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 tid e. How to deal with the tidal correction in gravimetric observations, espec ially the treatment of the permanent tide, has been discussed for a long ti me, since some practical and physical problems exist anyhow. A resolution a dopted by IAG (1983) was that the permanent tidal attraction of the Moon an d 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. (Po utanen, M., Vermeer, M., Makinen, J., 1996. The permanent tide in GPS posit ioning. 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 t he permanent tide. This research shows that horizontal components of the pe rmanent earth tides, which are not considered in recent studies, are also i mportant in GPS positioning and geoid determination. Since the tide-generat ing potential can be expanded into harmonics and divided into two parts (ge odetic coefficients and the group of harmonic waves), the permanent earth t ides can be easily obtained by multiplying the amplitude of the zero-freque ncy wavelength by the corresponding geoid geodetic coefficient. Formulas fo r both elastic and fluid cases are presented. Numerical results for the ela stic case show that he vertical permanent crust (zero crust), geoid and oce an 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, resp ectively. According to the solution of IAG (1983), the permanent vertical c omponents are kept in GPS positioning and geoid computation. Thus, it is na tural to include the horizontal components correspondingly. (C) 2001 Publis hed by Elsevier Science Ltd. All rights reserved.