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 aijkl(xi) can be described by the relation aijkl(xi)=f2(xi)Aijkl, where Aijkl are constants, independent of coordinates xi, and f2(xi) is a continuous smooth function of xi. The types of anisotropy (Aijkl) and inhomogeneity [f(xi)] 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 f2(xi)] and on the anisotropy perturbations (delta Aijkl), 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 f2(xi) 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.
Anisotropic medium, delay time between qS-waves, perturbation methods, shear wave splitting.
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