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Comparison with inversion results

I have shown that using the a posteriori weighting operator can improve amplitudes. However, it does that at the cost of increasing the noise as well. At this point, I would like to compare the result of the weighting operator with that of regularized least-squares inversion. The inversion scheme I chose to use is the geophysical preconditioned scheme explained by Prucha and Biondi (2002a). This iterative inversion uses the imaging operator described above. The regularization operator is a gradient operator along the ray parameter axis. It is designed to improve continuity and minimize amplitude variation due to illumination along the ray parameter axis.

 
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Figure 4
Top: stack of result of 10 iterations of geophysical preconditioned inversion. Bottom: ray parameter gathers after 10 iterations of geophysical preconditioned inversion, taken from between ${\rm CRP}=10 {\rm km}$ and ${\rm CRP}=12 {\rm km}$.
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I applied ten iterations of this regularized inversion to the same part of the Sigsbee2A dataset as shown above. The result can be seen in Figure [*]. The stacked result in the upper panel shows that we have extended the events even further under the salt edges than the result after model space weighting (Figure [*]). The events under the salt are stronger than the result of the migration (Figure [*]) but do not have the artificial amplitude variations or the increase in the strength of artifacts that are seen in the result of model space weighting. The fault underneath the salt nose is better focused. The stacked inversion result also has much cleaner shadow zones than both the migration and weighted results. In the ray parameter gathers, the inversion result shows better continuity and amplitude behavior than the migration result and is much cleaner than the weighted result. Overall, the inversion result is better than the model space weighted result. This can be seen even more clearly in Figure [*], which shows an enlarged view of the stacks in the area at the salt edge for the migration (left panel), the model space weighted result (center), and the regularized inversion result (right panel). The inversion result has done a better job of extending the reflectors beneath the salt and has fewer artifacts than either of the other results. However, the inversion result has a computational cost approximately seven times [*] greater than the weighted result.

 
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Figure 5
Results enlarged from ${\rm CRP}=9.75 {\rm km}$ to ${\rm CRP}=11.25 {\rm km}$.Left: stack of migration. Center: stack of model space weighted result. Right: stack of result after 10 iterations of preconditioned inversion.
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Next: Conclusions Up: M. Clapp: Illumination compensation: Previous: Result
Stanford Exploration Project
7/8/2003