I. N. Sinitsyn

Distributions of Fluctuations in Motion of the Earth's Pole

1. According to observation data and measurements made by the International Earth Rotation Service in the last 15‐20 years, motion of the Earth’s pole involves a principal component (free nutation and Chandlers wobble) with an amplitude of 0.20  —0.25  and a period of 433 ∠ 2 sidereal days [1], a regular annual component (365 sidereal days) with an amplitude of about 0.07  — 0.08  , and a comparatively slow irregular drift (trend) of the axis of the Earth’s figure. The annual wobbles of the Earth’s axis are caused by the moment of gravitational forces of the Sun, the Earth’s revolution around the Sun, and the diurnal tides of the mantle [2, 3]. The causes and mechanism of exciting the annual wobbles are usually attributed to seasonal geophysical phenomena [4, 5]. Measurements of motion of the Earth’s pole were statistically analyzed in many works (see, e.g., [6]). Analytical stochastic spectrally correlation models of motion of the Earth’s pole were developed in [7‐9] on the basis of celestial mechanics. In this paper continuing studies [7‐9], we consider one-dimensional distributions of fluctuations in motion of the deformable Earth.

Effect of “Colored” fluctuations on Earth-rotation irregularities

In [1], the correlation model of the intra-annual tidal irregularity of the Earth rotation is constructed. The model is based on taking into account additive parametrical harmonic and broadband random gravitational tidal fluctuations induced by the Sun and the Moon and dissipative fluctuations. We consider the effect of harmonic and “colored” random gravitational tidal fluctuations caused by the lunar‐solar perturbations on the correlation characteristics of the irregularity of the Earth’s rotation. 1. Nowadays, the unified precision uniform timeatomic international (TAI) [2] scale independent of the daily and orbital Earth motion is constructed and accepted as the standard. Its creation allows one to study the irregularity of the axial Earth’s rotation much more precisely than ever before. It became possible to measure the velocity of the Earth’s rotation at arbitrary not very long intervals of time. The further refinement of fluctuations of the irregularity of the Earth’s rotation depends on increasing the accuracy of determining the Universal-time (UT1) scale, which is related directly to the Earth’s rotation. For the practical determination of the Universal time UT1, the Earth-rotation parameter, i.e., the phase angle ϕ = ϕ ( t ) , which defines the Earth’s rotation around an instant axis, is used. In [3] such a function of the angle ϕ ( t ) (called the star angle ϕ s ( t ) ) is found; according to it, this angle is linearly related to UT1:

Effect of parametric and nonlinear perturbations on statistical dynamics of the Earth’s pole

We study the influence of additive and parametric slowly varying harmonic (at the Chandler frequency and doubled frequency) and stochastic Gaussian broadband perturbations on mathematical expectations, variances, and covariations of oscillations of the Earth’s pole. The influence of perturbations on both regular and irregular stochastic oscillations is considered in detail. Results of numerical experiments are presented. The developed models and software are included into information resources on the fundamental problem “Statistical dynamics of the Earth’s rotation” of Russian Academy of Sciences.

A correlation model for oscillations of the Earth’s pole with parametric perturbations

A differential correlation model for oscillations of the Earth’s pole is constructed. The model has gravitational-tidal, additive and parametric, slowly varying, harmonic (at the Chandler frequency and double this frequency), and random Gaussian, broadband perturbations. Special attention is paid to the analysis of trends and the amplitude-frequency characteristics of stochastic oscillations of the Earth’s pole. Numerical simulations show that first-approximation equations can be used to estimate the correlation characteristics of oscillations of the Earth’s pole to within 10%. The results of the model are compared with the results of statistical modeling of oscillations at the Chandler frequency. The model represents a base of informational resources for analytical modeling of the motion of the Earth’s pole over intervals of three to five years.

Amplitude—frequency analysis of Chandler oscillations of the Earth’s pole

An approximate nonlinear spectral-correlation model of fluctuations of the amplitude—frequency characteristics of the Chandler self-excited oscillations of the Earth’s pole is considered. The sensitivity of the model parameters to the asymmetry and anisotropy of fluctuation-dissipative moments of forces and to the effect of harmonic gravitation-tidal moments of forces is studied at Chandler frequency and frequencies close to it. The results of analytical and statistical modeling of the stability of the amplitude—frequency characteristics are presented. The influence of fluctuation disturbances of the white noise type on spectral-correlation characteristics of the oscillations is investigated.

A spectrum-correlation model for the fluctuations in the Chandler wobble

An approximate nonlinear spectral-correlation model for fluctuations in the amplitude-frequency responses for the Chandler wobble is considered. The sensitivity of the model parameters to the asymmetry and anisotropy of the fluctuation-dissipation force moments and the effects of the harmonic gravitational-tidal force moments of the Chandler and nearby frequencies is examined. Analytical and statistical modeling of the stability of the amplitude-frequency responses is presented.