Open AccessThe traveltime perturbations for seismic body waves in factorized anisotropic inhomogeneous media
Author(s) -
Červený Vlastislav,
SimõesFilho Ivan A.
Publication year - 1991
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1991.tb00822.x
Subject(s) - anisotropy , isotropy , perturbation (astronomy) , physics , shear waves , perturbation theory (quantum mechanics) , mathematical analysis , wave propagation , seismic wave , classical mechanics , shear (geology) , computational physics , geophysics , optics , mathematics , geology , quantum mechanics , petrology
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 ( q P , qS 1 and qS 2) propagating in the FAI medium depend, of course, both on the structural pertubations [δ f 2 ( x i )] and on the anisotropy perturbations (δ 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 (δ 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.