Advertisement

Perturbation theory for the stress tensor in the Moon’s body with tidal effects taken into account

  • V. P. PavlovEmail author
Article
  • 23 Downloads

Abstract

On the basis of the seismic data from the Apollo project, we show that one can use linear elasticity theory to process these data, which yields information on the mechanical parameters of the Moon’s body with an accuracy of 10%. Within this theory, we obtain a theoretical formula for the dependence of pressure on depth in the Moon’s body in the presence of tidal effects. We also derive theoretical dependence of the variations of the free energy density due to tidal effects on latitude and depth. In all these formulas the contribution of shear stresses is taken into account. It turns out that the main contribution is made by the Earth tides. Estimates for the dissipation of the energy of tidal oscillations show that this energy is certainly enough to explain where the energy released in deep focus moonquakes comes from.

Keywords

STEKLOV Institute Strain Tensor Homogeneous Equation Free Energy Density Ecliptic Plane 
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.
    K. E. Bullen and R. A. W. Haddon, “Derivation of an Earth model from free oscillation data,” Proc. Natl. Acad. Sci. USA 58(3), 846–852 (1967).CrossRefGoogle Scholar
  2. 2.
    F. D. Stacey and P. M. Davis, Physics of the Earth (Cambridge Univ. Press, Cambridge, 2008).CrossRefzbMATHGoogle Scholar
  3. 3.
    R. F. Garcia, J. Gagnepain-Beyneix, S. Chevrot, and P. Lognonné, “Very preliminary reference Moon model,” Phys. Earth Planet. Inter. 188, 96–113 (2011).CrossRefGoogle Scholar
  4. 4.
    P. Melchior, The Earth Tides (Pergamon, Oxford, 1966).Google Scholar
  5. 5.
    L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Nauka, Moscow, 1987), Theoretical Physics 7; Engl. transl.: Course of Theoretical Physics, Vol. 7: Theory of Elasticity (Elsevier, Oxford, 2012).zbMATHGoogle Scholar
  6. 6.
    Y. Nakamura, D. Lammlein, G. Latham, M. Ewing, J. Dorman, F. Press, and N. Toksöz, “New seismic data on the state of the deep lunar interior,” Science 181, 49–51 (1973).CrossRefGoogle Scholar
  7. 7.
    D. R. Lammlein, G. V. Latham, J. Dorman, Y. Nakamura, and M. Ewing, “Lunar seismicity, structure, and tectonics,” Rev. Geophys. Space Phys. 12(1), 1–21 (1974).CrossRefGoogle Scholar
  8. 8.
    Y. Nakamura, “New identification of deep moonquakes in the Apollo lunar seismic data,” Phys. Earth Planet. Inter. 139, 197–205 (2003).CrossRefGoogle Scholar
  9. 9.
    Y. Nakamura, “Farside deep moonquakes and the deep interior of the Moon,” J. Geophys. Res. 110(E1), E01001 (2005).Google Scholar
  10. 10.
    I. A. Volkov and Yu. G. Korotkikh, Equations of State of Damaged Viscoelastoplastic Media (Fizmatlit, Moscow, 2008) [in Russian].Google Scholar
  11. 11.
    M. G. Langseth, S. J. Keihm, and K. Peters, “Revised lunar heat-flow values,” in Proc. 7th Lunar Sci. Conf., Houston, 1976 (Pergamon, New York, 1976), Vol. 3, Geochim. Cosmochim. Acta, Suppl. 7, pp. 3143–3171.Google Scholar
  12. 12.
    N. R. Goins, A. M. Dainty, and M. N. Toksöz, “Seismic energy release of the Moon,” J. Geophys. Res. 86(B1), 378–388 (1981).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

Personalised recommendations