Tidal Love Numbers of Degrees 2 and 3

Abstract

In the coming years, the high-precision processing of large arrays of modern observational data from the Global Satellite Navigation System (GNSS) will require knowledge of the theoretical values of the tidal numbers h and l of degrees 2 and 3 with a relative error no worse than 10–4. This will make it possible to predict vertical and horizontal tidal displacements of the earth’s surface at the modern level. The paper presents the values of Love numbers h, k, and l of degrees 2 and 3 calculated for an inelastic ellipsoidal self-gravitating rotating earth without an ocean. Twelve different models are considered that differ from each other by the inclusion or exclusion of individual factors that affect the result. In particular, two different versions of the earth’s structure model are used, corrections for the relative and Coriolis accelerations are considered, and the values of the Love numbers are determined considering their latitude dependence. Lame elastic parameters were recalculated for the periods of semidiurnal and diurnal tidal waves using the logarithmic creep function to account for dissipation. The normalization of the obtained values of the Love numbers corresponds to International Earth Rotation and Reference Systems Service (IERS) Conventions regarding the calculation of tidal displacements of the earth’s surface. The values are compared with the results of widely known works of other authors. Currently, the results are used to develop a new version of the ATLANTIDA3.1 software for predicting earth tides.