## Ray tracing in factorized anisotropic inhomogeneous media

**Vlastislav Cerveny**
### 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})=*f*^{2}(*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.

### Whole paper

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*Geophys. J. int.*, **99** (1989), 91-100.

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