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4. , for the interpolation within ray cells, for the asymptotic summation of Gaussian beams, or for the asymptotic summation of Gaussian packets. Controlled initial-value ray tracing for the asymptotic summation of Gaussian beams differs from two-point ray tracing by no receivers specified along the reference surface. In controlled initial-value ray tracing for the asymptotic summation of Gaussian packets or for the interpolation within ray cells, no reference surface is usually 22 ˇ CERVENÝ ET AL.
The parameter, specifying the points along the characteristics, depends on the selected Hamiltonian. For Hamiltonians which are homogeneous functions in pi (with a possible additional constant), the parameter has the physical meaning of travel time τ . Consequently, we consider consistently with H(xi , pj ) = ˇ CERVENÝ ET AL. 10 Eqs. (21), (22) and (23) travel time τ to be the parameter along the ray. The characteristic of the eikonal equation is then described by six ordinary differential equations in xi and pi , dxi ∂H , = dτ ∂pi dpi ∂H .
If they lie at the end surface, the decomposition of the ray tube into ray cells is completed. If they are located at an interface, we continue the process of creating ray cells beyond this interface. We may again have to suspend proceeding along some ray(s) and we may create some degenerate ray cell(s), until we get time points of equal travel time at the top of the recently created ray cell. We can then continue with creating regular ray cells with equal travel time at their bottoms and tops.