New computational scheme for calculating the first-arrival travel times on a rectangular grid of points is proposed. Whereas the former "finite-difference" eikonal solvers are the methods of the first order, the new proposed method is of the second-order accuracy. It means that the relative propagation-velocity error of calculated travel time is proportional to the second power of the grid step. That is why 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, designed for models with structural interfaces which make the method unstable and generate travel-time errors of the first order. The equations for appropriate evaluation of the errors of calculated travel times in order to check their accuracy are also presented, and the proposed method is compared with other two numerical methods. The method is developed, described, and demonstrated in 2-D, but may also be extended to general 3-D models with structural interfaces.
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Klimes, L.: Grid travel-time tracing: second-order method for the first arrivals in smooth media. PAGEOPH, 148 (1996), 539-563.