Abstract
Traveltime tomography based on ray tracing requires the gradient or derivative of the traveltime error with respect to the velocity model parameters. This gradient can be computed by determining the Fréchet derivatives and solving a large sparse linear system. The perturbed traveltime equation offers an alternative way. A third, formal approach is the adjoint-state method. Here it is shown that the gradient obtained by the adjoint-state method is the same as the perturbed traveltime equation.
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