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Relinearization

As mentioned above tomography is actually a non-linear problem. We can potentially achieve a better result by relinearization around our updated slowness model. We can write our updated travel times in terms of non-linear iteration i,
\begin{displaymath}
\bf \Delta t_i = \bf \Delta t- \bf T_{i} ({\bf s_i} - {\bf s_0}).\end{displaymath} (5)
We performed two more non-linear iterations of tomography. The right panel of Figure [*] shows our updated ray field. The ray field shows moderate changes from the initial field (left panel of Figure [*]). After two additional non-linear iterations we get a moderately changed velocity model, shown in the left panel of Figure [*]. The overall reduction in the RMS travel-time error is about 80%, with the majority coming on the first iteration.

 
final
final
Figure 6
The final set of rays (right) and the final velocity model (left) after three non-linear iterations of tomography. Note how many of the feature seen in Figure [*] have become more defined.
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next up previous print clean
Next: Future Work Up: Clapp and Wilson: The Previous: Regularization
Stanford Exploration Project
10/23/2004