Transformations for dynamic ray tracing in anisotropic media with a homogeneous Hamiltonian of an arbitrary degree

Ludek Klimes


Six-dimensional dynamic ray tracing in (phase-space) Cartesian coordinates was introduced by Cerveny in 1972. In 1982, Hanyga showed that it reduces to 4-dimensional dynamic ray tracing in (phase-space) ray-centred coordinates. This paper concentrates on the explicit transformation equations of dynamic ray tracing between Cartesian and ray-centred coordinates. Many of the transformation equations have not been published before even for isotropic medium. Also proposed is an efficient way of reducing the number of equations being solved when numerically evaluating the paraxial-ray propagator matrices, both in Cartesian and ray-centred coordinates.


Anisotropy, paraxial rays, dynamic ray tracing, ray-centred coordinates.

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The version with a homogeneous Hamiltonian of the second degree was published previously in Wave Motion, 20 (1994), 261-272.
The differences between the two versions are marked with red.

In: Seismic Waves in Complex 3-D Structures, Report 12, pp. 67-78, Dep. Geophys., Charles Univ., Prague, 2002.
SW3D - main page of consortium Seismic Waves in Complex 3-D Structures .