A new computational scheme for calculating the first-arrival travel times on a rectangular grid of points is proposed. The new proposed method is of second-order accuracy. This means that the calculated travel time is proportional to the second power of the grid spacing. The method should be sufficiently accurate for all applications in smooth seismic models. On the other hand, the method is not, in its present form, proposed for models with structural interfaces which make the method unstable and generate travel-time errors of the first order. Equations are also presented for the appropriate evaluation of the errors of calculated travel times to check their accuracy, and the proposed method is compared with other numerical methods. The method is developed, described, and demonstrated in 2-D, but may also be extended to 3-D models and to general models with structural interfaces.
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