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, proposed for models with structural interfaces which make the method unstable and generate travel-time errors of the first order. The method is developed, described, and demonstrated only in 2-D.
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Klimes, L.: Grid travel-time tracing: second-order method for the first arrivals in smooth media. In: Seismic Waves in Complex 3-D Structures, Report 3, pp. 157-174, Dep. Geophys., Charles Univ., Prague, 1995.
Klimes, L.: Grid travel-time tracing: second-order method for the first arrivals in smooth media. PAGEOPH, 148 (1996), 539-563.