Chandler Components Research Articles

The fluctuation perturbations in the model of the Chandler wobble

The combinative model of the fluctuations of the Earth Pole taking into account the stochastic components of the Pole tide is developed. The effects of the fluctuation-dissipative perturbations on the frequency that is near to the Chandler one are investigated on the basis of analytical approach. We note that allowance for the small fluctuation-dissipation perturbations due to the pole tide leads to variations in the Chandler component of the oscillations.

Gravity fluctuations in studying the earth pole oscillation processes

Based on the dynamical Euler-Liouville equations, we consider a numerical-analytical model of the Earth pole oscillations in the first approximation under the gravitational tidal forces from the Sun and the Moon. The dynamics of the Earth pole motion is analyzed by taking into account the pole tide at the Chandler frequency. We note that allowance for the small fluctuation-dissipation perturbations due to the pole tide leads to variations in the Chandler component of the oscillations.

Terrestrial pole oscillations with allowance for fluctuation-dissipation perturbations

Based on a numerical-analytical model of the terrestrial pole oscillations, we investigate the effects of fluctuation-dissipation perturbations due to the pole tide. We consider the fluctuation perturbations at a frequency close to the Chandler one using the sea level data as an example. Allowance for the small irregular perturbations in tidal processes is shown to lead to variations in the Chandler component of the oscillations. We note that the amplitude of the Chandler pole oscillations is sensitive to the difference of the Chandler frequency and a frequency close to it and to the dissipation coefficients.

One hybrid model combining singular spectrum analysis and LS + ARMA for polar motion prediction

Accurate real-time polar motion parameters play an important role in satellite navigation and positioning and spacecraft tracking. To meet the needs for real-time and high-accuracy polar motion prediction, a hybrid model that integrated singular spectrum analysis (SSA), least-squares (LS) extrapolation and an autoregressive moving average (ARMA) model was proposed. SSA was applied to separate the trend, the annual and the Chandler components from a given polar motion time series. LS extrapolation models were constructed for the separated trend, annual and Chandler components. An ARMA model was established for a synthetic sequence that contained the remaining SSA component and the residual series of LS fitting. In applying this hybrid model, multiple sets of polar motion predictions with lead times of 360days were made based on an IERS 08 C04 series. The results showed that the proposed method could effectively predict the polar motion parameters.

Fluctuations of pole oscillations of deformable earth under nonstationary perturbations

An approach of celestial mechanics is used to consider variations in the tensor of inertia due to elastic deformations arising under the action of the centrifugal potential. The effects of influence of random actions are investigated in an example of fluctuation-dissipative perturbations of geophysical nature. A combined model of the Earth rotation fluctuations permits taking into account the stochastic components of the pole tide. It is shown that small irregular perturbations in tidal processes generate variations in the Chandler component of the pole oscillations.

A numerically analytical approach to studying oscillation processes for earth’s poles

The fine dynamic effects that make it possible to improve the accuracy of predicting the trajectory of pole motion are revealed by using a numerically analytical approach in modeling the pole oscillatory motion, the key component of which is the Chandler component.

The main properties and peculiarities of the Earth’s motion relative to the center of mass

The methods of theoretical and celestial mechanics and mathematical statistics have been used to prove that the Earth’s motion relative to the center of mass, the polar wobble, in the principal approximation is a combination of two circumferences with a slow trend in the mean position corresponding to the annual and Chandler components. It has been established that the parameters (amplitude and phase shift) of the annual wobble are stable, while those of the Chandler component are less stable and undergo significant variations over the observed time intervals. It has been proven that the behavior of these polar motion parameters is attributable to the gravitational-tidal mechanisms of their excitation.

Chandler wobble in variations of the Pulkovo latitude for 170 years

The work studies the Chandler component of polar motion, obtained from variations in the Pulkovo latitude over 170 years (1840–2009). To extend the time series of variations in the Pulkovo latitude back into the past until 1840, we used the first Pulkov observations on the basis of the Reynolds transit instrument in the prime vertical and on the basis of large vertical Ertel circle. We employed different methods of analysis of nonstationary time series, such as wavelet analysis, methods of bandpass filtering, singular spectral analysis, and Fourier and Hilbert transforms. Changes in the Pulkovo latitude from 1904–2006, as inferred from ZTF-135 observations and as calculated from international data, were compared. It was shown that time changes in the amplitude and phase of Chandler polar motion can be studied based on long-term observation time series of latitude at a single observatory, even if these observation records have gaps. We were the first to study the changes in the Chandler wobble for that long time series of variations in the Pulkovo latitude with the help of different methods. The long observation record and the methods of analysis of nonstationary time series had allowed us to identify two similar structures, both well apparent during the periods of 1845–1925 and 1925–2005 in the time variations of phase and amplitude. The presence of this structure indicates that low-frequency regularities may be present in the Chandler polar motion, and one of the manifestations of this may be the well known feature in the region of 1925. The superimposed epoch method was used to estimate the period of variations in the amplitude with a simultaneous change of phase of this oscillation, which was found to be 80 years. In addition, advantages of singular spectral analysis for studying the long-period time series with involved structure are demonstrated.

Rotational-oscillational motions of the nonrigid Earth about the center of mass

We use the model of a nearly axisymmetric viscoelastic rigid body to study perturbed rotational-oscillational motions of the Earth’s pole. We point out that the Chandler component of oscillations is of celestial-mechanics nature and is caused by the gravitational-tidal actions of the Sun and the Moon. We analyze the pole oscillation excitation mechanism at a frequency close to the Chandler frequency and show that the undamped pole oscillations are caused by the resonance harmonic of the external perturbation at a frequency close to the free nutation frequency. We discuss whether it is possible to solve the problem of constructing a short-term forecast of the pole motion on the basis of a polynomial filter obtained by the least-squares method without taking into account small-scale oscillations caused by wide-band random factors of arbitrary physical nature. In the present paper, we perform numerical simulation of tidal inhomogeneities in the Earth’s axial rotation. Attention is mainly paid to the analysis of day length variations on short time intervals with periods less than or equal to one year (interannual oscillations) and to their forecast.

Free Wobble of the Triaxial Earth: Theory and Comparisons with International Earth Rotation Service (IERS) Data

Earth’s free wobble is often referred to as the Euler wobble (for the rigid case) or the Chandler wobble for the real case. In this study, we investigate the theory of the free wobble of the triaxial Earth and demonstrate that: (1) the Euler period should actually be expressed by the complete elliptic integral of first kind, and (2) the trace of the free polar motion is elliptic, with the orientations of its semi-minor and major axes being approximately parallel to the Earth’s principal axes A and B, respectively. Numerical calculations show that, due to the triaxiality of the Earth, the spin rate ω 3 fluctuates with the semi-Euler/Chandler period, although its amplitude (about 10−19 rad/s) is rather small and beyond the present measurement accuracy; the tilt of the instantaneous spin axis (or the amplitude of the free wobble), θ, has a fluctuation whose amplitude is around 0.34 milli-arcsecond (mas), which could be detected by present observations. Thus, we conclude that the Earth’s triaxial nature has little impact on ω 3, but has an influence on the polar motion which should not be ignored. On the other hand, our study shows that there is a mechanism of frequency–amplitude modulation in the Chandler wobble which might be a candidate to explain the correlation between the amplitude and period of the Chandler wobble. We compare the theoretical polar parameters (m 1, m 2) with the observed values for the Chandler components obtained from the data EOP (IERS) C 04, and find that they coincide with each other quite well, especially for recent years. In addition, a polar wander towards 76.7°W, which is in agreement with previous results given by other scientists, is also obtained.

On the period and quality factor of the Chandler wobble

The motion of the Earth’s geophysical pole is modeled by numerical integration of the Liouville equations. The dependence of variable parameters of these equations (the period of free nutation T and the quality factor of the shell Q) is examined as a function of time and initial data sets used for constructing geophysical perturbing functions. In particular, we used oceanic perturbing functions constructed from TOPEX/POSEIDON altimetry data. The annual and Chandler components of the pole motion were also modeled. Apart from the subtraction of quadratic trends, initial data were not filtered or averaged. The performed analysis provided model values of T = 425–440 days and Q = 20–60, and Q was found to be somewhat unstable with time.

Modeling of the Earth’s pole motion from data on the atmospheric and oceanic angular momenta over 1980–2002

The model values of the mantle quality factor Q=40±20 and the Chandler wobble period T=435–436 days are obtained by numerical modeling of the yearly and Chandler components in the pole motion from data on the angular momenta of the atmosphere and the ocean. The oceanic and the atmospheric excitations account for about 65–70% of the dispersion of the observed pole motion.

A preliminary nonlinear analysis of the earth′s chandler wobble

The Chandler wobble (CW) is a resonant response of the Earth rotational pole wandering around its figure axis whose excitation mechanism is still uncertain. It appears as polar motion oscillations with an average period of about 433 days and a slowly varying amplitude in the range (0–300) milliarcsec (mas). We here perform a nonlinear analysis of the CW via a time‐delay coordinate embedding of its measured X and Y components and show that the CW can be interpreted as a low dimensional unstable deterministic process.In a first step the trend, annual wobble and CW are separated from the raw polar motion data time series spanning the period 1846–1997. The optimal delays as deduced from the average mutual information function are 105 and 115 days for the X and Y components respectively. Then from the global statistics of the false neighbours, the embedding dimension DE = 4 is estimated for both series. The local dimension DL can also be extracted from the time series by testing the predictive skill of local mappings fitted to the embedded data vectors. The result DL = 3 is quite robust and corroborate the idea that the CW behaves like a dissipative oscillator driven by a deterministic process. Indeed the orbit reconstructions in pseudo‐phase space both draw the figure of a perturbated 1‐torus.The computation of the Lyapunov spectra further shows that this torus‐like figure is an attractor with a 1D unstable manifold. The theoretical horizons of prediction deduced from the (positive) principal exponents are about 367 and 276 days for the X and Y Chandler components respectively. Moreover the local Lyapunov exponents exhibit significant variations with maxima (and corresponding losses of predictibility) in the decades 1860–1870 and 1940–1950.

Determination of the gravimetric factor at the Chandler period from Earth orientation data and superconducting gravimetry observations

Summary We have used more than 8 years’ worth of a combination of superconducting gravimeter (SG) data from the Strasbourg station and Very Long Baseline Interferometry (VLBI) Earth orientation data in order to determine the gravimetric factor at the Chandler period of 435 days. The method presented here takes advantage of the relation between the rotational potential and the gravity variation at the Earth’s surface. The length of the data set is a critical parameter in such a determination but appears to be long enough to separate the annual and Chandler components. Our results are in a good agreement with the long-period theoretical gravimetric factor relative to an elastic solid earth model and a static pole tide in the oceans. We also find that the effect of the atmosphere (computed from a global atmospheric model assuming a static response of the oceans to air-pressure changes) is not negligible and perturbs the amplitude of the Chandler wave observed in the gravimetric data.

Refinements of the polar motion frequency modulation hypothesis

In a previous paper (Carter, 1981) I suggested that the Chandler component of polar motion may be frequency modulated, as a function of the instantaneous polar motion magnitude. A composite of observational records compiled by S. C. Chandler and the International Latitude Service series suggests a variation in the magnitude at a frequency of approximately 0.0118 cycles per year (cpy). The spectrum produced by the resulting frequency modulation would depend on the modulation index. Comparison of spectra synthesized with various degrees of frequency modulation and those derived from observational data, suggest a frequency increase of 0.15 to 0.30 cpy/arc sec decrease in the polar motion magnitude. This degree of frequency modulation would cause ‘splitting’ of the Chandler component, producing dual spectral peaks at periods of 427 and 439 days, similar to that reported by several investigators beginning with Chandler (1901a, b).

Geodetic and geophysical implications of the homogeneous reduction of pole coordinates (1899–1979)

The new series ILS (H) of pole coordinates (1899.9–1979.0) computed in a homogeneous system has been employed for the determination of the period of Chandler's component of polar motion. The comparison with a value derived from a previous series ILS (VY) shows there is no significant variation in the period in spite of the known systematic errors affecting the ILS (VY) series. Any high precision geodetic network adjustment has to take account of the pole coordinates defined by the ILS (H) series. Such long series permitted the identification of another component of polar motion with a period of about 30 years. The polhode derived from the ILS (H) series shows greater regularity than previously deduced polhodes and, therefore, we can conclude that past investigations in geodesy and geophysics trying to correlated the irregularities of the polhode with different geophysical phenomena, for instance, earthquakes, may have to be revised.

Estimates of Chandler's Component of Polar Motion as Derived from Various Data Sets

AbstractDes groupes de données provenant de plusieurs combinaisons de techniques classiques et modernes (Doppler et laser vers des satellites artificiels) ont été analysés par des méthodes autoregressives, simsoidales et autorégressives avec moyenne mobile (ARMA) pour obtenir des estimations de la fréquence de Chandler et du facteur de qualité de cette composante du mouvement du pǒle. La mδthode ARMA présente des avantages sur les autres méthodes et les résultats obtenus ne mettent pas en évidence une variation temporelle des paramètres du mouvement du pǒle. Les inconvénients du lissage des groupes de données et de l'utilisation de courts intervalles de temps pour les données sont clairement démontrés. L'importance est placée sur un besoin pour des séries d'observations longues et régulières avec techniques modernes.

On the Separation of the Spectral Components of Polar Motion

Summary This paper presents a novel method for the separation of the annual and Chandler spectral components in astronomic latitude or polar motion data. The method relies upon the high resolving power of maximum entropy spectral analysis. This separation technique is applied to astronomic latitude data from 10 International Polar Motion Service stations for the time interval 1962.0 to 1971.0, and is also applied to the two orthogonal polar motion components as determined from the data of these 10 stations. The results of this separation technique are compared with those from a method used by S. Yumi of the International Polar Motion Service. There is good agreement between the methods for the annual component determination. It was found that the annual component amplitude and phase varied widely among the ten stations. There is not good agreement between the methods for the Chandler component determination. However, evidence is given that the results of the novel separation technique are more internally consistent than those for the previously used separation method. The Chandler polar motion is plotted for the 2 years 1963.0 to 1965.0. This Chandler polar motion was determined by a least-squares fit to the 10 IPMS stations’ data after the individually determined annual components were removed from each station'sdata.