Open AccessRay perturbation theory for heterogeneous hexagonal anisotropic media
Author(s) -
Farra V.
Publication year - 1989
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1989.tb02054.x
Subject(s) - paraxial approximation , anisotropy , hamiltonian (control theory) , propagator , ray tracing (physics) , physics , perturbation (astronomy) , computational physics , geometry , optics , quantum mechanics , mathematics , mathematical optimization , beam (structure)
SUMMARY A Hamiltonian formalism is proposed for the calculation of rays in an anisotropic medium. This technique leads to a unified approach to calculate paraxial rays and rays perturbed by small changes of elastic parameters. We first study the perturbation of initial conditions (paraxial ray tracing). A set of rays propagating in the vicinity of a central ray is traced with the help of the so‐called paraxial ray propagator. The interaction of these paraxial rays with an interface is simplified considerably in the Hamiltonian formulation. In the second part of the paper, the efficient determination of the rays and the propagator is discussed for a hexagonal anisotropic medium. We propose a finite element approach where the medium is divided into a set of elements with simple elastic parameter distributions. Analytical expressions of rays, paraxial rays and traveltimes are obtained for elliptical anisotropy. Expressions for general hexagonal anisotropy are obtained using ray perturbation theory. Examples of the calculation of rays and synthetic seismograms are presented.