A STOCHASTIC MODEL FOR POLAR MOTION WITH APPLICATION TO SMOOTHING, PREDICTION, AND COMBININGy

We describe here a simple stochastic model for polar motion, which is a generalization of the Jeereys (1940) formulation for bivariate continuous stochastic processes. This model, further referred to as Jeereys model, is derived from the polar motion dynam-ical equation under assumption that the excitation is an isotropic white noise process. The Jeereys model is shown to be superior with respect to the traditionally applied sinusoidal model, both from theoretical point of view and as checked by the goodness-of-t criterion. This model, represented by its covariance function, served us as a basis for elaborating two algorithms for processing the related observations, namely the least squares collocation and the Kalman lter. We consider one class of possible applications, including smoothing, prediction, and combining of the polar motion series. 1. INTRODUCTION Stochastic modeling of time series has recently gained wide acceptance in various elds of science, including polar motion investigations. It was not just a sophisticated computational technique for data processing, but was indicated by the physics of natural phenomena. In the case of polar motion, earlier investigators had at once faced the problem that common deterministic models failed to account for the behaviour of the series of latitude observations, unless being highly complicated. As early as by the end of the last century, Chandler (1892) himself noticed that the free wobble of the Earth did not conform to a harmonic model but its amplitude and phase were changing in time. Jeereys (1940) was the rst who proposed for polar motion a stochastic model borrowed from the celebrated paper by Yule (1927). He represented the Chandler motion as a free vibration excited by a series of irregular impulses. Such a model may be fully speciied by three parameters, namely eigenfrequency F c ; quality factor Q c expressing damping,