On the Secular Pole Motion and the Chandler Wobble

Abstract

Summary The Earth's pole motion is characterized by an annual term, the Chandler wobble, and a strong secular motion. The annual is nearly periodic and the Chandler wobble is nearly a damped oscillation, but data are so limited that little about the secular term can be learned by conventional statistical analysis. Instead, we have used a new technique called ' cumulative range analysis ', which is effective in studying long-run dependence. The secular motion was found to follow a nearly Gaussian two-dimensional generalization of ' I/f noise'. The process yielding this kind of noise, for which the power diverges very slowly, can be imagined lying between stationary processes, such as white noise, for which the power is constant, and expanding processes, such as Brownian motion, for which the power diverges rapidly. One can prove that, for ' I/f noises ', uncertainty is left unchanged by averaging. Thus, one should expect the scatter of time averaged pole positions to be independent of the averaging times and nearly the same as the scatter of the monthly positions. This inference was checked empirically and verified. Averaging secular positions does not increase precision. Cumulative range analysis was also applied to the Chandler peak, confirming the accepted damped oscillator model, and yielding for Q an estimate between 30 and 35.