Ray tracing in factorized anisotropic inhomogeneous media

Summary

A concept of a factorized anisotropic inhomogeneous (FAI) medium is introduced. In the FAI medium, the position dependent density normalized elastic parameters a_ijkl(x_i) can be factorized in the following sense: a_ijkl(x_i)=f²(x_i)A_ijkl, where A_ijkl are constants, independent of Cartesian coordinates x_i, and f(x_i) is an arbitrary continuous function of x_i. Thus, all the density normalized elastic parameters a_ijkl(x_i) in the FAI medium depend on the coordinates x_i in the same way, but the generality of anisotropy and of inhomogeneity is not restricted. The factorization of a_ijkl(x_i) 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.

Keywords

Anisotropic medium, ray tracing, dynamic ray tracing.

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