Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-12T18:38:47.332Z Has data issue: false hasContentIssue false
  • English
  • Français

Observational and Theoretical Modeling of Nutation

Published online by Cambridge University Press:  14 August 2015

P.M. Mathews  and
T.A. Herring
P.M. Mathews
Affiliation:
Department of Physics, University of Madras, India
T.A. Herring
Affiliation:
Department of Earth, Atmospheric and Planetary Sciences, MIT, USA

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The IERS nutation series was developed as a nutation series which would match observations and could be used with geodetic systems which have sensitivity to nutations but are not able to determine accurately corrections to the IAU-1980 nutation series. After experimentation with different methods for parameterizing the nutation estimation problem, the best fit to the VLBI observed nutation angle data was found by estimating selected coefficients in the Mathews et al. (1991a) nutation response function (see equation (1) below), along with other parameters to be discussed below. The estimation of the response function coefficients was also found to account for mantle anelasticity and the loading part of the ocean tide correction and therefore no corrections were applied for these effects. Their contributions should be absorbed into the estimated response coefficients. These initial analyses also showed: setting the inner-core response to zero yielded better fits to the nutation angle data than the Mathews et al. (1991b) theoretical response and resonance frequency; the amplitude of the RFCN free mode appeared to be time dependent; and the prograde annual nutation was significantly affected by the SI thermal tide which is not proportional to the S1 gravitational potential.

The data set used to estimate the IERS conventions series was the GSFC nutation angle data set with 2040 pairs of adjustments to the IAU 1980 nutations in obliquity and longitude spanning the interval between 1979 and 1995. Here we also compare the IERS conventions series with a US Naval Observatory analysis of VLBI data between 1979 and August 1997. This data set consists of 2152 pairs of nutation angle estimates and extends by 1.8 years the interval covered by the GSFC data set. It also contains less pre-1984 data than the GSFC data set which accounts for the smaller increase in total number of observations than would be expected for the additional time interval covered.

Type
II. Joint Discussions
Information
Highlights of Astronomy , Volume 11 , Issue 1: Highlights of Astronomy. As presented at the XXIIIrd General Assembly of the IAU (Part A), 1997 , 1998 , pp. 177 - 181
Copyright
Copyright © Kluwer 1998

References

Bretagnon, P., Rocher, P. and Simon, J.-L. (1997) Theory of rotation of the rigid Earth. Astron. Astrophys., 319, pp. 305–317.Google Scholar
Buffett, B.A. (1992) Constraints on magnetic energy and mantle conductivity from the forced nutations of the Earth. J. Geophys. Res., 97, pp. 19, 581-19, 597.Google Scholar
Buffett, B.A., Mathews, P.M., Herring, T.A. and Shapiro, I.I. (1993) Forced nutations of the Earth: Contributions from the effects of ellipticity and rotation on the elastic deformations. J. Geophys. Res., 98, pp. 21, 659-21, 676.Google Scholar
Defraigne, P. (1997) Geophysical model of the dynamical flattening of the Earth in agreement with the precession constant. Geophys. J. Int., 130, pp. 47–56.Google Scholar
Dehant, V. and Defraigne, P. (1997) New transfer functions for nutations of a non-rigid Earth. J. Geophys. Res., accepted.Google Scholar
Fukushima, T. (1991) Effects of geodesic precessions annual effect. Astron. Astrophys., 244, pp. L11.Google Scholar
Gwinn, C.R., Herring, T.A. and Shapiro, I.I. (1986) Geodesy by radio interferometry: Studies of the forced nutations of the Earth, 2. Interpretation. J. Geophys. Res., 91, pp. 4755–4765.Google Scholar
Herring, T.A., Buffett, B.A., Mathews, P.M. and Shapiro, L.I. (1991) Forced nutations of the Earth: Influence of inner core dynamics, III. Data analysis. J. Geophys. Res., 96, pp. 8259–8273.Google Scholar
Herring, T.A., Gwinn, C.R. and Shapiro, I.I. (1986) Geodesy by radio interferometry: Studies of forced nutations of the Earth, 1. Data analysis, J. Geophys. Res., 91, pp. 4745–4754.Google Scholar
Mathews, P.M., Buffett, B.A., Herring, T.A. and Shapir, I.I. (1991a) Forced nutations of the Earth: Influence of inner core dynamics, I. Theory. J. Geophys. Res., 96, pp. 8219–8242.Google Scholar
Mathews, P.M., Buffett, B.A., Herring, T.A. and Shapiro, I.I. (1991b) Forced nutations of the Earth: Influence of inner core dynamics, II. Numerical results and comparisons. J. Geophys. Res., 96, pp. 8243–8257.Google Scholar
Roosbeek, F. and Dehant, V. (1997) RDAN97: An analytical development of the rigid Earth nutation series using the torque approach. Celest. Mech., submitted.Google Scholar
Schastok, J. (1997) A new nutation series for a more realistic model Earth. Geophys. J. Int., 130, pp. 137–150.Google Scholar
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touzé, M., Francou, G. and Laskar, J. (1994) Numerical Ex¬pressions for Precession Formulae and Mean Elements for the Moon and Planets. Astron. Astrophys., 282, pp. 663–683.Google Scholar
Souchay, J. and Kinoshita, H. (1996) Corrections and new developments in rigid-Earth nutation I. theory Lunisolar influence including indirect planetary effects. Astron. Astrophys., 312, pp. 1017–1030.Google Scholar
Souchay, J. and Kinoshita, H. (1997) Corrections and new developments in rigid-Earth nutation theory, II. Influence of second-order geopotential and direct planetary effect. Astron. Astrophys., 318, pp. 639–652.Google Scholar
Wahr, J.M. (1981) The forced nutations of an elliptical, rotating, elastic, and oceanless Earth. Geophys. J. R. Astron. Soc., 64, pp. 705–727.Google Scholar
Wahr, J.M. and Bergen, Z. (1986) The effects of mantle anelasticity on nutations, Earth tides and tidal variations in rotation rate, Geophys. J. R. Astron. Soc., 87, pp. 633–668.Google Scholar
Williams, J.G. (1994) Contributions to the Earth’s obliquity rate, precession, and nutation. Astron. J., 108, pp. 711–724.Google Scholar