Analytical Solutions of Love Numbers for a Hydrostatic Ellipsoidal Incompressible Homogeneous Earth
- 166 Downloads
Tidal forces acting on the Earth cause deformations and mass redistribution inside the planet involving surface motions and variation in the gravity field, which may be observed in geodetic experiments. Because for space geodesy it is now necessary to achieve the mm level in tidal displacements, we take into account the hydrostatic flattening of the Earth in the computation of the elasto-gravitational deformations. Analytical solutions are derived for the semi-diurnal tides on a slightly elliptical homogeneous incompressible elastic model. That simple analytical Earth’s model is not a realistic representation of any real planet, but it is useful to understand the physics of the problem and also to check numerical procedures. We rediscover and discuss the Love’s solutions and obtain new analytical solutions for the tangential displacement. We extend these analytical results to some geodetic responses of the Earth to tidal forces such as the perturbation of the surface gravity field, the tilt and the deviation of the vertical with reference to the Earth’s axis.
Keywordsbody tides elasto-gravitational deformations Love numbers
Unable to display preview. Download preview PDF.
- Dahlen, F. A., Tromp, J. 1998Theoretical Global SeismologyPrinceton University PressNew JerseyGoogle Scholar
- Dehant, V.: 1995, ‘Report of the Working Group on theoretical tidal model’, Proc. 12th Int. Symp. on Earth tides, Science Press, Beijing China, 17–18.Google Scholar
- Heiskanen, W., Moritz, H. 1967Physical GeodesyW. H. Freeman and CompanySan Fransisco, LondonGoogle Scholar
- Melchior, P. 1966The Earth tidesPergamon PressOxford-London-Edinburgh-New York-Paris-FrankfurtGoogle Scholar
- Métivier, L., Greff-Lefftz, M., Diament, M. 2005‘A new approach to compute accurate gravity variations for a realistic Earth model with lateral variations’Geophys. J. Int.62570574Google Scholar