Tilts due to the free nutation of the Earth's axis in the results of geodetic observations

Summary

Simple expressions for the deformation of equipotential surfaces and changes of the deflections of the vertical are derived at points of the Earth's surface, which are due to the variations of the rotational component of the gravity potential under free nutation of the Earth's axis of rotation (pole wandering). The results of the solution of this problem given in[1] are discussed. The values of the tilts and the changes of geoid heights for extreme deviations of the poles are considered from the point of view of the effect on measuring tilts and on levelling. An elastically deformable Earth is assumed. It is concluded that reductions with respect to the mean Earth's pole are not realistic at the present degree of accuracy of levelling. The necessity to reduce long-term tilt observations, or the possibility of determining the time variations of the rotational axis from the analysis of these observations is pointed out.