TIDAL LOVE NUMBERS OF DEGREES 2 and 3

E.A. Spiridonov

Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russia

Abstract. For high-precision processing of large arrays of modern observations of the Global Satellite Navigation System (GNSS), in the coming years it will be necessary to know the theoretical values of tidal numbers h and l of degrees 2 and 3 with a relative error not worse than 10–4. This will allow to predict the vertical and horizontal tidal displacements of the Earth's surface at the modern level. In this paper, the values ​​of the Love, h, k and l numbers of degrees 2 and 3 calculated for an inelastic ellipsoidal self-gravitating rotating Earth without the ocean are presented. 12 different models that differ from each other by including or switching off certain influencing factors are considered. In particular, three different versions of the Earth's structure models are applied. Corrections for relative and Coriolis accelerations are taken into account. The values ​​of the Love numbers are determined with considering their latitude dependence. To take into account the dissipation, the elastic parameters of Lame were recalculated for the periods of semidiurnal and diurnal tidal waves using the logarithmic creep function. The normalization of the obtained values of Love numbers corresponds to Conventions of the International Earth Rotation Service (IERS) regarding the calculation of tidal displacements of the earth's surface. The obtained values are compared with the results of widely known works of other authors. The results will be applied to the development of a new version of the program for tidal prediction ATLANTIDA3.1.

Keywords: Love numbers, tidal displacements of the Earth's surface, GNSS observations, Earth tides prediction, the program for tidal prediction ATLANTIDA3.1.

About the author

SPIRIDONOV Evgeny A. – Ph. D. (phys. and math.), leading researcher, Schmidt Institute of

Physics of the Earth, Russian Academy of Sciences. Moscow, Russia. Tel.: +7 (915) 141-78-76.

E-mail: sp287@mail.ru