On the period and damping of polar motion

Abstract

The theory of the Chandler wobble is an old and rather complicated branch of mathematical geophysics which includes both the methods of the elastic and hydrodynamic equations solutions, describing the reaction of mantle, liquid core and ocean to the variable centripetal force. This theory has recently attracted increased attention in view of (1) the substantial improvement of geodetic measurements (such as very long base line interferometry, satellite measurements, etc.) requires a corresponding refinement of the theory and (2) the last achievement in modeling the Earth's inner structure gave the possibility to calculate the period and damping of Chandler wobble with much higher accuracy. The comparison of these theoretical results with the results of measurements can isolate mantle anelasticity effects, thus permitting the determination of the Earth's anelastic properties at extremely low frequencies. Obviously, information of such kind is very important for modeling of many geodynamical processes. In this paper the influence of the mantle's anelasticity, the Earth's liquid core and oceanic pole tides on the Chandler wobble is considered. In section 2 different approaches to determine the effects of mantle anelasticity are compared with each other. It is shown that the results obtained by use of complex Love Numbers and by consideration of energy dissipation are in a good agreement; numerical results are presented. The consideration of the liquid core effects (in section 3) is based on the work by Molodensky and Zharkov (1982) an approach which takes into account the torque acting between liquid core and deformable mantle instead of the consideration of momentum equations for the system of mantle plus core. This approach gives the possibility to use hydrostatical approximation and to avoid the essential difficulties which are connected with the dynamical equations in the liquid core. The errors of hydrostatical approximation are estimated and are found to be small. The influence of the oceanic pole tides, both in statical and dynamical approximations, are considered in section 4. The attention is drawn to the fact that the solutions of Laplace's tidal equations at low frequencies significantly depend on terms of the order of the ratio of the frequency σ to the angular velocity of the Earth's rotation ω. For the case σ=0 there is an infinite set of solutions, satisfying the fixed boundary conditions; the solutions become unstable in the limit σ/ω→0 hence even very small errors of numerical integration significantly affect the final results. From our point of view, this circumstance can explain some disagreements, arising in the dynamical theory of pole tides; it is necessary to take it into account in the numerical modeling.