Six-dimensional dynamic ray tracing in (phase-space) Cartesian coordinates was introduced by Cerveny [Geophys.J.R.astr.Soc. 29(1972), 1-13]. Hanyga [Tectonophysics 90(1982), 243-251] 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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For the generalization of this paper
from a homogeneous Hamiltonian of the second degree
towards a homogeneous Hamiltonian of an arbitrary degree, refer to
Klimes, L. (2002): Transformations for dynamic ray tracing in anisotropic media with a homogeneous Hamiltonian of an arbitrary degree. In: Seismic Waves in Complex 3-D Structures, Report 12, pp. 67-78, Dep. Geophys., Charles Univ., Prague.