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Both reflection tomography and transmission tomography start from the idea that we can use the following fitting goal to invert the unknown slowness model **s** from traveltime **t** :
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(1) |

The operator **T(s)** is usually constructed in terms of rays passing through the slowness model **s**, so it is model dependent and therefore non-linear. By doing a Taylor expansion and ignoring the second and higher order terms, we can linearize this problem:
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(2) |

Here and are the change of slowness and corresponding change of travel time, respectively. The tomography operator now is model-independent. To use the fitting goal (2) for inversion, we need some prior information about the unknown slowness field to construct an initial model, then construct by ray tracing through it. If the initial model does not seriously deviate from the true slowness field, we can use the operator to invert the change of slowness from the change of traveltime . After we obtain , we can update the initial model to obtain more accurate slowness field.

** Next:** Integrated tomography for slowness
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Stanford Exploration Project

7/8/2003