## The traveltime perturbations for seismic body waves in factorized
anisotropic inhomogeneous media

**Vlastislav Cerveny** ** & **
**Ivan A. Simoes-Filho**
### Summary

The traveltime perturbation equations for the quasi-compressional and
the two quasi-shear waves propagating in a factorized anisotropic
inhomogeneous (FAI) media are derived. The concept of FAI media
simplifies considerably these equations. In the FAI medium, the density
normalized elastic parameters *a*_{ijkl}(*x*_{i})
can be described by the relation
*a*_{ijkl}(*x*_{i})=*f*^{2}(*x*_{i})*A*_{ijkl},
where *A*_{ijkl} are constants,
independent of coordinates *x*_{i},
and *f*^{2}(*x*_{i}) is a continuous smooth
function of *x*_{i}. The types of anisotropy
(*A*_{ijkl}) and inhomogeneity
[*f*(*x*_{i})] are not restricted.
The traveltime perturbations of individual
seismic body waves (qP, qS1 and qS2) propagating in the FAI medium
depend, of course, both on the structural perturbations
[*delta* *f*^{2}(*x*_{i})] and
on the anisotropy perturbations (*delta* *A*_{ijkl}),
but both these effects are
fully separated. The perturbation equations for the time delay
between the two qS-waves propagating in the FAI medium are simplified
even more. If the unperturbed (background) medium is isotropic,
the perturbation of the time delay does not depend on the structural
perturbations *delta* *f*^{2}(*x*_{i}) at all.
This striking result, valid of course
only in the framework of first-order perturbation theory, will
simplify considerably the interpretation of the time delay between
the two split qS-waves in inhomogeneous anisotropic media. Numerical
examples are presented.

### Keywords

Anisotropic medium, delay time between qS-waves, perturbation
methods, shear wave splitting.

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*Geophys. J. int.*, **107** (1991), 219-229.

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