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Physics of the Earth’s Interior, Deformation and Rotation

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Dynamics of Extended Celestial Bodies and Rings

Part of the book series: Lecture Notes in Physics ((LNP,volume 682))

Abstract

This paper presents a theoretical basis for elastic and viscoelastic deformations of the Earth and analyses the rotation of a deformable planet having a fluid core and a solid inner core. Section 2 reviews the concepts that become indispensable when we pass from the model of the Earth as a rigid body to its more realistic model as a deformable planet. In this realistic model, variations in the physical parameters allow us to understand convection within the mantle, stratification into solid and fluid parts, and evolution of the Earth’s density and inertia tensor. Section 3 addresses detailed problems in the theory of deformations, in particular the effect of rheology. Finally Sect. 4 studies how a deformable, stratified Earth actually rotates.

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References

  1. D’Alembert, J., 1749. Recherche sur la précession des equinoxes et sur la nutation de l’axe de la Terre, dans le système newtonien. Paris. Ed. David l’aîné.

    Google Scholar 

  2. Alterman, Z., Jarosch, H. and Pekeris, C.H., 1959. Oscillation of the Earth. Proc. R. Soc. London, A252, 80–95.

    ADS  Google Scholar 

  3. Anderson, D.L., 1982. The Earth’s Core and the phase diagram of iron. Phil. Trans. R. Soc. Lond., A306, 21–35.

    Article  ADS  Google Scholar 

  4. Anderson, D.L., Isaak, D. and Oda, H., 1992. High-Temperature elastic constant data on minerals relevant to Geophysics. Review of Geophysics, 30, 1, 57–90.

    Article  ADS  Google Scholar 

  5. Buffett, B., 1992. Constraints on magnetic energy and mantle conductivity from the forced nutations of the Earth, J. Geophys. Res., 97, B13, 19581–19597.

    Article  ADS  Google Scholar 

  6. Buffett, B., Mathews, P.M., and Herring, T.A., 2002. Modeling of nutation and precession; effects of electromagnetic coupling. J. Geophys. Res., 107, no 4, 15 pp.

    Article  Google Scholar 

  7. Bullen, K.E., 1942. The density variation of the Earth’s central core. Bull. Seismol. Soc. Amer., 32, 19–29.

    Google Scholar 

  8. Bullen, K.E., 1975. The Earth’s density. Chapman and Hall, London.

    Google Scholar 

  9. Cameron A.G.W., 1988. Origin of the solar system. Annu. Rev. Astron. Astrophys., 26, 441–472.

    Article  ADS  Google Scholar 

  10. Chandler, S.C., 1891. On the variation of the latitude. Astronomical Journal, No 248 and 249.

    Google Scholar 

  11. Coirier, J., 2001. Mécanique des milieux continus. Dunod, Paris.

    Google Scholar 

  12. Dahlen, F.A. and Tromp, J., 1998. Theoretical Global Seismology. Princeton University Press.

    Google Scholar 

  13. Darwin, G.H., 1883. Attempted evaluation of the rigidity of the Earth from the tides of long period. Scientific Papers I, 9, 340–346.

    Google Scholar 

  14. Darwin, G.H., 1878. On the influence of geological changes on the Earth’s axis of rotation. Phil. Trans. R. Soc., London, 167, part I, 271–313. See also: Darwin, 1879, Phil. Trans. R. Soc., London, 170, 1–35; Darwin, 1880 Phil. Trans. R. Soc., London, 170, 497–530.

    Google Scholar 

  15. Defraigne, P., Dehant, V. and Hinderer, J., 1995. Correction to ’Stacking gravity tide measurements and nutation observations in order to determine the complex eigenfrequency of the Nearly Diurnal Free Wobble’, J. Geophys. Res.,100, 2041–2042.

    Article  ADS  Google Scholar 

  16. Deparis, V. and Legros, H., 2000. Voyage à l’intérieur de la Terre. CNRS Edition 2000.

    Google Scholar 

  17. Dziewonski, A.M., and Anderson, D.L., 1981. Preliminary Reference Earth Model PREM, Phys. Earth Planet. Int., 25, 297–356.

    Article  ADS  Google Scholar 

  18. Euler, L., 1749. Recherche sur la précession des équinoxes et sur la nutation de l’axe de la Terre. Mémoire de l’Académie Royale des Sciences de Berlin; reedition in “Commentationes astronomicae”, Societatis Scientiarum Naturalum Helveticae, Leo Courvoisier, 1941.

    Google Scholar 

  19. Euler, L., 1758. Du mouvement de rotation des corps solides autour d’un axe variable. Mémoire de l’Académie des Sciences de Berlin (14), 1765.

    Google Scholar 

  20. Farrell, W.E., 1972. Deformation of the Earth by Surface Loads. Reviews of Geophysics and Space Physics, 10, no 3, 761–797.

    Article  MathSciNet  ADS  Google Scholar 

  21. Gegout, P., 1995. De la variabilité de la rotation de la Terre et du champ de gravité, conséquente aux dynamiques de l’Atmosphère et des Océans. Thesis, Strasbourg, France.

    Google Scholar 

  22. Gold, T., 1955. Instability of the Earth’s axis of rotation. Nature, 175, 526–529.

    Article  ADS  Google Scholar 

  23. Greff-Lefftz, M. and Legros, H., 1999. Magnetic field and rotational eigenfrequencies, Phys. Earth Planet. Int., 112, 21–41.

    Article  ADS  Google Scholar 

  24. Greff-Lefftz, M., Legros, H., Dehant, V., 2000. Influence of the inner core viscosity on the rotational eigenmodes of the Earth. Phys. Earth Planet. Int., 122, vol 3–4, 187–203.

    Article  ADS  Google Scholar 

  25. Greff-Lefftz, M., Dehant, V. and Legros, H., 2002. Effects of inner core viscosity on gravity changes and spatial nutations induced by luni-solar tides. Phys. Earth Planet. Int., 129, 31–41.

    Article  ADS  Google Scholar 

  26. Gutenberg, B., 1914. Über Erdbebenwellen VII A, Nach. Ges. Wiss. Gottingen Math. Phys. Kl. 166–218.

    Google Scholar 

  27. Haskell, N.A., 1935. The motion of a viscous fluid under a surface load, Physics, 6, 265.

    Article  MATH  Google Scholar 

  28. Heiskanen, W. and Moritz, H., 1967. Physical Geodesy. W.H. Freeman and Company, San Fransisco-London.

    Google Scholar 

  29. Hess, H.H., 1962. History of ocean basin. In A.E.J. Engel Petrologic studies, Boulder Colorado Geological Society of America.

    Google Scholar 

  30. Hopkins, W., 1839. Researches in Physical Geology. On the phenomena of Precession and Nutation, assuming the fluidity of the Interior of the Earth. Phil. Trans. R. Soc. London, 129, 381–423. and also Phil. Trans. R. Soc. London, 130, 193–208.

    Google Scholar 

  31. Hopkins, W., 1847. Geological theories of elevation of earthquakes. Report of the British Association for the Advancement of Science for 1847.

    Google Scholar 

  32. Hough, S.S., 1895. The oscillations of a rotating ellipsoidal shell containing fluid. Phil. Trans. R. Soc. London, 186, 469–505.

    Article  MATH  ADS  Google Scholar 

  33. Inglis, D.R., 1957. Shifting of the Earth’s axis of rotation. Reviews Modern Physics, 29, 9–19.

    Article  ADS  Google Scholar 

  34. Jameson, T.F., 1865. On the history of the last geological changes in Scotland. Quart. J. Geol. Soc. London, 21, 178.

    Google Scholar 

  35. Jeffreys, H., 1926. The viscosity of the Earth, Monthly Notices R. astr. Soc., 1, 84–112.

    Google Scholar 

  36. Jeffreys, H., 1930. The resonance theory of the origin of the Moon. Monthly Not. R. astr. Soc., 91, 169–173.

    MATH  ADS  Google Scholar 

  37. Jeffreys, H., 1951. The Earth, 3thedition. Cambridge University Press.

    Google Scholar 

  38. Jeffreys, H., and Vicente, R.O., 1957. The theory of nutation and the variation of latitude. Monthly Not. R. astr. Soc., 117, 142–173.

    MATH  MathSciNet  ADS  Google Scholar 

  39. Lambeck, K., 1980. The Earth’s variable rotation. Cambridge University Press, Cambridge.

    Book  Google Scholar 

  40. Lehmann, I., 1936. Publication du Bureau Central Seismologique International. Travaux scientifiques 14, 87–115.

    Google Scholar 

  41. Le Pichon, X., 1968. Sea-floor spreading and continental drift. J. Geophys. Res., 73, 3661–3697.

    Article  ADS  Google Scholar 

  42. Liu, L.G., 1976. The high-pressure phase of Mg Si O3. Earth Planet. Sci. Lett., 31, 200–208.

    Article  Google Scholar 

  43. Love, A.E.H., 1909. The yielding of the Earth to disturbing forces. Proc. R. Soc. London, A82, 73–88.

    ADS  Google Scholar 

  44. Love, A.E.H., 1911. Some Problems of Geodynamics. Cambridge University Press.

    Google Scholar 

  45. Mac Kenzie, D.P. and Parker, R.L., 1967. The North Pacific: an example of Tectonics on a sphere. Nature, 216, 1276–1279.

    Article  ADS  Google Scholar 

  46. Mathews, P.M., Buffett, B.A., Herring, T.A. & Shapiro, I.I., 1991. Forced nutations of the Earth: influence of inner core dynamics: I. Theory, J. Geophys. Res.,96, B5, 8219–8242.

    Article  ADS  Google Scholar 

  47. Mathews, P.M., Herring, T.A., and Buffett, B.A., 2002. Modeling of nutationprecession: New nutation series for nonrigid Earth and Insights into the Earth’s interior. J. Geophys. Res., 107,no4, 30 pp.

    Google Scholar 

  48. Milankovitch, M., 1934. Der Mechanismus des Polverlagerungen und die daraus sich ergebenden Polbahnkurven. Gerlands Beitr. Geophys., 42, 70–97.

    MATH  Google Scholar 

  49. Molodensky, M.S., 1961. The theory of nutation and diurnal Earth tides. Commun. Observ. Roy. Belg., 188, 25–56.

    Google Scholar 

  50. Moritz, H., 1990. The Figure of the Earth. Wichmann Ed.

    Google Scholar 

  51. Munk, W.H. and MacDonald, G.J.F. 1960. The Rotation of the Earth, Cambridge University Press, Cambridge.

    Google Scholar 

  52. Newcomb, S., 1892. On the dynamics of the Earth’s rotation with respect to periodic variations of latitude. Monthly Not. R. astr. Soc., 52, 336–341.

    MATH  ADS  Google Scholar 

  53. Newton, I., 1687. Principes mathématiques de la philosophie naturelle. Translation into French by La Marquise du Chastelet 1756. Reedition A. Blanchard 1966, Paris.

    Google Scholar 

  54. O’Connell, R.J. and Budiansky, B., 1978. Measures of dissipation in visco-elastic media. Geophys. Res. Let., 5, 5–8.

    Article  ADS  Google Scholar 

  55. Patterson, Cl., 1956. Age of Meteorites and the Earth. Geochimica et Cosmochimica Acta, vol 10, 230–237.

    Article  ADS  Google Scholar 

  56. Peltier, W.R., 1989. Mantle convection, Plate Tectonics and Global Dynamics. Gordon and Breach Science publishers.

    Google Scholar 

  57. Peltier, W.R., 1974. Impulse response of a Maxwell Earth. Rev. Geophys. Space Physics, 12, 649–669.

    Article  ADS  Google Scholar 

  58. Poirier, J.P., 1991. Introduction to the Physics of the Earth Interior. Cambridge University Press.

    Google Scholar 

  59. Poincaré, H., 1910. Sur la précession des corps déformables. Bull. astr., 27, 321–356.

    Google Scholar 

  60. Roosbeek, F., 1995. RATGP95: a harmonic development of the tide-generating potential using an analytical method. Geophys. J. Int.,126, 197–204.

    Article  ADS  Google Scholar 

  61. Safronov, V.S., 1969. Evolution of the protoplanetary cloud and formation of the Earth and Planets. Translated by The Israel Program for Scienti.c Translation 1972.

    Google Scholar 

  62. Sasao, T., Okubo, S. and Saito, M., 1980. A simple theory on the dynamical effects of a stratified fluid core upon the nutational motion of the Earth, Proc. IAU Symp. 78, ’Nutation and the Earth’s rotation’, Kiev 165–183, eds Fedorov, E.P., Smith, M.L., & Bender, P.L., Reidel, Dordrecht.

    Google Scholar 

  63. Schiaparelli, I.V., 1889. De la rotation de la Terre sous l’influence des actions géologiques. St Petersbourg. Imprimerie de l’Académie Impériale des Sciences. Vass. Ostr., 9ieme ligne, no 12.

    Google Scholar 

  64. Schubert, G., Turcotte, D.L, and Olson P., 2001. Mantle convection in the Earth and Planets. Cambridge University Press.

    Google Scholar 

  65. Smith, M., 1974. The scalar equations of infinitesimal elastic-gravitational motion for a rotating, slightly elliptical Earth, Geophys. J. Int. astr. Soc., 37, 491–526.

    Article  MATH  ADS  Google Scholar 

  66. Stacey, F.D., 1992. Physics of the Earth (Third Edition). Brookfield Presse, Australia.

    Google Scholar 

  67. Suess, E. La face de la Terre. Translation into French by E. de la Margerie. Paris. Armand Colin 1897–1918.

    Google Scholar 

  68. Takeuchi, H., 1950. On the Earth tides of the compressible Earth of variable Density and Elasticity. Trans. Amer. Geophys. Union, 31, no 5, 651–689.

    Google Scholar 

  69. Thomson, Sir W., 1862. Dynamical Problems regarding Elastic Spheroidal Shells and Spheroids of Incompressible Liquid. Phil. Trans. R. Soc. Lond., vol. 153, 583–608.

    Google Scholar 

  70. Thomson, Sir W. and Tait, P.G., 1879. Treatise on Natural Philosophy. Cambridge University Press.

    Google Scholar 

  71. Wahr, J.M., 1981. Body tides on the elliptical, rotating, elastic and oceanless Earth. Geophys. J. R. astr. Soc., 64, 677–703.

    MATH  ADS  Google Scholar 

  72. Wetherill G.W., 1980. Formation of the terrestrial planets. Annu. Rev. Astron. Astrophys., 18, 77–113.

    Article  ADS  Google Scholar 

  73. Williamson, E.D. and Adams, L.H., 1923. Density distribution in the Earth. J. Wash Acad. Sci., 13, 413–428.

    Google Scholar 

  74. Yuen, D.A. and Peltier, W.R., 1983. Normal modes of the viscoelastic Earth. Geophys. J.R. astr. Soc., 69, 495–526.

    Google Scholar 

  75. Zschau, J., 1978. Tidal friction in the solid Earth. In ‘Tidal Friction and the Earth’s rotation’, Brosche P. and Sunderman, J., Springer-Verlag Berlin.

    Google Scholar 

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Author information

Authors and Affiliations

  1. E.O.S.T., 5 rue René Descartes, 67084 Strasbourg-Cedex, FRANCE

    Hilaire Legros

  2. I.P.G.P., 4 place Jussieu, 75252 Paris-Cedex 05, FRANCE

    Marianne Greff

  3. Trinity Hall, CB2 1TJ, Cambridge, UK

    Marianne Tokieda

Authors
  1. Hilaire Legros
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  2. Marianne Greff
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  3. Marianne Tokieda
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Editors and Affiliations

  1. Observatoire de Paris, Av. de L’Observatoire 61, 75014, Paris, France

    Jean Souchay

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Legros, H., Greff, M., Tokieda, M. (2006). Physics of the Earth’s Interior, Deformation and Rotation. In: Souchay, J. (eds) Dynamics of Extended Celestial Bodies and Rings. Lecture Notes in Physics, vol 682. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32455-0_2

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