would be produced from these flat layers with the adjoint of the migration scheme described in the previous subsection, using the velocity model from Figure [*]. I then migrated that data to get the weighting operator defined in equation (2). The lower panel of Figure [*] shows this weighting operator.

The weighting operator in Figure [*] is displayed as a flattened cube. The front of the cube shows a common ray parameter slice in which the high values of the weighting operator can be seen in the shadow zones. The top of the cube is shown above the common ray parameter slice and shows a depth slice. In this depth slice, we can see that the weighting operator indicates that the subsalt illumination along CRPs is becoming worse with larger ray parameters. The side of the cube shows a ray parameter gather taken from a CRP at the salt edge. This view shows how illumination varies along ray parameter and with depth. It also shows some vertical striping that I believe is caused by the way I took the smoothed analytic signal envelope. We must keep this in mind as we apply this weighting function to the image.

 
mod.mig
mod.mig
Figure 2
Top: stack of migration. Bottom: ray parameter gathers from migration, taken from between ${\rm CRP}=10 {\rm km}$ and ${\rm CRP}=12 {\rm km}$.
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next up previous print clean
Next: Result Up: Application Previous: Imaging and illumination
Stanford Exploration Project
7/8/2003