Vibration eigenfrequencies of an elastic sphere with large radius
Article Sidebar
Main Article Content
Abstract
An estimation is given for the free vibration eigenfrequencies (normal modes) of a homogeneous solid sphere with a large radius, with application to Earth's free vibrations. The free vibration eigenfrequencies of a fluid sphere are also derived as a particular case. Various corrections arising from static and dynamic gravitation, rotation, and inhomegeneities are estimated, and a tentative notion of an earthquake temperature is introduced.
Downloads
Article Details
Copyright (c) 2024 Apostol BF.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Licensing and protecting the author rights is the central aim and core of the publishing business. Peertechz dedicates itself in making it easier for people to share and build upon the work of others while maintaining consistency with the rules of copyright. Peertechz licensing terms are formulated to facilitate reuse of the manuscripts published in journals to take maximum advantage of Open Access publication and for the purpose of disseminating knowledge.
We support 'libre' open access, which defines Open Access in true terms as free of charge online access along with usage rights. The usage rights are granted through the use of specific Creative Commons license.
Peertechz accomplice with- [CC BY 4.0]
Explanation
'CC' stands for Creative Commons license. 'BY' symbolizes that users have provided attribution to the creator that the published manuscripts can be used or shared. This license allows for redistribution, commercial and non-commercial, as long as it is passed along unchanged and in whole, with credit to the author.
Please take in notification that Creative Commons user licenses are non-revocable. We recommend authors to check if their funding body requires a specific license.
With this license, the authors are allowed that after publishing with Peertechz, they can share their research by posting a free draft copy of their article to any repository or website.
'CC BY' license observance:
|
License Name |
Permission to read and download |
Permission to display in a repository |
Permission to translate |
Commercial uses of manuscript |
|
CC BY 4.0 |
Yes |
Yes |
Yes |
Yes |
The authors please note that Creative Commons license is focused on making creative works available for discovery and reuse. Creative Commons licenses provide an alternative to standard copyrights, allowing authors to specify ways that their works can be used without having to grant permission for each individual request. Others who want to reserve all of their rights under copyright law should not use CC licenses.
Aki K, Richards PG. Quantitative Seismology. University Science Books, Sausalito, CA. 2009.
Ben-Menahem A, Singh JD. Seismic Waves and Sources. Springer, New York. 1981.
Lamb H. On the vibrations of an elastic sphere. Proc. London Math. Soc. 1882; 13:189-212.
Lamb H. On the oscillations of a viscous spheroid. Proc. London Math. Soc. 1881; 13:51-66.
Hansen WW. A new type of expansion in radiation problems. Phys. Rev. 1935; 47:139-143.
Bromwich TJI'A. On the influence of gravity on elastic waves, and, in particular, on the vibrations of an elastic globe. Proc. London Math. Soc. 1898; 30:98-120.
Landau L, Lifshitz E. Course of Theoretical Physics, Theory of Elasticity, Elsevier, Oxford. 1986; 7.
Apostol BF. Elastic waves inside and on the surface of an elastic half-space. Q. J. Mech. Appl. Math. 2017; 70:281-308.
Apostol BF. Elastic displacement in a half-space under the action of a tensor force. A general solution for the half-space with point forces. J. Elast. 2017; 126:231-244.
Barrera RG, Estevez GA, Giraldo J. Vector spherical harmonics and their applications to magnetostatics. Eur. J. Phys. 1985; 6:287-294.
Abramowitz M, Stegun IA. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. National Bureau of Standards, USA Government Printing Office, Washington. 1964.
Mendiguren J. Identification of free oscillation spectral peaks for 1970 July 31 Colombian deep shock using the excitation criterion. Geophys. J. Roy. Astron. Soc. 1973; 33:281-321.
Mendiguren J. High-resolution spectroscopy of the Earth's free oscillations, knowing the earthquake source mechanism. Science. 1973; 179:179-180.
Gilbert F, Dziewonski AM. An application of the normal mode theory to the retrieval of the structural parameters and source mechanisms from seismic spectra. Phil. Trans. Roy. Soc. (London). 1975; A278:187-269.
Haskell NA. The dispersion of surface waves in multilayered media, Bul. Seism. Soc. Am. 1953; 43:17-34.
Ewing M, Jardetzky W, Press F. Elastic Waves in Layered Media. McGraw-Hill, NY. 1957.
Benioff H, Gutenberg B, Richter CF. Progr. Report. Trans. Am. Geophys. Union. 1954; 35:979-987.
Benioff H, Press F, Smith SW. Excitation of the free oscillations of the Earth by earthquakes. J. Geophys. Res. 1961; 66:605-620.
Ness NF, Harrison JC, Slichter LB. Observations of the free oscillations of the Earth. J. Geophys. Res. 1961; 66:621-629.
Alsop LE, Sutton GH, Ewing M. Free oscillations of the Earth observed on strain and pendulum seismographs. J. Geophys. Res. 1961; 66:631-641.
Kanamori H. The energy release in great earthquakes. J. Geophys. Res. 1977; 82:2981-2987.
Block B, Dratler J, Moore RD. Earth and normal modes from a magnitude earthquake. Nature. 1970; 226:343-344.
Lehmann I. Publications du Bureau Central Seismologique International, Serie A, Travaux Scientifiques. 1936; 14:87-115.
Dziewonski AM, Gilbert F. Solidity of the inner core of the Earth inferred from normal mode observations. Nature. 1971; 234:465-466.
Pekeris CL, Accad Y. Dynamics of the liquid core of the Earth. Phil. Trans. Roy. Soc. London.1972; A273:237-260.
Dahlen FA, Smith ML. The influence of rotation on the free oscillations of the Earth. Phil. Tras. Roy. Soc. London. 1975; A279:583-629.