Ray tracing in factorized anisotropic inhomogeneous media

Abstract

A concept of a factorized anisotropic inhomogeneous (FAI) medium is introduced. In the FAI medium, the position dependent density normalized elastic parameters aijkl(Xi) can be factorized in the following sense: aijkl(Xi) =f2(xi)Aijkl, where Aijkl are constants, independent of Cartesian coordinates xi, and f(xi) is an arbitrary continuous function of xi. Thus, all the density normalized elastic parameters aijkl(xi) in the FAI medium depend on the coordinates xi in the same way, but the generality of anisotropy and of inhomogeneity is not restricted. The factorization of aijkl(xi) leads to a factorization of certain important ray theory expressions and equations (eikonal equation, etc.), and to particularly simple ray tracing and dynamic ray tracing. For certain types of FAI media, these equations may even be solved analytically or semianalytically. Copyright © 1989, Wiley Blackwell. All rights reserved