Chandler Wobble Amplitude Research Articles

Measuring chandler wobble amplitude variations using IERS EOP C04 data

We analyzed the Earth's long-term polar motion using the time series IERS EOP C04 (International Earth Rotation and Reference Systems Service - IERS; Earth Orientation Parameters - EOP; Combination of four (04) techniques - C04), from 1984 to 2023, to determine the variation of the Chandler wobble amplitude. To compare the results based on the C04 with the so-called Belgrade latitude data (Belgrade Lunette Zenithale - BLZ series 1949-1985) results, we calculated the latitude variations at the BLZ point using the C04 coordinates (x, y). The secular part of these latitude variations was determined by applying the least-squares method (LSM) and removed from the data to obtain the residuals. We used Direct Fourier transforms to extract annual and semiannual oscillations and to remove them from the residuals (resulting in a new set of residuals). These new residuals were divided into 33 independent 1.2-year subintervals. For each subinterval, we calculated the amplitude, period, and phase of the Chandler nutation using LSM. The quasi-periodic instability of 33 values of the Chandler wobble amplitude is detected with a period of 54.5 years using LSM (it was 38.5 years from the BLZ data 1949-1985); the amplitude of that quasi-periodic variation is 0 .''087 (0 .''06 from BLZ data). The amplitude of the Chandler nutation varies between minimum of 0 .''012 (at 2019.3) and a maximum of 0 .''23 (at 1994.1); the period is stable, but the phase is not stable. We applied the Abbe's criterion to explain the variability in 33 values of the Chandler wobble amplitude and the hypothesis that there is no trend in these 33 values is rejected based on the criterion. The obtained amplitude modulation is in accordance with previous studies, but also with our own results based on the BLZ data. Probably, the cause lies in the hydro-atmospheric circulation that could influence calculated quasi-periodic variation. A possible explanation can be found in the change in core-mantle electromagnetic coupling (in agreement with the last few years' investigations). In recent papers, it has been indicated that the effects of geomagnetic jerks are more important for exciting a free nutation than the net effect of atmosphere and oceans.

Multi-frequency lunar perturbations in the Earth pole oscillatory process

The influence of the dynamic effects of the Earth-Moon system spatial motion on the perturbed Chandler wobble of the Earth pole is studied on the basis of the celestial mechanical approach and the analysis of astrometric data of observations of International Earth Rotation and Reference Systems Service. The additional harmonic of the oscillatory process with a frequency close to the Chandler frequency is determined. It is shown that the found harmonic leads to variations in the Chandler wobble amplitude with a period of about 40 years.

Free motion of the deformable Earth’s pole

Free motion of the Earth pole is studied on the base of Euler-Liouville dynamic equations of the deformable Earth motion around its center of mass. The dependence of the external influence amplitude from dissipation coefficients is found for the stationary mode of the Earth pole oscillations on the Chandler frequency and external disturbance with the Chandler frequency. It is shown that the Chandler wobble amplitude is sensitive to the difference between the Chandler frequency and those close to it and to the nonlinear dissipation coefficients. The stability conditions of the steady Chandler wobble are defined.

Mars rotation determination from a moving rover using Doppler tracking data: What could be done?

This paper is a case study providing some insights on what improvement could be achieved on the Mars Orientation and rotation Parameters (MOP) determination using radio tracking data from a moving rover. Thanks to high-performance mobility systems onboard new generation of rovers like ExoMars 2020, the position of the rover can be precisely known with respect to its previous position. This characteristic, together with the long life of the rovers and their steerable high-gain-antenna communication system, is shown here to provide an unexpected opportunity to improve the MOP determination. This paper presents the results of numerical simulations involving radio-science experiments between the moving rover and the Earth ground stations as well as between the rover and an orbiting spacecraft. The benefits of combining both links (direct-to-Earth and rover-orbiter) for the MOP determination is also assessed. The impacts of the spacecraft position accuracy as well as the frequency band used to communicate with it are quantified. It is shown that, after one Martian year of operation, the polar motion could be determined with 5 milliarcsecond (mas) of precision (formal error) from the rover-orbiter Doppler link, while it cannot be determined with usual equatorial lander-to-Earth radio link. This would allow for the first time the direct detection of the Chandler wobble amplitude in the polar motion of Mars, which is an important quantity to constrain the planet interior and atmospheric models. Although the moving rover Doppler data alone barely improve the current precision on the other MOP (like the length-of-day and nutation), a combination of those together with historical and future lander data would definitely help to fill gaps in the MOP signal and to decorrelate between the estimated parameters, thereby reducing the uncertainties in their determination.

“Escargot Effect” and the Chandler Wobble Excitation

We study the Chandler wobble (CW) of the pole from 1846 to 2017 extracted by the Panteleev filtering. The CW has period of 433 days, average amplitude of 0.13 milliarcseconds (mas) which is changing, and phase jump by ϕ in 1930-th. The CW amplitude strongly (almost to zero) decreases in 1930-th and 2010-th with the phase jump in 1930th. The envelope model contains 83- and 42-years quasi-periodicities. We think the first one can be represented by the 166-years changes of the envelope, crossing zero in 1930th. We reconstruct Chandler input excitation based on the Euler-Liouville equation. Its amplitude has ∼ 20-years variations. We explain this based on simple model and prove, that they appear in consequence of 42-years modulation of CW. The excitation amplifies the amplitude of CW for ∼ 20 years then damps it for another ∼ 20 years.The analysis of the modulated CW signal in a sliding window demonstrates the specific effect, we called the “escargot effect”, when instantaneous “virtual” retrograde component appears in the purely prograde (at long-time interval) signal. Chandler excitation envelope shape is similar to this instantaneous retrograde component, which reflects the changes of ellipticity of the approximation ellipse.

Variable Chandler and Annual Wobbles in Earth’s Polar Motion During 1900–2015

The Chandler wobble (CW) and annual wobble (AW) are the two main components of polar motion, which are difficult to separate because of their very close periods. In the light of Fourier dictionary and basis pursuit method, a Fourier basis pursuit (FBP) spectrum is developed, which can reduce spectral smearing and leakage caused by the finite length of the time series. Further, a band-pass filtering method based on FBP spectrum (FBPBPF), which can effectively suppress the edge effect, is proposed in this paper. The simulation test results show that the FBPBPF method can effectively suppress the edge effect caused by spectral smearing and leakage and that its reconstruction accuracy at the boundary is approximately three times higher than the Fourier transform band-pass filtering method, which is based on Hamming windowed FFT spectrum, in extracting quasi-harmonic signals. The FBPBPF method is then applied to Earth’s polar motion data during 1900–2015. Through analyzing the amplitude and period variations of CW and AW, and calculating the eccentricity variation of the AW, we found that: (1) the amplitude of the CW is currently at a historic minimum level, and it is even possible to diminish further until a complete stop; and (2) the eccentricity of the AW has a gradually decreased fluctuation during the last 116 years.

Long-term polar motion prediction using normal time–frequency transform

This paper presents normal time–frequency transform (NTFT) application in harmonic/quasi-harmonic signal prediction. Particularly, we use the normal wavelet transform (a special NTFT) to make long-term polar motion prediction. Instantaneous frequency, phase and amplitude of Chandler wobble, prograde and retrograde annual wobbles of Earth’s polar motion are analyzed via the NTFT. Results show that the three main wobbles can be treated as quasi-harmonic processes. Current instantaneous harmonic information of the three wobbles can be acquired by the NTFT that has a kernel function constructed with a normal half-window function. Based on this information, we make the polar motion predictions with lead times of 1 year and 5 years. Results show that our prediction skills are very good with long lead time. An abnormality in the predictions occurs during the second half of 2005 and first half of 2006. Finally, we provide the future (starting from 2013) polar motion predictions with 1- and 5-year leads. These predictions will be used to verify the effectiveness of the method proposed in this paper.

The Earth’s variable Chandler wobble

Aims. We investigated the causes of the Earth’s Chandler wobble variability over the past 60 years. Our approach is based on integrating of the atmospheric and oceanic angular momentum computed by global circulation models. We directly compared the result of the integration with the Earth’s pole coordinate observed by precise astrometric, space, and geodetic techniques. This approach differs from the traditional approach in which the observed polar motion is transformed into a so-called geodetic excitation function, and compared afterwards with the angular momentum of the external geophysical fluid layers.Methods. In the time domain, we integrated the atmospheric angular momentum time series from the National Center for Environmental Prediction/National Center for Atmospheric Research Reanalysis project and the oceanic angular momentum data from the ECCO consortium. We extracted the Chandler wobble from this modeled polar motion by singular spectrum analysis, and compared it with the Chandler wobble extracted from the observed polar motion given by the International Earth Rotation and Reference Systems Service data.Results. We showed that the combination of the atmosphere and the oceans explains most of the observed Chandler wobble variations, and is consistent with results reported in the literature and obtained with the traditional approach. Our approach allows one to appreciate the separate contributions of the atmosphere and the oceans to the various bumps and valleys observed in the Chandler wobble. Though the atmosphere explains the Chandler wobble amplitude variations between 1949 and 1970, the reexcitation of the Chandler wobble that begins in the 1980s, after a minimum around 1970, and that reaches its maximum in the late 1990s is due to the oceans, while the atmospheric contribution remains stable within the same period.

Chandler wobble: two more large phase jumps revealed

Investigations of the anomalies in the Earth rotation, in particular, the polar motion components, play an important role in our understanding of the processes that drive changes in the Earth's surface, interior, atmosphere, and ocean. This paper is primarily aimed at investigation of the Chandler wobble (CW) at the whole available 163-year interval to search for the major CW amplitude and phase variations. First, the CW signal was extracted from the IERS (International Earth Rotation and Reference Systems Service) Pole coordinates time series using two digital filters: the singular spectrum analysis and Fourier transform. The CW amplitude and phase variations were examined by means of the wavelet transform and Hilbert transform. Results of our analysis have shown that, besides the well-known CW phase jump in the 1920s, two other large phase jumps have been found in the 1850s and 2000s. As in the 1920s, these phase jumps occurred contemporarily with a sharp decrease in the CW amplitude.

Nonlinear mechanism for polar motion with period of 7 months

The 7 month-period (sub-Chandler) wobble is considered with respect to the nonlinear dynamical equation of polar motion. Starting with the frequency modulation of Chandler wobble (CW) in the model developed by introduction of damping from perturbed visco-elastic deformation, the rotation equation of the CW becomes a resonance model with a time-dependent parameter. According to evolution calculation, the parameter resonance model is essentially identical to the reality of CW observations. If the frequency of CW is modulated about 3 by visco-elastic deformation, then the amplitude of CW will be modulated by greater than 70 . On the other hand, bifurcation may occur according to the nonlinear dynamical system of the parameter resonance model, i.e. a pair of solutions splitting from the main CW. One is the 7-month-period wobble and the other is a motion with a period of about 28 months. Although the latter is very weak, the 7-month-period wobble will be observed as the stability condition is satisfied. The maximum amplitude is about 22.89 mas and the average 12.65 mas. This is identical to what is observed in reality.

Random walk of the Earth's pole related to the Chandler wobble excitation

The equation governing the polar motion shows that the polar secular drift and the Chandler wobble amplitude are related to each other. In particular, a drift of the mean pole position comes out as a consequence of the maintenance of the Chandler wobble by possible step perturbations of the Earth's inertia tensor. The minimum excitation functions necessary to explain the Chandler wobble amplitude variations for the period 1901—84 are derived from the Chandler term, with the hypothesis that the excitations follow a uniform random distribution in time. It is shown that they have the statistical properties of the steps of a two-dimensional random walk. These functions are then used to derive, from a statistical simulation, a lower limit of the secular drift which may result from the excitation of the Chandler wobble. The drift generated by the random walk is of the same order of magnitude as the observed secular drift for the period 1901—84, but their time dependence is different. This indicates that the observed secular drift cannot be explained as the consequence of an excitation of the Chandler wobble by random steps of the Earth's inertia tensor. However, the possible contribution of the Chandler wobble excitation to the polar drift has to be taken into account when other mechanisms, such as lithospheric rebound related to deglaciation, are proposed.

Reevaluation of the Chandler wobble seismic excitation from recent data

Since 1977, seismic moment tensors of major earthquakes have been systematically determined while high accuracy polar motion data have been made available from space techniques. The seismic excitation of the Chandler wobble during the period 1977–1983 has been obtained using the centroid moment tensor solutions of 1287 strong and moderate earthquakes occurring during that period. Changes in the Earth inertia tensor induced by earthquakes, which are derived from the elastic theory of dislocation, are assumed to be step functions of time. From a comparison between the derived synthetic Chandler wobble and the observed one, it turns out that seismic excitation is far too small (by about two orders of magnitude) to explain the Chandler wobble amplitude variations during 1977–1983, in particular the increase in the wobble amplitude between 1980 and 1983. During the last two decades, seismic moments of major earthquakes remained on the level of 10 27 to 10 28 dyne cm, whereas in the past, events of high magnitudes corresponding to seismic moments on the order of 10 30 to 10 31 dyne cm have been frequently reported. As the later values are those needed to explain the amplitude variations of the Chandler wobble, the problem of the validity of magnitude estimations in the past and frequency of occurrence of great earthquakes is raised, as well as the question of validity of previous positive conclusions on the influence of earthquakes on the Chandler wobble excitation.

Random and long periodic variations in the earth's motion

Abstract Observations of the Earth's rotation exhibit random, secular and periodic variations in rate (changes in the length of the day l.o.d.) and in direction (polar motion). These variations are of great significance, because they are probably associated with geophysical phenomena. A matter of particular interest is the question of whether these fluctuations in the l.o.d. and in polar motion can arise from a common geophysical cause. Comparison of the values of l.o.d. with the amplitude of Chandler wobble for the last 80 years indicates that this hypothesis cannot be disregarded; however the data on long period fluctuations are difficult to interpret and the evidence is too poor to permit any conclusion. Also the nature of these fluctuations is not at all clear, because apparent periodic variations can also arise from a random process. Periods of about 4 and 7 years found by us and other authors, however, should be real and associated with meteorological effects.

On the amplitude of the Chandler wobble

The change in the inertia tensor of the Earth, due to the mass shift following a seismic event, has been computed by several authors for non-rotating earth models. Rotation is taken into account in the present paper, and the additional change in the inertia tensor is computed for an equivalent earth model, in which the axis of geometrical symmetry becomes tilted instead of the axis of greatest inertia. Rotation is thus seen to produce an increase by a factor 1.4 in the amplitude variation of the Chandler wobble, with respect to the non-rotating case, which, when added to the 1.4 amplitude increase due to the precessional re-adjustment of the equatorial bulge, gives a factor of 2 increase of the Chandler wobble amplitude with respect to the case of a rigid earth model.

The energy release in great earthquakes

The conventional magnitude scale M suffers saturation when the rupture dimension of the earthquake exceeds the wavelength of the seismic waves used for the magnitude determination (usually 5–50 km). This saturation leads to an inaccurate estimate of energy released in great earthquakes. To circumvent this problem the strain energy drop W (difference in strain energy before and after an earthquake) in great earthquakes is estimated from the seismic moment M0. If the stress drop Δσ is complete, W = W0 = (Δσ/2μ)M0 ∼ M0/(2×104), where μ is the rigidity; if it is partial, W0 gives the minimum estimate of the strain energy drop. Furthermore, if Orowan's condition, i.e., that frictional stress equal final stress, is met, W0 represents the seismic wave energy. A new magnitude scale Mw is defined in terms of W0 through the standard energy-magnitude relation log W0 = 1.5Mw + 11.8. Mw is as large as 9.5 for the 1960 Chilean earthquake and connects smoothly to Ms (surface wave magnitude) for earthquakes with a rupture dimension of about 100 km or less. The Mw scale does not suffer saturation and is a more adequate magnitude scale for great earthquakes. The seismic energy release curve defined by W0 is entirely different from that previously estimated from Ms. During the 15-year period from 1950 to 1965 the annual average of W0 is more than 1 order of magnitude larger than that during the periods from 1920 to 1950 and from 1965 to 1976. The temporal variation of the amplitude of the Chandler wobble correlates very well with the variation of W0, with a slight indication of the former preceding the latter. In contrast, the number N of moderate to large earthquakes increased very sharply as the Chandler wobble amplitude increased but decreased very sharply during the period from 1945 to 1965, when W0 was largest. One possible explanation for these correlations is that the increase in the wobble amplitude triggers worldwide seismic activity and accelerates plate motion which eventually leads to great decoupling earthquakes. This decoupling causes the decline of moderate to large earthquake activity. Changes in the rotation rate of the earth may be an important element in this mechanism.