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The finite-difference method greatly simplifies traveltime calculations on a regular grid. The algorithm has the advantage over Vidale's method that all points can be treated equally; i.e., minimum traveltime points do not have to be found at each extrapolation step, and the difference scheme vectorizes fully. The method allows efficient calculation of Greens's functions in Kirchhoff methods, and fast traveltime computations in iterative tomography schemes.

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