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If the initial conditions xi = xi0 and pi = pi0 are specified for τ = τ0 in such a way that H(xi0 , pj 0 ) = 0, see (20), ray tracing system (24) can be solved by conventional numerical methods (predictor-corrector, for example). We then speak of initial-value ray tracing and of initial-value rays. Relation (20) must be satisfied along the whole ray and can be used to check and control the accuracy of ray tracing. For heterogeneous isotropic media, the ray tracing system reads, see (21) and (24), η(τ ) = dxi = V 2 pi , dτ ∂V 2 dpi 1 .

Sides of the basic triangles. In this way, several pairs of boundary rays may be found along one side of the triangle. In the second step, the boundary between one ray history and the other ray histories is traced, see Fig. 2. 3). In this way, we obtain homogeneous polygons, which should then be divided into homogeneous triangles. In the third step, the homogeneous polygons should be divided into homogeneous triangles. The division of homogeneous polygons into triangles, not too different from equilateral, requires tracing several new rays, situated both on the long sides of the homogeneous polygons and inside the homogeneous polygons, see Fig.

The solid light-grey region is not covered by ray cells. (c) Differences of the bilinearly interpolated travel times from the exact solution. 308 s. The grey scale is the same as in (a). The solid light-grey region is not covered by ray cells. (d) Differences of the bicubically interpolated travel times from the exact solution. 017 s. The grey scale is the same as in (a). The solid light-grey region is not covered by ray cells. ray parameters γ1 , γ2 , and the interpolation should be performed for each set of coordinates w1 , w2 , wB .

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