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Models of density and mechanical Q-factor distributions according to new data on the nutations and free oscillations of the Earth: 2. Comparison with astrometric data

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Abstract

In the first part of the paper [Molodenskii, 2011], we considered the problem of ambiguity in the solution of the inverse problem of retrieval of density distribution in the Earth’s core and mantle and determination of the Q factors in the mantle from the entire set of modern data on seismic velocities (V p and V S ), the frequencies f i and quality factors Q i of free oscillations of the Earth, and the amplitudes and phases of its forced nutations. We have constructed the model distributions of these parameters, in which the root-meansquared (rms) deviations of all observed values from the predicted ones are much smaller than in the PREM model. Below, we compare the observed amplitudes of the forced nutation with the values predicted by our model. In order to understand how rigid are the constraints imposed by the amplitudes of forced nutation, we not only calculate the deviations of the observed amplitudes of nutation from the predictions by our model but also estimate the changes in these deviations caused by small variations in several parameters of the model. To the parameters to be varied we refer those which have no or barely any effect on the periods and damping constants of free oscillations but have a pronounced effect on the amplitudes of forced nutation. These parameters include (1) the rheological properties of the mantle in the interval of periods from an hour to a day; (2) the dynamical flattening of the liquid core; (3) the dynamic flattening of the solid inner core; (4) the viscosity of the liquid core; and (5) the moment of inertia of the solid inner core. In addition, we estimate the effects of variations in the moment of inertia of the liquid core to be small (±0.2%) and not to affect, within the observation error, the periods of free oscillations. We show that the uncertainty in the model depth distributions of density considerably decreases when the new data on the amplitudes and phases of the forced nutation of the Earth are taken into account. With these data, it is possible to estimate the creep function for the lower mantle in a wide range of periods from a second to a day.

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References

  • Aldridge, K.D., Axisymmetric Inertial Oscillations of a Fluid in a Rotating Spherical Shell, Mathematica, 1972, vol. 19, pp. 163–168.

    Google Scholar 

  • Dehant, V., Core Undertones in an Elliptical Uniformly Rotating Earth, in Structure and Dynamics of the Earth’s Deep Interior (Proc. Symp. U2, 19th General Assembly of the IUGG. Vancouver, Canada, 1987), Smylie D.E. and Hide, R., Eds., Washington, DC: AGU, 1987, Geophysical Monograph 46, vol. 1, pp. 29–34.

    Google Scholar 

  • Groten, E. and Molodensky, S.M., Anelastic Properties of the Mantle and Love Numbers Consistent with Modern VLBI Data, J. Geodesy, 1996, vol. 270, no. 1, pp. 603–621.

    Google Scholar 

  • Gwinn, C.R., Herring, T.A., and Shapiro, I.I., Geodesy by Radio Interferometry: Studies of the Forced Nutation of the Earth. 2.Interpretation, J. Geophys. Res., 1986, vol. 91, no. B5, pp. 4755–4765.

    Article  Google Scholar 

  • Herring, T.A., Gwinn, C.R., and Shapiro, I.I., Geodesy by Radio Interferometry: Studies of the Forced Nutation of the Earth. 1. Data Analysis, J. Geophys. Res., 1986, vol. 91, no. B5, pp. 4745–4754.

    Article  Google Scholar 

  • IERS Annual Report 2010, Paris: Observatoire de Paris, 2010.

  • Jeffreys, H. and Vicente, R., The Theory of Diurnal Earth Tides and Nutation. II. Roche’s Model of the Liquid Core, Mon. Not. R. Astron. Soc., 1957, vol. 109, pp. 670–687.

    Google Scholar 

  • Jeffreys, H., The Earth: Its Origin, History and Physical Constitution, Cambridge, UK: Cambridge University Press, 1976, 6-th rev. edit.

    Google Scholar 

  • Jeffreys, H., On Some Difficulties in the Theory of Nutation, Geoph. J. Roy. Astr. Soc, 1978, vol. 54, pp. 711–712.

    Google Scholar 

  • Kinoshita, H., Theory of the Rotation of the Rigid Earth, Celest. Mech., 1977, vol. 15, pp. 277–326.

    Article  Google Scholar 

  • Lamb, H., Hydrodynamics, Cambridge: Cambridge University Press, 1932.

    Google Scholar 

  • Masters, T.G. and Shearer, P.M., Seismic Models of the Earth: Elastic and Anelastic, in Global Earth Physics. A Handbook of Physical Constants, Ahrens, T.J., Ed., Washington, DC: AGU, 1995, pp. 88–103.

    Google Scholar 

  • Mathews, P.M., Buffett, B.A., Herring, T.A., and Shapiro, I.I., Forced Nutations of the Earth: Influence of Inner Core Dynamics: II. Numerical Results and Comparisons, J. Geophys. Res., 1991, vol. 96, pp. 8243–8257.

    Article  Google Scholar 

  • Melchior, P., The Tides of the Planet Earth, New York: Pergamon, 1978.

    Google Scholar 

  • Melchior, P., The Physics of the Earth’s Core, Oxord, NY: Pergamon Press, 1986.

    Google Scholar 

  • Mikhailov, A.A., Zemlya i ee vrashenie (The Earth and Its Rotation), Moscow: Nauka, Bibliotechka Kvant, 1984.

    Google Scholar 

  • Molodensky, M.S., Theory of Nutation and Diurnal Tides of the Earth, in Zemnye prilivy i nutatsiya Zemli (Earth’s Tides and Nutations), Moscow: Akad. Nauk SSSR, 1961, pp. 3–25.

    Google Scholar 

  • Molodensky, S.M., Estimation of the Elastic Earth’s Tides Deviation from Static, Izv. Akad. Nauk SSSR, Fiz. Zemli, 1978, no. 12, pp. 3–14.

  • Molodensky, S.M., Effects of Oceans and Viscous Shells on the Earth’s Nutation, Izv. Akad. Nauk SSSR, Fiz. Zemli 1981, no. 6, pp. 3–18.

  • Molodensky, S.M. and Sasao, T., On One New Approach to the Theory of the Earth’s Nutation, Fiz. Zemli, 1995, no. 12, pp. 24–38.

  • Molodensky, S.M. and Groten, E., On Atmospheric Excitation of Out-Of-Phase Nutational Components, Astronomy and Astrophysics, 1997, vol. 327, pp. 800–812.

    Google Scholar 

  • Molodensky, S.M. and Groten, E., On the Dynamical Effects of An Inhomogeneous Liquid Core in the Theory of Nutation, J. of Geodesy, 1998, vol. 72, pp. 385–403.

    Article  Google Scholar 

  • Molodensky, S.M., Some Physical Aspects of the Earth Rotation, Acta Geod. Geophys. Hungarica, 1999, vol. 34, no. 4. pp. 397–420.

    Google Scholar 

  • Molodensky, S.M., On the Earth’s Forced Nutation, Fiz. Zemli, 2000, no. 9, pp. 3–14 [Izv. Phys. Earth (Engl. Transl.), 2000, vol. 36, no. 9, pp. 763–776].

  • Molodensky, S.M. and Groten, E., On the Upper Bound of the Liquid Core Viscosity, Studia Geophys. Geod, 2001, vol. 45, pp. 12–36.

    Article  Google Scholar 

  • Molodensky, S.M., Influence of the Electromagnetic Core-Mantle Coupling on the Earth’s Nutation: 1. Main Relations, Fiz. Zemli, 2004, no. 8, pp. 3–20 [Izv. Phys. Earth (Engl. Transl.), 2004, vol. 40, no. 8, pp. 613–622].

  • Molodensky, S.M. and Molodenskaya, M.S., On Mechanical Q Parameters of the Lower Mantle Inferred from Data on the Earth’s Free Oscillations and Nutation, Fiz. Zemli, 2009, no. 9, pp. 16–24 [Izv. Phys. Earth (Engl. Transl.), 2009, vol. 45, no. 9, pp. 744–752].

  • Molodensky, S.M., Correctives to the Scheme of the Earth’s Structure Inferred from New Data on Nutation, Tides, and Free Oscillations, Fiz. Zemli, 2010, no. 7, pp. 3–28 [Izv. Phys. Earth (Engl. Transl.), 2010, vol. 46, no. 7, pp. 555–579].

  • Molodensky, S.M., Models of Density and Mechanical Q-Factor Distributions according to New Data on the Nutations and Free Oscillations of the Earth: 1. Ambiguity in the Inverse Problem, Fiz. Zemli, 2011, no. 7, pp. 3–15 [Izv. Phys. Earth (Engl. Transl.), 2011, vol. 47, no. 4, pp. 263–275].

  • Pertsev, B.P., On Secular Deceleration of the Earth’s Rotation, Fiz. Zemli, 2000, no. 3, pp. 35–39 [Izv. Phys. Earth (Engl. Transl.), 2000, vol. 36, no. 3, pp. 218–222].

  • Sasao, T. S., Okubo, S., and Saito, M.A., Simple Theory of Dynamical Effects of Stratified Fluid Core upon Nutational Motion of the Earth, Proc. IAU Symp. 78 on Nutation and the Earth’s Rotation (Kiev, 1977), Fedorov, E., Smith, M., and Bender, P., Eds., Boston: D. Reidel Pub., pp. 165–183.

    Google Scholar 

  • Wahr, J., The Forced Nutations of an Elliptical, Rotating, Elastic and Oceanless Earth, Geophys. J. R. Astr. Soc., 1981, vol. 64, pp. 705–727.

    Google Scholar 

  • Zharkov, V.N., Molodensky, S.M., Brzezinski, A., Groten, E., and Varga, P., The Earth and its Rotation. Low Frequency Geodynamics, Heidelberg: Wichmann, 1999.

    Google Scholar 

  • Zhu, S.Y. and Groten, E., Various Aspects of Numerical Determination of Nutation Constants: I. Improvement of Rigid Earth Nutation, Astr. J., 1998, vol. 98

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  1. Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, ul. Bol’shaya Gruzinskaya 10, Moscow, 123995, Russia

    S. M. Molodensky

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Original Russian Text © S.M. Molodensky, 2011, published in Fizika Zemli, 2011, No. 7, pp. 3–18.

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Molodensky, S.M. Models of density and mechanical Q-factor distributions according to new data on the nutations and free oscillations of the Earth: 2. Comparison with astrometric data. Izv., Phys. Solid Earth 47, 559–574 (2011). https://doi.org/10.1134/S1069351311070056

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