Abstract
In order to consider the effect of anisotropy on the periods of the oscillations of the Earth, the problem of toroidal oscillations of a transradially isotropic elastic sphere is considered. At each point, the medium is assumed to be transversely isotropic about the radius through the point. The roots of the frequency equation are obtained for different values of the anisotropy parameter α. It is found that, for large order oscillations, the percentage change in the frequency of the toroidal oscillations on account of the anisotropy is nearly equal to ¦α-1¦ × 100.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Backus G E 1967 Converting vector and tensor equations to scalar equations in spherical coordinates;Geophys. J. R. Astron. Soc. 13 71–101
Ben-Menahem A and Singh S J 1981Seismic Waves and Sources (New York: Springer Verlag)
Datta S K and Shah A H 1970 Diffraction of SH waves in a spherically isotropic medium by a rigid or fluid spherical core;Geophys. J. R. Astron. Soc. 21 33–46
Eringen A C and Suhubi E S 1975Elastodynamics (New York: Academic Press) Vol. 2
Helbig K 1966 A graphical method for the construction of rays and travel times in shperically layered media Part 2: Anisotropic case, theoretical consideration;Bull. Seismol. Soc. Am. 56 527–559
Love A E H 1927A treatise on the mathematical theory of elasticity (Cambridge: University Press)
Sato R, Lapwood E R and Singh K 1971 SH waves in a transversely isotropic medium III. Transradially isotropic sphere;Geophys. J. R. Astron. Soc. 22 181–200
Singh S J 1974 Toroidal oscillations of transradially isotropic stratified earth models;Geophys. Res. Bull. 12 157–164
Vlaar N J 1969 Rays and travel times in a spherical anisotropic earth;Bull. Seismol. Soc. Am. 59 1051–1060
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gupta, A., Singh, S.J. Toroidal oscillations of a transradially isotropic elastic sphere. Proc. Indian Acad. Sci. (Earth Planet Sci.) 99, 383–391 (1990). https://doi.org/10.1007/BF02841866
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02841866