L. V. Rykhlova

A gravitational-tidal mechanism for the Earth’s polar oscillations

Perturbed, rotational-oscillational motions of the Earth induced by the gravitational torques exerted by the Sun and Moon are studied using a linear mechanical model for a viscoelastic rigid body. A tidal mechanism is identified for the excitation of polar oscillations, i.e., for oscillations of the angular-velocity vector specified in a fixed coordinate frame, attributed to the rotational-progressive motion of the barycenter of the Earth-Moon “binary planet” about the Sun. The main features of the oscillations remain stable and do not change considerably over time intervals significantly exceeding the precessional period of the Earth’s axis. A simple mathematical model containing two frequencies, namely, the Chandler and annual frequencies, is constructed using the methods of celestial mechanics. This model is adequate to the astrometric measurements performed by the International Earth Rotation Service (IERS). The parameters of the model are identified via least-squares fitting and a spectral analysis of the IERS data. Statistically valid interpolations of the data for time intervals covering from several months to 15–20 yr are obtained. High-accuracy forecasting of the polar motions for 0.5–1 yr and reasonably trustworthy forecasting for 1–3 yr demonstrated by observations over the last few years are presented for the first time. The results obtained are of theoretical interest for dynamical astronomy, geodynamics, and celestial mechanics, and are also important for astrometrical, navigational, and geophysical applications.

Forecasting the polar motions of the deformable Earth

A mathematical model for the complicated phenomenon of the polar oscillations of the deformable Earth that adequately describes the astrometric data of the International Earth Rotation Service is constructed using celestial mechanics and asymptotic techniques. This model enables us to describe the observed phenomena (free nutation, annual oscillations, and trends) simply and with statistical reliability. The model contains a small number of parameters determined via a least-squares solution using well-known basis functions. Interpolations of the polar trajectory for intervals of 6 and 12 yrs and forecasts for 1–3 yrs are obtained using the theoretical curve. The calculated coordinates demonstrate a higher accuracy than those known earlier.

Analysis of multifrequency effects in oscillations of the earth's pole

A least-squares analysis of measurements of the Earth-rotation parameters is used to interpolate these data in order to redict the polar motion using a basic mathematical model that includes two frequencies: the Chandler and annual frequencies. A model taking into account the oscillations induced by the influence of the Moon is considered. The manifestation of high-frequency lunar oscillations in the beat period is demonstrated, together with the feasibility of interpolating these oscillations over short time intervals. A comparative analysis of models taking into account the monthly and bi-weekly frequencies is presented. A reasonable model explaining anomalous phenomena in the six-year beating is proposed.

A Model for the polar motion of the deformable Earth adequate for astrometric data

Refined analytical expressions for the frequencies corresponding to the Chandler motion of the pole and the diurnal rotation of the deformable Earth are derived. Numerical estimates of the period and amplitude of the polar oscillations are presented. The trajectory of the Chandler polar motion derived via numerical modeling is in qualitative and quantitative agreement with experimental data from the International Earth Rotation Service (IERS). An evolutionary model describing slow variations in the Earth’s rotation parameters under the action of the dissipative moments of the tidal gravitational forces on time scales considerably longer than the precession period of the Earth’s axis is constructed. The axis of the Earth’s figure tends to approach the angular momentum vector of the proper rotation.

Rotational-oscillatory variations in the Earth rotation parameters within short time intervals

A mathematical model for rotational-oscillatory motions of the Earth is constructed by applying celestial mechanics to the spatial problem of the Earth-Moon system subject to the Sun’s gravitation. Some basic phenomena associated with tidal irregularity in the Earth’s axial rotation and the polar oscillations are studied. It is shown that the perturbing component of the gravitational-tidal forces orthogonal to the plane of the lunar orbit is responsible for some short-term perturbations in the Moon’s motion. The constructed model for the rotational-oscillatory motions of the deformable Earth includes both the main high-amplitude perturbations and more complex small-scale motions attributed to short-term lunar perturbations with combinational frequencies. Numerical modeling (interpolation and forecasting) of the Earth rotation parameters within various time intervals based on astrometric data obtained by the International Earth Rotation Service is presented.

High-accuracy forecasting of the Earth’s polar motion

The fundamental astrometrical problem of high-accuracy interpolation of the trajectory of the Earth’s pole and construction of an adequate theoretical model for associated complex multifrequency oscillations are considered. Measurements of the Earth-rotation parameters demonstrate the possibility of adjusting the filtering algorithm to make it suitable for practical navigational applications associated with a need for reliable high-accuracy predictions over the required time scales (short-and medium-terms). Numerical simulations and tests of the procedure used to optimize the adjustment parameters are presented.

Modeling intraday oscillations of the Earth’s pole

An amplitude-frequency analysis of a few-parameter model for intraday oscillations of the Earth’s pole induced by gravitational-tidal torques exerted by the Sun and the Moon is presented. The characteristic features of the intraday oscillations in the polar coordinates are found using the dynamical Euler-Liouville equations, taking into account irregular perturbations. The modeling results for the polar motion are compared with high-accuracy VLBI observations over short time intervals. An amplitude-frequency analysis of the polar oscillations and the second zonal harmonic c20 of the geopotential is presented.

Some improved methods for modeling the Earth’s polar motion

Some improved methods for modeling the motions of the Earth’s pole determined by gravitational-tidal, fluctuating-dissipative perturbations occurring on various time scales are presented. The main attention is paid to dynamical linear-regression models and dynamical filtering models, which take into account dynamical measurement errors. Computer simulations of the oscillatory motion of the Earth’s pole for 1995–2010 are also presented.

Irregularities in the Earth's Rotation and the Overall Angular Momentum of the Atmosphere

Methods of celestial mechanics are used to refine a mathematical model for irregularity in the axial rotation of the Earth proposed earlier. This refinement applies corrections (residuals) introduced by perturbations of zonal tides. We examine intraday and near-diurnal variations in the Earth’s axial rotation, and a celestial-mechanical model explaining the origin of the intraday and near-diurnal oscillations in the rotational angular velocity is constructed. The correspondence between the variations of the intrayear rotational irregularity and the overall angular momentum of the atmosphere is analyzed.

Intrayear irregularities of the Earth’s rotation

The methods of celestial mechanics can be used to construct a mathematical model for the perturbed rotational motions of the deformable Earth that can adequately describe the astrometric measurements of the International Earth Rotation Service (IERS). This model describes the gravitational and tidal influences of the Sun and Moon. Fine resonant interactions of long-period zonal tides (annual, semiannual, monthly, and biweekly) with the diurnal and semidiurnal tides are revealed. These interactions can be reliably confirmed via a spectral analysis of the IERS data. Numerical modeling of tidal irregularities of the Earth’s axial rotation was carried out, focusing on the analysis and forecasting of variations of the day length occurring within short time intervals of a year or shorter (intrayear variations).