Chandler Period Research Articles

On the Chandler Period of Venus

On the Chandler Period of Venus

Free decay and excitation of the chandler wobble: self-consistent estimates of the period and quality factor

The period TCW and quality factor QCW of the Chandler wobble (CW) as well as polar motion (PM) transfer functions are all determined by the Earth’s layered structure, mass distribution, elasticity, rheology and energy dissipation, via the Earth’s dynamic figure parameters and complex degree-2 Love numbers. However, most previous studies used geophysical excitations derived from real-valued PM transfer functions to invert for TCW and QCW, thus leading to results that are not self-consistent. By separating the observed PM into the freely decaying CW and the excited PM, a traverse-based method is proposed to search values of TCW and QCW that can fit both sides simultaneously, yielding the self-consistent estimates of TCW = 430.4 mean solar days and QCW = 130. This implies the degree-2 tidal Love number k = 0.35011 − 0.00226i and load Love number k' = − 0.36090 + 0.00233i, and the PM transfer functions TNL = 1.80001 − 0.00692i (non-loading) and TL = 1.15040 − 0.00023i (loading) valid at the Chandler period.

Анализ вариаций в движении Северного полюса для повышения точности координатно-временных определений

This article considers a method for predicting the coordinates of the north pole, taking into account the influence of trend, quasi-periodic, regular and high-frequency variations. The necessary graphic material is given, illustrating the picture of the listed variations from 2000 to the present. In particular, a regular change in the amplitude of the Chandler period (СP) is shown. So, from 2006 to 2017, the amplitude of the СP gradually decreases from the maximum to zero, and from 2020 to the present, it has been steadily increasing. Based on the analysis of the behavior of trend changes in the pole coordinates, it is shown that at present the movement of the average pole is directed towards the Greenwich meridian, and not towards North America, as it is given in a number of literary sources. The practical implementation of the proposed method resulted in the creation of programs for predicting the coordinates of the pole and Universal Time for periods from one to 90 days. At the same time, the accuracy of forecasts calculated using these programs exceeds the accuracy of similar forecasts posted on the website of the International Earth Rotation Service. The problem of high-precision prediction of the coordinates of the pole and the Universal Time has now acquired particular relevance, especially in the light of the adopted Federal Target Program for the development of GLONASS up to 2030. In the field of improving the accuracy of ephemeris-time support (ETS).

О периоде движения полюса оси вращения упругой Луны

Numerous studies present results of investigating the rotational and translational-rotational motion of a viscoelastic Earth and its Moon. However, they primarily focus on the dynamics of the Earth--Moon system. Further contemporary studies of the Moon will necessarily involve investigating how the elastic properties of the Moon manifest in its physical libration (in the modern era). The following lines of research are particularly noteworthy: effects of the liquid and solid nuclei of the Moon, as well as the Moon mantle elasticity, on its rotational motion, taking into account a highly precise description of the orbital motion of the Moon and the motion being driven by resonance. This paper identifies significant effects to be taken into account when interpreting observation results. We used the Liouville problem equations stated in Andoyer variables along with the perturbation theory to describe the rotational motion of the Moon. We show that accounting for the elastic properties of the Moon in its model means that its pole oscillation period becomes significantly longer than the period yielded by the classic solid Moon model. The paper presents the Chandler period values for comparison, calculated according to the formulas provided. The investigation results are relevant to the updated Russian lunar program for the 2021--2040 period.

Chandler period estimated from frequency domain expression solving the Liouville equation for polar motion

SUMMARY Accurate determination of the Chandler wobble (CW) period (TCW) and quality factor (QCW) is of great significance to our understanding of the Earth's dynamic figure parameters, elasticity, rheology and energy dissipation. TCW and QCW were typically determined in the time domain using the digital filter designed by Wilson; however, we developed an alternative method to estimate TCW in the frequency domain. We adopted the frequency domain expression solving the Liouville equation for polar motion (eq. 3 in the following) rather than the time domain to separate the free-damping CW and excited parts. Next, we substituted various excitation functions derived from the outputs of several general circulation models and selected monthly gravity models into the above frequency domain expression; hence we estimate TCW. The preferred TCW value using this method and the least difference combination mgm90 model is 430.4 ± 2.0 mean solar days. Comparing with previous studies within the error range, our results provide an independent way of estimating TCW.

Spectral analysis of multi-year GNSS code multipath time-series

In the presented study multi-year time series of changes in the L1 pseudo-range multipath are analysed. Data from 8 stations of the EUREF Permanent Network (EPN) were used in the study. Periodic components present in the signal and their stability over time were analysed. Also, the type of background noise was determined, based on the spectral index. In some cases, the presence of weak components with a 1/2 and 1/3 of the Chandler period has also been found. Time-frequency analysis shows that periodic signals are not stationary in most of the examined cases, and particular signal components occur only temporarily. The analysed signals were characterised by pink noise in the lower frequency range and by white noise for higher frequencies, which is also characteristic for time series of coordinates obtained from GNSS measurements.

Chandler Wobble and Free Core Nutation: Theory and Features

Being a torque free motion of the rotating Earth, Chandler wobble is the major component in the Earth’s polar motion with amplitude about 0.05-0.2 arcsec and period about 430-435 days. Free core nutation, also called nearly diurnal free wobble, exists due to the elliptical core-mantle boundary in the Earth and takes almost the whole part of un-modelled variation of the Earth’s pole in the celestial sphere beside precession and nutation. We hereby present a brief summary of their theories and report their recent features acquired from updated datasets (EOP C04 and ECMWF) by using Fourier transform, modelling, and wavelet analysis. Our new findings include (1) period-instability of free core nutation between 420 and 450 days as well as its large amplitude-variation, (2) re-determined Chandler period and its quality factor, (3) fast decrease in Chandler amplitude after 2010.

Viscoelastic tides: models for use in Celestial Mechanics

This paper contains equations for the motion of linear viscoelastic bodies interacting under gravity. The equations are fully three dimensional and allow for the integration of the spin, the orbit, and the deformation of each body. The goal is to present good models for the tidal forces that take into account the possibly different rheology of each body. The equations are obtained within a finite dimension Lagrangian framework with dissipation function. The main contribution is a procedure to associate to each spring–dashpot model, which defines the rheology of a body, a potential and a dissipation function for the body deformation variables. The theory is applied to the Earth (solid part plus oceans) and a comparison between model and observation of the following quantities is made: norm of the Love numbers, rate of tidal energy dissipation, Chandler period, and Earth–Moon distance increase.

Moon's perigee mass as a missing component of the Earth's precession‐nutation theory

AbstractIn this work, the nutation momentum acting upon the Earth from the Moon's perigee mass that has not been taken into account in the Earth's precession‐nutation theory was revealed. This missing momentum exhibits itself in the so‐called “local latitude variation” with the Chandler's period. The results of our work raise the question of updating the Earth's precession‐nutation theory and revising some postulates of the time service, astronomy, geophysics, satellite navigation, etc. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Polar motion excitations for an Earth model with frequency‐dependent responses: 1. A refined theory with insight into the Earth's rheology and core‐mantle coupling

AbstractThis study aims to improve the polar motion theory by developing refined frequency‐dependent transfer functions with the most current models for ocean tides, the Earth's rheology, and core‐mantle coupling. First, we present a power law for mantle anelasticity constrained by the Chandler period TCW and quality factor QCW and an empirical quasi‐fluid rheology model with a linear dependence on frequency, which is suitable for a period as long as ~18.6 years. Then we adopt the diurnal ocean tides from the International Earth Rotation and Reference Systems Service Conventions (2010), the long‐period ocean model of Dickman and Gross (2010), and the equilibrium ocean pole tide model of Desai (2002) to calculate the oceanic corrections to the Love numbers. Further, we present discussions on the geophysical and observational aspects of the Chandler period TCW and quality factor QCW, and provide preferred values and intervals for TCW and QCW, which allow us to place some constraints on the mantle anelasticity and core‐mantle coupling ratio ηCW. Although ηCW is affected by uncertainties in TCW and QCW, we find its real part should be around 2%–3% while its imaginary part might be only a few thousandths. Finally, the frequency‐dependent polar motion transfer functions T L and T NL are determined based on the models of frequency‐dependent Love numbers and core‐mantle coupling discussed above. Our transfer functions are related to the values of TCW and QCW, however, our analyses demonstrate that our transfer functions are rather stable and not sensitive to perturbations in TCW and QCW.

Oceanic excitation of polar motion: Identification of specific oceanic areas important for polar motion excitation

In this paper regional values of the oceanic excitation function of polar motion are computed from bottom pressure and oceanic current fields from the ECCO/JPL data-assimilating model kf080 for the period 1993–2009. The influence of different geographic regions of the ocean on the excitation of polar motion is determined by calculating correlations and covariances between these regional excitations and either the global non-atmospheric excitation or the global oceanic excitation. The non-atmospheric excitation is estimated by subtracting the atmospheric signal from the excitation computed from geodetic observations of polar motion; the global oceanic excitation function is equivalent to the sum of the oceanic excitation function computed in every grid point. Our attention focuses on the regional distribution of the oceanic polar motion excitation for two time scales: the seasonal spectral band and the band around the Chandler period. We identified the southern Indian Ocean and the South Pacific Ocean as important regions for non-atmospheric polar motion excitation. The maximum of variability over the southern Indian Ocean is especially important in the case of annual oscillation. The Atlantic Ocean makes less significant contribution to the non-atmospheric polar motion excitation than the Pacific and Indian Ocean in both considered spectral ranges. Inland seas like the Mediterranean and the Sea of Japan have high covariance with the global signals.

The period and Q of the Chandler wobble of Mars

The calculations of the Chandler wobble period T W have been performed for a set of interior structure models of Mars with 50- and 100-km thick crust and averaged crustal density varying in the range 2700–3200 kg/m 3. The models satisfy new values for the moment of inertia and the elastic tidal Love number k 2 s . The observational data constrain the radius of a liquid core to be within 1700–1800 km. Because of inelasticity the value of T W depends on frequency (as the Love number depends on frequency). We assume that the power creep function is valid for description of inelastic processes in Martian interiors in the range of periods from T 2 Ph =5.55 h to T W ≈200 days. Then the dynamical shear modulus μ 0( σ) and dissipative factor Q μ ( σ) varies with frequency σ as σ n . As a reference frequency we used the frequency of Phobos’ tidal wave σ t . The substitution of k( σ t ) in the formula for T W gives the estimate for the minimum model value of the Chandler period 202.8 ⩽ T W t ⩽ 203 .4 days. For the exponent of creep function 0.1⩽ n⩽0.2 (by analogy with the calculations for the Earth) the shift of the Chandler period to longer periods due to inelasticity δT W is in the interval 0.981⩽ δT W ⩽1.42 days. Combining both estimates we obtain the interval for the model value of Chandler wobble period of Mars as 203.8⩽ T W t + δT W ⩽204.8

Inversion of polar motion data: Chandler wobble, phase jumps, and geomagnetic jerks

We reconsider the analysis of the polar motion with a method totally different from the wavelet analysis used in previous papers. The total polar motion is represented as the sum of oscillating annual and Chandler terms whose amplitude and phase perturbations are inverted with a nonlinear simulated annealing method. The phase variations found in previous papers are confirmed with the huge phase change (≈3π/2) occurring in the 1926–1942 period and another less important one (≈π/3) in the 1970–1980 epoch. The best Chandler period, Tc, is found to be 434 ± 0.5 mean solar days. The epochs of significant phase changes found in the Chandler wobble are also those where important geomagnetic jerks occur in the secular variation of the geomagnetic field. Turbulent viscous friction produced by small‐scale topography at the core‐mantle boundary might be responsible for the observed phase jumps.

Loading effect of a self-consistent equilibrium ocean pole tide on the gravimetric parameters of the gravity pole tides at superconducting gravimeter stations

Abstract The gravimetric parameters of the gravity pole tide are the amplitude factor δ , which is the ratio of gravity variations induced by polar motion for a real Earth to variations computed for a rigid one, and the phase difference κ between the observed and the rigid gravity pole tide. They can be estimated from the records of superconducting gravimeters (SGs). However, they are affected by the loading effect of the ocean pole tide. Recent results from TOPEX/Poseidon (TP) altimeter confirm that the ocean pole tide has a self-consistent equilibrium response. Accordingly, we calculate the gravity loading effects as well as their influence on the gravimetric parameters of gravity pole tide at all the 26 SG stations in the world on the assumption of a self-consistent equilibrium ocean pole tide model. The gravity loading effect is evaluated between 1 January 1997 and 31 December 2006. Numerical results show that the amplitude of the gravity loading effect reaches 10 −9 m s −2 , which is larger than the accuracy (10 −10 m s −2 ) of a SG. The gravimetric factor δ is 1% larger at all SG stations. Then, the contribution of a self-consistent ocean pole tide to the pole tide gravimetric parameters cannot be ignored as it exceeds the current accuracy of the estimation of the pole tide gravity factors. For the nine stations studied in Ducarme et al. [Ducarme, B., Venedikov, A.P., Arnoso, J., et al., 2006. Global analysis of the GGP superconducting gravimeters network for the estimation of the pole tide gravimetric amplitude factor. J. Geodyn. 41, 334–344.], the mean of the modeled tidal factors δ m = 1.1813 agrees very well with the result of a global analysis δ CH = 1.1816 ± 0.0047 in that paper. On the other hand, the modeled phase difference κ m varies from −0.273° to 0.351°. Comparing to the two main periods of the gravity pole tide, annual period and Chandler period, κ m is too small to be considered. Therefore, The computed time difference κ L induced by a self-consistent ocean pole tide produces a negligible effect on κ m . It confirms the results of Ducarme et al., 2006, where no convincing time difference was found in the SG records.

Estimation of the pole tide gravimetric factor at the chandler period through wavelet filtering

SUMMARY Wavelet analysis for filtering is used to improve estimation of gravity variations induced by Chandler wobble. This method eliminate noise in superconducting gravimeter (SG) records with bandpass filters derived from Daubechies wavelet. The SG records at four European stations (Brussels, Membach, Strasbourg and Vienna) are analysed in this study. First, the earth tidal constituents are removed from the observed data by using synthetic tides, then the gravity residuals are filtered into a narrow period band of 256‐512 d by a wavelet bandpass filter. These data are submitted to three regression analysis methods for estimating the gravimetric factor of the Chandler wobble. After processing by wavelet filtering, SG records can provide amplitude factors δ and phase lags κ of the Chandler wobble with much smaller mean square deviation (MSD) than these provided by former studies. It is mainly because the wavelet method can effectively eliminate instrumental drift and provide smoothed data series for the regression analysis.

Construction of Martian Interior Model

We present the results of extensive numerical modeling of the Martian interior. Yoder et al. in 2003 reported a mean moment of inertia of Mars that was somewhat smaller than the previously used value and the Love number k 2 obtained from observations of solar tides on Mars. These values of k 2 and the mean moment of inertia impose a strong new constraint on the model of the planet. The models of the Martian interior are elastic, while k 2 contains both elastic and inelastic components. We thoroughly examined the problem of partitioning the Love number k 2 into elastic and inelastic components. The information necessary to construct models of the planet (observation data, choice of a chemical model, and the cosmogonic aspect of the problem) are discussed in the introduction. The model of the planet comprises four submodels—a model of the outer porous layer, a model of the consolidated crust, a model of the silicate mantle, and a core model. We estimated the possible content of hydrogen in the core of Mars. The following parameters were varied while constructing the models: the ferric number of the mantle (Fe#) and the sulfur and hydrogen content in the core. We used experimental data concerning the pressure and temperature dependence of elastic properties of minerals and the information about the behavior of Fe(γ-Fe ), FeS, FeH, and their mixtures at high P and T. The model density, pressure, temperature, and compressional and shear velocities are given as functions of the planetary radius. The trial model M13 has the following parameters: Fe#=0.20; 14 wt % of sulfur in the core; 50 mol % of hydrogen in the core; the core mass is 20.9 wt %; the core radius is 1699 km; the pressure at the mantle-core boundary is 20.4 GPa; the crust thickness is 50 km; Fe is 25.6 wt %; the Fe/Si weight ratio is 1.58, and there is no perovskite layer. The model gives a radius of the Martian core within 1600–1820 km while ≥30 mol % of hydrogen is incorporated into the core. When the inelasticity of the Martian interior is taken into account, the Love number k 2 increases by several thousandths; therefore, the model radius of the planetary core increases as well. The prognostic value of the Chandler period of Mars is 199.5 days, including one day due to inelasticity. Finally, we calculated parameters of the equilibrium figure of Mars for the M13 model: J 2 0 = 1.82 × 10−3, J 4 0 = −7.79 × 10−6, e c-m D = 1/242.3 (the dynamical flattening of the core-mantle boundary).

Free polar motion of a triaxial and elastic body in Hamiltonian formalism: Application to the Earth and Mars

The purpose of this paper is to show how to solve in Hamiltonian formalism the equations of the polar motion of any arbitrarily shaped elastic celestial body, i.e. the motion of its rotation axis (or angular momentum) with respect to its figure axis. With this aim, we deduce from canonical equations related to the rotational Hamiltonian of the body, the analytical solution for its free polar motion which depends both on the elasticity and on its moments of inertia. In particular, we study the influence of the phase angle δ, responsible for the dissipation, on the damping of the polar motion. In order to validate our analytical equations, we show that, to first order, they are in complete agreement with those obtained from the classical Liouville equations. Then we adapt our calculations to the real data obtained from the polar motion of the Earth (polhody). For that purpose, we characterize precisely the differences in radius J − χ and in anglel − θ between the polar coordinates (χ, θ )a nd (J, l) representing respectively the motion of the axis of rotation of the Earth and the motion of its angular momentum axis, with respect to an Earth-fixed reference frame, after showing the influence of the choice of the origin on these coordinates, and on the determination of the Chandler period as well. Then we show that the phase lag δ responsible for the damping for the selected time interval, between Feb. 1982 and Apr. 1990, might be of the order of δ ≈ 6 ◦ , according to a numerical integration starting from our analytical equations. Moreover, we emphasize the presence in our calculations for both χ and θ, of an oscillation with ap eriodTChandler/2, due to the triaxial shape of our planet, and generally not taken into account. In a last step, we apply our analytical formulation to the polar motion of Mars, thus showing the high dependence of its damping on the poorly known value of its Love number k. Moreover we emphasize the large oscillations of Mars' polar motion due to the triaxiality of this planet.

Period variations of the Chandler wobble

Variations in the period of the Chandler wobble have been discussed since its discovery by Chandler in 1892. Various authors engaged in the investigation of polar motion time series suggest both a variable and an invariable period. It cannot be resolved by the analysis of time series whether the Chandler period is variable. By studying the influence of mass redistributions on the Chandler period it has been found that it is in fact variable, but the magnitude of such variation is much smaller than that found by polar motion time series analysis. For the currently available time series of polar motion, it is sufficient to assume an invariable Chandler period.

COUPLED OSCILLATIONS IN THE EARTH-MOON SYSTEM AND GEOPHYSICAL PROCESSES

In the Earth-Moon system, oscillations of close frequencies can be transformed as a result of the degree of coupling. The observed extended period of the Chandler oscillations can be explained by coupling of the oscillations. The problem of amplitude and period variations of the main oscillations of the Earth poles is treated on the basis of parametric excitement. For the first instability region an equation is obtained to determine the amplitudes of possible steady-state solutions. The variation limits of Chandler period oscillations and the relation between amplitudes of a possible steady-state solution for two periodic polar motion components are computed. The possible influence of energy exchange in coupled Earth-Moon oscillations on excitement and self-excitement in geophysical processes is discussed. As an illustration the interaction between the Earth's angular velocity variations and variations in the Siberian anticyclone parameters are considered.

Free oscillations of parameters of the Earth's motion in the Earth-Moon system

When the coupled Earth-Moon system is considered rather than a closed terrestrial system (the Earth's atmosphere, ocean, inner and outer cores, and mantle), an eigenfrequency of free oscillations of the Earth is transformed into an eigenfrequency of the Earth-Moon system, making it possible to understand the increase in the Chandler period in a natural way. The eigenmodes of the coupled Earth-Moon system are determined by solving a linear, homogeneous set of equations with two degrees of freedom.