Search
• Papers

## Love Numbers for the Inelastic Rotating Earth

Transactions of IAA RAS, issue 45, 97–104 (2018)

Keywords: tidal Love numbers, earth tides, displacements of the earth's surface, tidal prediction.

### Abstract

High-precision processing of modern GNSS observations makes it necessary to know theoretical values of the tidal numbers h and l with a better than $10^{–4}$ relative error. This allows us to predict vertical and horizontal displacements of the earth's surface with the contemporary accuracy. The values of Love numbers are obtained in this paper for 12 different models. A generalization of the Mikhail Molodensky’s problem to the case of a rotating inelastic asymmetric earth is made for this purpose. The system of equations of the sixth order includes corrections for relative and Coriolis accelerations [1, 2]. The calculated second-order Love numbers are determined taking into account their latitudinal dependence. This normalization of the obtained values of Love numbers corresponds to the IERS Conventions [3]. Their comparison with the results of widely known works of other authors [4, 5] is made. The results are meant to be used soon in the tidal prediction program ATLANTIDA 3.1_2017 [1, 6].

### Citation

Text
BibTeX
RIS
E. A. Spiridonov, O. Yu. Vinogradova. Love Numbers for the Inelastic Rotating Earth // Transactions of IAA RAS. — 2018. — Issue 45. — P. 97–104. @article{spiridonov2018, abstract = {High-precision processing of modern GNSS observations makes it necessary to know theoretical values of the tidal numbers h and l with a better than $10^{–4}$ relative error. This allows us to predict vertical and horizontal displacements of the earth's surface with the contemporary accuracy. The values of Love numbers are obtained in this paper for 12 different models. A generalization of the Mikhail Molodensky’s problem to the case of a rotating inelastic asymmetric earth is made for this purpose. The system of equations of the sixth order includes corrections for relative and Coriolis accelerations [1, 2]. The calculated second-order Love numbers are determined taking into account their latitudinal dependence. This normalization of the obtained values of Love numbers corresponds to the IERS Conventions [3]. Their comparison with the results of widely known works of other authors [4, 5] is made. The results are meant to be used soon in the tidal prediction program ATLANTIDA 3.1_2017 [1, 6].}, author = {E.~A. Spiridonov and O.~Yu. Vinogradova}, doi = {10.32876/ApplAstron.45.97-104}, issue = {45}, journal = {Transactions of IAA RAS}, keyword = {tidal Love numbers, earth tides, displacements of the earth's surface, tidal prediction}, pages = {97--104}, title = {Love Numbers for the Inelastic Rotating Earth}, url = {http://iaaras.ru/en/library/paper/1824/}, year = {2018} } TY - JOUR TI - Love Numbers for the Inelastic Rotating Earth AU - Spiridonov, E. A. AU - Vinogradova, O. Yu. PY - 2018 T2 - Transactions of IAA RAS IS - 45 SP - 97 AB - High-precision processing of modern GNSS observations makes it necessary to know theoretical values of the tidal numbers h and l with a better than $10^{–4}$ relative error. This allows us to predict vertical and horizontal displacements of the earth's surface with the contemporary accuracy. The values of Love numbers are obtained in this paper for 12 different models. A generalization of the Mikhail Molodensky’s problem to the case of a rotating inelastic asymmetric earth is made for this purpose. The system of equations of the sixth order includes corrections for relative and Coriolis accelerations [1, 2]. The calculated second-order Love numbers are determined taking into account their latitudinal dependence. This normalization of the obtained values of Love numbers corresponds to the IERS Conventions [3]. Their comparison with the results of widely known works of other authors [4, 5] is made. The results are meant to be used soon in the tidal prediction program ATLANTIDA 3.1_2017 [1, 6]. DO - 10.32876/ApplAstron.45.97-104 UR - http://iaaras.ru/en/library/paper/1824/ ER -