The effect of solid tide in geopotential field of an elastic and inelastic earth

Document Type : Research


1 Royal Institute of Technology (KTH), SE 100 44, Stockholm, Sweden and Islamic Azad University, Shahr-e-Rey branch, P.O.Box 18735-334, Tehran, Iran

2 K.N.Toosi University of Technology, P.O.Box 15875-4416,Tehran, Iran


In this paper the influence of solid tide on the Earth gravity field is considered. In this consideration the Earth can be regarded as either an elastic or inelastic body. Each one of these elastic and inelastic bodies has two main tidal components, frequency dependent and frequency independent components. In this article how to compute the effect of these components in the Earth’s gravity field is presented. In this investigation, an attempt is made to find out whether the Earth should be regarded as an elastic or inelastic body in practical applications. Computations show equivalent effects on the gravity field due to the elastic and inelastic Earth model. The effect of the frequency dependent component of solid tide due to the elastic and inelastic Earth is much smaller than the frequency independent components. It depends on time and tidal constituents and it should be considered in precise applications. Comparisons between the solid tides due to the elastic and inelastic Earth model show that the inelastic Earth is contracted at poles about 3 mm and expanded at equator about 2.5 mm more than the elastic case.


Buffet, A., 1985, Short arc orbit improvement of GPS satellite MSc thesis in Geodesy and Geomatics Engineering, University of Calgary, Canada.
Eanes, R. J., Schutz, B., and Tapley, B.,
1983, Earth and ocean tide effects on
 lageos and starlette, in Proceedings
of the ninth international symposium on earth tides, J. T. Kuo (ed), E. Sckweizerbart’sche Verlagabuchhandlung, Stuttgart.
Eshagh, M., 2003, Precise orbit determination of a low Earth orbiting satellite, K. N. Toosi University, Faculty of Geodesy and Geomatic Engineering, Department of Geodesy Engineering M. Sc thesis.
Mathews, P. M., Buffett, B. A., and Shapiro, I. I., 1995, Love numbers for a rotating spheroidal Earth: New definitions and numerical values, Geophys. Res. Lett., 22, 579-582.
McCarthy, D. D., 1996, IERS Technical Note 21 IERS conventions, US Naval Observatory, Central Bureau of IERS-Observatoty de Paris. 61, avenue del’Observatoire, F-75014 PARIS-France.
McCarthy, D. D., and Petit, G., 2003, IERS Technical Note 32 IERS conventions, US Naval Observatory, Central Bureau of IERS-Observatoty de Paris. 61, avenue del’Observatoire, F-75014 PARIS-France.
Santos, M. C., 1994, On real time orbit improvement for GPS satellites. Ph.D thesis, University of New Brunswick of Canada Department of Geodesy and Geomatic Engineering.
Su. H., 2000, Orbit determination of IGSO, GEO and MEO satellites, Ph.D dissertation in Geodesy, University of Bundeswehr, Munich. Germany.
Wahr, J. M., 1981, The Force Nutation of an Elliptical, Rotating, Elastic, and Oceanless Earth, Geophys, J. Roy. Astron. Soc., 64, 705-727.
Wahr, J. M., and Bergen, Z., 1986, The effect of mantle elasticity on nutations, Earth tides, and tidal variations in the rotation rate Geophys. J. Int., 104, 541-553.
Widmer, R., Masters, G., and Gilbert, F., 1991, Spherically symmetric attenuation within the Earth from normal mode data, Geophys, J. Roy. Astron. Soc., 633-668.
Wolf, R., 2000., Satellite orbit and ephemeris determination using inter satellite links Ph.D dissertation, University of Bundeswehr, Munich, Germany.