Permanent components of the crust, geoid and ocean depth tides

• The tidal deformation caused by the luni-solar potential includes not only a periodic part, but also a time-independent part, called the permanent tide. How to deal with the tidal correction in gravimetric observations, especially the treatment of the permanent tide, has been discussed for a long time, since some practical and physical problems exist anyhow. A resolution adopted by IAG (1983) was that the permanent tidal attraction of the Moon and the Sun should be eliminated, but the permanent tidal deformation of the Earth be maintained. This is called zero gravity, and the geoid associated with it is the zero geoid. As to the crust deformation, Poutanen et al. (Poutanen, M., Vermeer, M., Makinen, J., 1996. The permanent tide in GPS positioning. Journal of Geodesy 70, 499-504.) suggested that co-ordinates should be reduced to the zero crust, i.e. the crust that includes the effect of the permanent tide. This research shows that horizontal components of the permanent earth tides, which are not considered in recent studies, are also important in GPS positioning and geoid determination. Since the tide-generating potential can be expanded into harmonics and divided into two parts (geodetic coefficients and the group of harmonic waves), the permanent earth tides can be easily obtained by multiplying the amplitude of the zero-frequency wavelength by the corresponding geoid geodetic coefficient. Formulas for both elastic and fluid cases are presented. Numerical results for the elastic case show that he vertical permanent crust (zero crust), geoid and ocean depth tides reach -12.0, -5.8 and 6.1 cm at the poles, and 5.9, 2.9 and -3.0 cm at the equator, respectively. The horizontal permanent crust, geoid and ocean depth tide components reach as much as 2.5, 8.7 and 6.3 cm, respectively. According to the solution of IAG (1983), the permanent vertical components are kept in GPS positioning and geoid computation. Thus, it is natural to include the horizontal components correspondingly.

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