Advertisement

Physics of the Earth’s Interior, Deformation and Rotation

  • Hilaire Legros
  • Marianne Greff
  • Marianne Tokieda
Part of the Lecture Notes in Physics book series (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.

Keywords

Inner Core Mantle Convection Inertia Tensor Love Number Partial Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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. 2.
    Alterman, Z., Jarosch, H. and Pekeris, C.H., 1959. Oscillation of the Earth. Proc. R. Soc. London, A252, 80–95. ADSGoogle Scholar
  3. 3.
    Anderson, D.L., 1982. The Earth’s Core and the phase diagram of iron. Phil. Trans. R. Soc. Lond., A306, 21–35. ADSCrossRefGoogle Scholar
  4. 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. ADSCrossRefGoogle Scholar
  5. 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. ADSCrossRefGoogle Scholar
  6. 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. CrossRefGoogle Scholar
  7. 7.
    Bullen, K.E., 1942. The density variation of the Earth’s central core. Bull. Seismol. Soc. Amer., 32, 19–29. Google Scholar
  8. 8.
    Bullen, K.E., 1975. The Earth’s density. Chapman and Hall, London. Google Scholar
  9. 9.
    Cameron A.G.W., 1988. Origin of the solar system. Annu. Rev. Astron. Astrophys., 26, 441–472. CrossRefADSGoogle Scholar
  10. 10.
    Chandler, S.C., 1891. On the variation of the latitude. Astronomical Journal, No 248 and 249. Google Scholar
  11. 11.
    Coirier, J., 2001. Mécanique des milieux continus. Dunod, Paris. Google Scholar
  12. 12.
    Dahlen, F.A. and Tromp, J., 1998. Theoretical Global Seismology. Princeton University Press. Google Scholar
  13. 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. 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. 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. CrossRefADSGoogle Scholar
  16. 16.
    Deparis, V. and Legros, H., 2000. Voyage à l’intérieur de la Terre. CNRS Edition 2000. Google Scholar
  17. 17.
    Dziewonski, A.M., and Anderson, D.L., 1981. Preliminary Reference Earth Model PREM, Phys. Earth Planet. Int., 25, 297–356. CrossRefADSGoogle Scholar
  18. 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. 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. 20.
    Farrell, W.E., 1972. Deformation of the Earth by Surface Loads. Reviews of Geophysics and Space Physics, 10, no 3, 761–797. MathSciNetADSCrossRefGoogle Scholar
  21. 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. 22.
    Gold, T., 1955. Instability of the Earth’s axis of rotation. Nature, 175, 526–529. ADSCrossRefGoogle Scholar
  23. 23.
    Greff-Lefftz, M. and Legros, H., 1999. Magnetic field and rotational eigenfrequencies, Phys. Earth Planet. Int., 112, 21–41. CrossRefADSGoogle Scholar
  24. 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. CrossRefADSGoogle Scholar
  25. 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. CrossRefADSGoogle Scholar
  26. 26.
    Gutenberg, B., 1914. Über Erdbebenwellen VII A, Nach. Ges. Wiss. Gottingen Math. Phys. Kl. 166–218. Google Scholar
  27. 27.
    Haskell, N.A., 1935. The motion of a viscous fluid under a surface load, Physics, 6, 265. zbMATHCrossRefGoogle Scholar
  28. 28.
    Heiskanen, W. and Moritz, H., 1967. Physical Geodesy. W.H. Freeman and Company, San Fransisco-London. Google Scholar
  29. 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. 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. 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. 32.
    Hough, S.S., 1895. The oscillations of a rotating ellipsoidal shell containing fluid. Phil. Trans. R. Soc. London, 186, 469–505. zbMATHADSCrossRefGoogle Scholar
  33. 33.
    Inglis, D.R., 1957. Shifting of the Earth’s axis of rotation. Reviews Modern Physics, 29, 9–19. CrossRefADSGoogle Scholar
  34. 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. 35.
    Jeffreys, H., 1926. The viscosity of the Earth, Monthly Notices R. astr. Soc., 1, 84–112. Google Scholar
  36. 36.
    Jeffreys, H., 1930. The resonance theory of the origin of the Moon. Monthly Not. R. astr. Soc., 91, 169–173. zbMATHADSGoogle Scholar
  37. 37.
    Jeffreys, H., 1951. The Earth, 3thedition. Cambridge University Press. Google Scholar
  38. 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. zbMATHMathSciNetADSGoogle Scholar
  39. 39.
    Lambeck, K., 1980. The Earth’s variable rotation. Cambridge University Press, Cambridge. CrossRefGoogle Scholar
  40. 40.
    Lehmann, I., 1936. Publication du Bureau Central Seismologique International. Travaux scientifiques 14, 87–115. Google Scholar
  41. 41.
    Le Pichon, X., 1968. Sea-floor spreading and continental drift. J. Geophys. Res., 73, 3661–3697. ADSCrossRefGoogle Scholar
  42. 42.
    Liu, L.G., 1976. The high-pressure phase of Mg Si O3. Earth Planet. Sci. Lett., 31, 200–208. CrossRefGoogle Scholar
  43. 43.
    Love, A.E.H., 1909. The yielding of the Earth to disturbing forces. Proc. R. Soc. London, A82, 73–88. ADSGoogle Scholar
  44. 44.
    Love, A.E.H., 1911. Some Problems of Geodynamics. Cambridge University Press. Google Scholar
  45. 45.
    Mac Kenzie, D.P. and Parker, R.L., 1967. The North Pacific: an example of Tectonics on a sphere. Nature, 216, 1276–1279. CrossRefADSGoogle Scholar
  46. 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. ADSCrossRefGoogle Scholar
  47. 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. 48.
    Milankovitch, M., 1934. Der Mechanismus des Polverlagerungen und die daraus sich ergebenden Polbahnkurven. Gerlands Beitr. Geophys., 42, 70–97. zbMATHGoogle Scholar
  49. 49.
    Molodensky, M.S., 1961. The theory of nutation and diurnal Earth tides. Commun. Observ. Roy. Belg., 188, 25–56. Google Scholar
  50. 50.
    Moritz, H., 1990. The Figure of the Earth. Wichmann Ed. Google Scholar
  51. 51.
    Munk, W.H. and MacDonald, G.J.F. 1960. The Rotation of the Earth, Cambridge University Press, Cambridge. Google Scholar
  52. 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. zbMATHADSGoogle Scholar
  53. 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. 54.
    O’Connell, R.J. and Budiansky, B., 1978. Measures of dissipation in visco-elastic media. Geophys. Res. Let., 5, 5–8. ADSCrossRefGoogle Scholar
  55. 55.
    Patterson, Cl., 1956. Age of Meteorites and the Earth. Geochimica et Cosmochimica Acta, vol 10, 230–237. CrossRefADSGoogle Scholar
  56. 56.
    Peltier, W.R., 1989. Mantle convection, Plate Tectonics and Global Dynamics. Gordon and Breach Science publishers. Google Scholar
  57. 57.
    Peltier, W.R., 1974. Impulse response of a Maxwell Earth. Rev. Geophys. Space Physics, 12, 649–669. ADSCrossRefGoogle Scholar
  58. 58.
    Poirier, J.P., 1991. Introduction to the Physics of the Earth Interior. Cambridge University Press. Google Scholar
  59. 59.
    Poincaré, H., 1910. Sur la précession des corps déformables. Bull. astr., 27, 321–356. Google Scholar
  60. 60.
    Roosbeek, F., 1995. RATGP95: a harmonic development of the tide-generating potential using an analytical method. Geophys. J. Int.,126, 197–204. ADSCrossRefGoogle Scholar
  61. 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. 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. 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. 64.
    Schubert, G., Turcotte, D.L, and Olson P., 2001. Mantle convection in the Earth and Planets. Cambridge University Press. Google Scholar
  65. 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. zbMATHADSCrossRefGoogle Scholar
  66. 66.
    Stacey, F.D., 1992. Physics of the Earth (Third Edition). Brookfield Presse, Australia. Google Scholar
  67. 67.
    Suess, E. La face de la Terre. Translation into French by E. de la Margerie. Paris. Armand Colin 1897–1918. Google Scholar
  68. 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. 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. 70.
    Thomson, Sir W. and Tait, P.G., 1879. Treatise on Natural Philosophy. Cambridge University Press. Google Scholar
  71. 71.
    Wahr, J.M., 1981. Body tides on the elliptical, rotating, elastic and oceanless Earth. Geophys. J. R. astr. Soc., 64, 677–703. zbMATHADSGoogle Scholar
  72. 72.
    Wetherill G.W., 1980. Formation of the terrestrial planets. Annu. Rev. Astron. Astrophys., 18, 77–113. ADSCrossRefGoogle Scholar
  73. 73.
    Williamson, E.D. and Adams, L.H., 1923. Density distribution in the Earth. J. Wash Acad. Sci., 13, 413–428. Google Scholar
  74. 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. 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

Copyright information

© Springer 2006

Authors and Affiliations

  • Hilaire Legros
    • 1
  • Marianne Greff
    • 2
  • Marianne Tokieda
    • 3
  1. 1.E.O.S.T.FRANCE
  2. 2.I.P.G.P.FRANCE
  3. 3.Trinity HallCambridgeUK

Personalised recommendations