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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*,
| |
(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
**

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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Stanford Exploration Project

10/23/2004