Reduced Hamiltonian in ray tracing systems for anisotropic inhomogeneous media

Summary

The reduced Hamiltonian and its applications in the ray theory of isotropic inhomogeneous media have been well known for a long time. In this article, an analogous reduced Hamiltonian is introduced for anisotropic inhomogeneous media. The reduced Hamiltonian is closely connected with the evolution Hamilton-Jacobi equation, with the factorization of the elastodynamic equation, and with the parabolic equation method. The determination of the reduced Hamiltonian is based on the same 6x6 eigenvalue problem which has been successfully exploited in the 6x6 propagator techniques for 1-D anisotropic inhomogeneous media and in the computation of 6x6 R/T coefficients from anisotropic transition layers. The reduced Hamiltonian ray tracing system, consisting of four ordinary differential equations of the first order, applicable to inhomogeneous anisotropic media, is derived and discussed. It is proved that this system remains valid even for P and S waves propagating in isotropic inhomogeneous media, where it yields the well-known results.

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