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

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)=f²(x_i)A_ijkl, where A_ijkl are constants, independent of coordinates x_i, and f²(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 f²(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 f²(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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