Polar Motion Research Articles

Inner core static tilt inferred from intradecadal oscillation in the Earth’s rotation

The presence of a static tilt between the inner core and mantle is an ongoing discussion encompassing the geodynamic state of the inner core. Here, we confirm an approximate 8.5 yr signal in polar motion is the inner core wobble (ICW), and find that the ICW is also contained in the length-of-day variations of the Earth’s rotation. Based on the determined amplitudes of the ICW and its good phase consistency in both polar motion and the length-of-day variations, we infer that there must be a static tilt angle θ between the inner core and the mantle of about 0.17 ± 0.03°, most likely towards ~90°W relative to the mantle, which is two orders of magnitude lower than the 10° assumed in certain geodynamic research. This tilt is consistent with the assumption that the average density in the northwestern hemisphere of the inner core should be greater than that in the other regions. Further, the observed ICW period (8.5 ± 0.2 yr) suggests a 0.52 ± 0.05 g/cm3 density jump at the inner core boundary.

Comparing Experimentally-Measured Sand’s Times with Concentrated Solution Theory Predictions in a Polymer Electrolyte

We compare the electrochemically measured Sand’s time, the time required for the cell potential to diverge when the applied current density exceeds the limiting current, with theoretical predictions for a 0.47 M poly(ethylene oxide) (5 kg mol−1)/LiTFSI electrolyte. The theoretical predictions are made using concentrated solution theory which accounts for both concentration polarization and polymer motion, using independently measured parameters that depend on concentration, c: conductivity (κ), salt diffusion coefficient (D), cationic transference number with respect to the solvent velocity (), thermodynamic factor and partial molar volume of the salt (); is the mean molar activity coefficient of the salt. We find quantitative agreement between experimental data and theoretical predictions. We derive a generalized analytical expression for Sand’s time for electrolytes based on dilute solution theory. This expression correctly predicts the divergence of the Sand’s time at the limiting current, in agreement with experimental data and concentrated solution theory predictions. When the applied current is large compared to the limiting current, the analytical expression approaches the standard expression for Sand’s time used in the literature.

Precise prediction of polar motion using sliding multilayer perceptron method combining singular spectrum analysis and autoregressive moving average model

The precise prediction of polar motion parameters is needed for the astrogeodynamics, navigation and positioning of the deep space probe. However, the current prediction methods are limited to predicting polar motion for specific periods, either short- or long-term. In this study, a sliding multilayer perceptron (MLP) method combined singular spectrum analysis (SSA) and autoregressive moving average (ARMA) for short- and long-term polar motion prediction was proposed. MLP was introduced into PM prediction due to its automatic learning characteristics and its ability to effectively process nonlinear and multi-dimensional data. The SSA was used to extract and predict the principal components of polar motion, while the remaining components were predicted using ARMA. In the meantime, SSA and ARMA were used to provide training data and target learning data for the MLP model. MLP input data were constructed by sliding processing with a window of 7 days, composed of n series of the same length (18 years). Finally, MLP was employed to predict the residuals generated during SSA and ARMA prediction. To evaluate the accuracy of the proposed method, the polar motion prediction was applied for a 364-day lead time based on the IERS EOP 14C04 product. The method outperformed the IERS Bulletin A, as demonstrated by the mean-absolute errors of the x and y components of polar motion on the 30th day, which were lower (5.14 mas and 3.37 mas, respectively) than those predicted by IERS Bulletin A (6.66 mas and 3.94 mas). Similarly, the mean-absolute errors on the 364th day were 17.79 mas and 16.29 mas, respectively, compared to the 19.24 mas and 18.81 mas predicted by IERS Bulletin A.Graphical

Analysis of sub-daily polar motion derived from GPS with different temporal resolutions

Analysis of sub-daily polar motion derived from GPS with different temporal resolutions

Deep ensemble geophysics-informed neural networks for the prediction of celestial pole offsets

SUMMARY Celestial Pole Offsets (CPO), denoted by dX and dY, describe the differences in the observed position of the pole in the celestial frame with respect to a certain precession-nutation model. Precession and nutation components are part of the transformation matrix between terrestrial and celestial systems. Therefore, various applications in geodetic science such as high-precision spacecraft navigation require information regrading precession and nutation. For this purpose, CPO can be added to the precession-nutation model to precisely describe the motion of the celestial pole. However, as Very Long Baseline Interferometry (VLBI)—currently the only technique providing CPO—requires long data processing times resulting in several weeks of latency, predictions of CPO become necessary. Here we present a new methodology named Deep Ensemble Geophysics-Informed Neural Networks (DEGINNs) to provide accurate CPO predictions. The methodology has three main elements: (1) deep ensemble learning to provide the prediction uncertainty; (2) broad-band Liouville equation as a geophysical constraint connecting the rotational dynamics of CPO to the atmospheric and oceanic Effective Angular Momentum (EAM) functions and (3) coupled oscillatory recurrent neural networks to model the sequential characteristics of CPO time-series, also capable of handling irregularly sampled time-series. To test the methodology, we use the newest version of the final CPO time-series of International Earth Rotation and Reference Systems Service (IERS), namely IERS 20 C04. We focus on a forecasting horizon of 90 days, the practical forecasting horizon needed in space-geodetic applications. Furthermore, for validation purposes we generate an independent global VLBI solution for CPO since 1984 up to the end of 2022 and analyse the series. We draw the following conclusions. First, the prediction performance of DEGINNs demonstrates up to 25 and 33 percent improvement, respectively, for dX and dY, with respect to the rapid data provided by IERS. Secondly, predictions made with the help of EAM are more accurate compared to those without EAM, thus providing a clue to the role of atmosphere and ocean on the excitation of CPO. Finally, free core nutation period shows temporal variations with a dominant periodicity of around one year, partially excited by EAM.

Universal Time Effects on Substorm Growth Phases and Onsets

AbstractUniversal Time (UT) variations in many magnetospheric state indicators and indices have recently been reviewed by Lockwood and Milan (2023, https://doi.org/10.3389/fspas.2023.1139295). Key effects are introduced into magnetospheric dynamics by the eccentric nature of Earth's magnetic field, features that cannot be reproduced by a geocentric field model. This paper studies the UT variation in the occurrence of substorm onsets and uses a simple Monte‐Carlo model to show how it can arise for an eccentric field model from the effect of the diurnal motions of Earth's poles on the part of the geomagnetic tail where substorms are initiated. These motions are in any reference frame that has an X axis that points from the center of the Earth to the center of the Sun and are caused by Earth's rotation. The premise behind the model is shown to be valid using a super‐posed epoch study of the conditions leading up to onset. These studies also show the surprising degree of preconditioning ahead of the growth phase that is required, on average, for onset to occur. A key factor is the extent to which pole motions caused by Earth's rotation influence the near‐Earth tail at the relevant X coordinate. Numerical simulations by a global MHD model of the magnetosphere reveal the effect required to generate the observed UT variations and with right order of amplitude, albeit too small by a factor of about one third. Reasons why this discrepancy may have arisen for the simulations used are discussed.

On the external forcing of global eruptive activity in the past 300 years

The decryption of the temporal sequence of volcanic eruptions is a key step in better anticipating future events. Volcanic activity results from a complex interaction between internal and external processes, with time scales spanning multiple orders of magnitude. We review periodicities that have been detected or correlated with volcanic eruptions/phenomena and interpreted as resulting from external forces. Taking a global perspective and longer time scales than a few years, we approach this interaction by analyzing three time-series using singular spectral analysis: the global number of volcanic eruptions (NVE) between 1700 and 2022, the number of sunspots (ISSN), a proxy for solar activity, and polar motion (PM) and length of day (lod), two proxies for gravitational force. Several pseudo-periodicities are common to NVE and ISSN, in addition to the 11-year Schwabe cycle that has been reported in previous work, but NVE shares even more periodicities with PM. These quasi-periodic components range from −5 to −130 years. We interpret our analytical results in light of the Laplace’s paradigm and propose that, similarly to the movement of Earth’s rotation axis, global eruptive activity is modulated by commensurable orbital moments of the Jovian planets together with Pluto, whose influence is also detected in solar activity.

Modulation of Mars’ diurnal polar motion by atmospheric dust cycles

The atmospheric dust cycle plays a crucial role in impacting the atmosphere of Mars, and may also introduce changes in angular momentum that can influence the planet's polar motion. However, the potential connections between polar motion and atmospheric dust cycles have not yet been explored. In this study, we computed atmosphere-excited polar motion and the atmospheric dust cycle index (ADCI) separately from the Mars Climate Database and observed dust optical depth for Martian Years 24–33. We found a strong correlation between diurnal polar motion amplitude change and ADCI, with significance levels above 99%. Our results suggest that atmospheric dust cycles significantly modulate diurnal polar motion. Wavelet transform analyses further revealed other factors, such as water ice clouds, may be responsible for higher frequency modulations of polar motion apart from the dust-related signals. Interdisciplinary studies involving Mars' atmospheric activities and rotational variations can significantly advance our understanding of planetary atmospheric science and global rotational dynamics.

Improving the accuracy of polar motion prediction using a hybrid least squares and long short-term memory model

Earth rotation parameters (ERPs) are essential for transforming between the celestial and terrestrial reference frames, and for high-precision space navigation and positioning. Among the ERPs, polar motion (PM) is a critical parameter for analyzing and understanding the dynamic interaction between the solid Earth, atmosphere, ocean, and other geophysical fluids. Traditional methods for predicting the change in ERPs rely heavily on linear models, such as the least squares (LS) and the autoregressive (AR) model (LS + AR). However, variations in ERP partly reflect non-linear effects in the Earth system, such that the predictive accuracy of linear models is not always optimal. In this paper, long short-term memory (LSTM), a non-linear neural network, is employed to improve the prediction of ERPs. Polar motion prediction experiments in this study are conducted using the LSTM model and a hybrid method LS + LSTM model based on the IERS EOP14C04 time series. Compared with Bulletin A, the PMX and PMY prediction accuracy can reach a maximum of 33.7% and 31.9%, respectively, with the LS + LSTM model. The experimental results show that the proposed hybrid model displays a better performance in mid- and long-term (120–365 days) prediction of polar motion.Graphical

On the importance of accurate pole and station coordinates for VLBI Intensive baselines

Very long baseline interferometry (VLBI) is a geodetic technique capable of deriving the complete set of Earth orientation parameters, including the highly variable Earth’s phase of rotation. This observable can be expressed through UT1–UTC, the difference between the Universal Time and the Coordinated Universal Time. The so-called Intensive sessions, or Intensives, are typically 1-h sessions between two to three stations that are observed daily with the primary goal of determining UT1–UTC with a short latency. In this publication, we examine the impact of erroneous a priori information on the UT1–UTC estimation with VLBI Intensive sessions in a systematic way and on a global scale. Our findings are based on a simulation study which is carried out on a regular 10 times 10 degree grid of artificial telescopes. In the simulations, realistic errors are introduced in the station coordinates, polar motion and nutation to get a global picture of the impact of these errors on the estimation of UT1–UTC. Our results reveal that in contrast to errors in the horizontal components of the station coordinates, an error in the station height only slightly affects the UT1–UTC estimate. North–south-oriented baselines are in general strongly affected by errors in the a priori information. In all cases, very short and very long baselines as well as baselines with a midpoint close to the equatorial plane are less robust. On the other hand, east–west-oriented baselines, except equatorial baselines, seem to be rather resistant against errors of these a priori values.

Geophysically Informed Machine Learning for Improving Rapid Estimation and Short‐Term Prediction of Earth Orientation Parameters

AbstractRapid provision of Earth orientation parameters (EOPs, here polar motion and dUT1) is indispensable in many geodetic applications and also for spacecraft navigation. There are, however, discrepancies between the rapid EOPs and the final EOPs that have a higher latency but the highest accuracy. To reduce these discrepancies, we focus on a data‐driven approach, present a novel method named ResLearner, and use it in the context of deep ensemble learning. Furthermore, we introduce a geophysically constrained approach for ResLearner. We show that the most important geophysical information to improve the rapid EOPs is the effective angular momentum functions of atmosphere, ocean, land hydrology, and sea level. In addition, semidiurnal, diurnal, and long‐period tides coupled with prograde and retrograde tidal excitations are important features. The influence of some climatic indices on the prediction accuracy of dUT1 is discussed, and El Niño Southern Oscillation is found to be influential. We developed an operational framework, providing the improved EOPs on a daily basis with a prediction window of 63 days to fully cover the latency of final EOPs. We show that under the operational conditions and using the rapid EOPs of the International Earth Rotation and Reference Systems Service (IERS), we achieve improvements as high as 60%, thus significantly reducing the differences between rapid and final EOPs. Furthermore, we discuss how the new final series IERS 20 C04 is preferred over 14 C04. Finally, we compare against EOP hindcast experiments of the European Space Agency, on which ResLearner presents comparable improvements.

Dynamic mode decomposition and bivariate autoregressive short-term prediction of Earth rotation parameters

Abstract In this contribution two new approaches are applied to predict polar motion and length-of-day. The first one is based on Dynamic Mode Decomposition (DMD), that is purely data-driven and is capable of reconstructing and forecasting time series in one numerical procedure. The other one is based on a vector autoregression of order p – VAR(p), which is a vector counterpart of AR(p) that accounts for an evolution of variables in time and a coevolution with other variables. DMD was applied to polar motion and length-of-day whilst VAR(p) to a joint prediction of polar motion. A prediction experiment concerned 30-day forecast horizon with a 7-day shift. It was performed separately for years 2017–2022 giving 48 predictions within each year. This study uses IERS EOP 14 C04 (IAU2000) as a reference for all computations and a mean absolute prediction error (MAPE) as a measure of prediction quality. For DMD, MAPEs for x coordinate of the pole vary from 0.22–0.30 mas for the 1st day and 6.64–8.56 mas for the 30th day of prediction depending on the year whilst those values vary from 0.20–0.27 mas and 5.27–7.66 mas for VAR(p) based prediction. Corresponding values for y coordinate of the pole vary from 0.15–0.23 mas and 4.27–5.93 mas for DMD, whilst 0.13–0.21 mas and 3.46–3.82 mas for VAR(p). In case of LOD forecast, MAPEs vary from 0.023–0.031 ms for the 1st day and 0.142–0.205 ms for the 30th day depending on the year.

Tunneling time and Faraday/Kerr effects in systems

We review the generalization of tunneling time and anomalous behaviour of Faraday and Kerr rotation angles in parity and time systems. Similarities of two phenomena are discussed, both exhibit a phase transition-like anomalous behaviour in a certain range of model parameters. Anomalous behaviour of tunneling time and Faraday/Kerr angles in systems is caused by the motion of poles of scattering amplitudes in the energy/frequency complex plane.

Analysis of The Itsg-Grace Daily Models in The Determination of Polar Motion Excitation Function

ABSTRACT The main aim of this study is to evaluate the usefulness of Institute of Geodesy at Graz University of Technology (ITSG) daily gravity field models in the determination of hydrological angular momentum (HAM) at nonseasonal time scales. We compared the equatorial components (χ1 and χ2) of HAM calculated with the ITSG daily gravity field models (ITSG-Gravity Recovery and Climate Experiment [ITSG-GRACE] 2016 and ITSG-GRACE 2018) with HAM and sea-level angular momentum (SLAM) from hydrological land surface discharge model (LSDM) and the hydrological signal in the polar motion excitation (known as geodetic residuals [GAO]). Data from ITSG have a daily temporal resolution and allow us to determine oscillations with higher frequencies than the more commonly used monthly data. We limited our study to the period between 2004 and 2011 because of the gaps in GRACE observations before and after this period. We evaluated HAM obtained from ITSG GRACE models in spectral and time domains and determined the amplitude spectra of the analyzed series in the spectral range from 2 to 120 days. Our analyses confirm the existence of a sub-monthly signal in the HAM series determined from ITSG daily data. We observed a similar signal in LSDM-based HAM, but with notably weaker amplitudes. We also observed common peaks around 14 days in the amplitude spectra for the GAO- and ITSG-based series, which may be related to the Earth’s tides. ITSG daily gravity field models can be useful to determine the equatorial components of HAM at nonseasonal time scales.

A modified stochastic model for LS+AR hybrid method and its application in polar motion short-term prediction

Short-term (up to 30 days) predictions of Earth Rotation Parameters (ERPs) such as Polar Motion (PM: PMX and PMY) play an essential role in real-time applications related to high-precision reference frame conversion. Currently, least squares (LS) + auto-regressive (AR) hybrid method is one of the main techniques of PM prediction. Besides, the weighted LS + AR hybrid method performs well for PM short-term prediction. However, the corresponding covariance information of LS fitting residuals deserves further exploration in the AR model. In this study, we have derived a modified stochastic model for the LS + AR hybrid method, namely the weighted LS + weighted AR hybrid method. By using the PM data products of IERS EOP 14 C04, the numerical results indicate that for PM short-term forecasting, the proposed weighted LS + weighted AR hybrid method shows an advantage over both the LS + AR hybrid method and the weighted LS + AR hybrid method. Compared to the mean absolute errors (MAEs) of PMX/PMY short-term prediction of the LS + AR hybrid method and the weighted LS + AR hybrid method, the weighted LS + weighted AR hybrid method shows average improvements of 6.61%/12.08% and 0.24%/11.65%, respectively. Besides, for the slopes of the linear regression lines fitted to the errors of each method, the growth of the prediction error of the proposed method is slower than that of the other two methods.

High-precision polar motion prediction using EOP_20_C04 and EAM based on CSLS+AR and CSLS+LSTM methods

SUMMARY High-precision prediction of polar motion (PM) plays an important role in fields such as astronomy, geodesy, navigation and aerospace. Incorporating information on the effective angular momentum (EAM) of the geophysical fluid is an effective way to improve the precision of PM prediction. Based on the EOP_20_C04 data set and the EAM function, this study applies complex segmented least-squares (CSLS) + the long short term memory (LSTM) neural network and CSLS + autoregression (AR) models to predict PM. For the 6-d PM prediction, the mean absolute errors (MAEs) achieved by CSLS+AR are 1.03 and 0.8 mas in the X- and Y-directions, respectively, corresponding to reductions of 45.80 and 31.97 per cent when compared to predictions reported routinely in Bulletin A of the International Earth Rotation and Reference Systems Service (IERS). For the 365-d PM prediction, the MAEs gained by CSLS+LSTM model are 14.58 and 10.59 mas in the X- and Y-directions, respectively, corresponding to reductions of 28.17 and 51.09 per cent compared to predictions of the Bulletin A, and the prediction accuracy attained by CSLS+LSTM is higher than other prediction schemes. The experimental results show that, when considering EAM information, the CSLS+AR model can achieve better prediction accuracy for short-term PM prediction, however, the CSLS+LSTM model is more effective for medium- and long-term PM prediction owning to the excellent nonlinear fitting capability of the LSTM deep learning algorithm.

A new medium-long term polar motion prediction method based on sliding average within difference series

Abstract In response to the problem that the input data and combination method of existing polar motion (PM) prediction methods are relatively single, which leads to the limited satisfaction of PM prediction accuracy by major satellite navigation orbiting systems and deep space exploration projects. This study borrows the idea of differential method and proposes to push back the forecast after selecting several samples within the PM Y, X and Y–X series by sliding average. In the constructed new series, the high-frequency terms are effectively attenuated. Then, the pushing back forecasts are combined in pairs with those of the traditional method. After least-squares extrapolation and autoregressive (LS + AR) modeling, the optimal combination was found. Among them, the prediction of PMX is obtained by subtracting the forecast of PMY of traditional method and the prediction of PM(Y–X) of the sliding average method, the forecast of PMY is obtained by adding the forecast of PMX of the sliding average method and the forecast of PM(Y–X) of the traditional method. The results of the 418-week hindcast experiment from 2012 to 2021 show that the proposed method has a greater improvement than the traditional method, and the corresponding 1–365-day mean absolute error (MAE) are improved by 31.46% and 21.11%, respectively, on average. It has certain advantages over the IERS Bulletin-A in the medium-long term, and the 150-day lead time predictions, the MAE of PMX and PMY were 14.678 and 17.232 mas, respectively, which were less than the 17.833 and 20.769 mas predicted by IERS Bulletin A. This not only verifies that the stability and ability of the proposed method have some competitive ability, but also provides new ideas for other time-series forecasting studies.

Evaluation of the first three years of Vgos 24 h sessions using a Kalman filter with C5++

We analyzed the first three years of VGOS 24 h sessions, and evaluated the performance in terms of Earth orientation parameters (EOP) and station positions. We estimated radio source coordinates which might be of particular importance in VGOS due to the different observing frequencies compared to legacy S/X VLBI. We investigated the impact of this procedure in the determination of the celestial reference, and detected possible increased crosstalk between radio source positions and nutation. We, thus, created an updated source coordinate catalogue that contains information from the VGOS observations and utilized that as our a priori for further analysis. We found that this procedure significantly attenuates mean biases in the estimated EOP time series. We then utilized a kalman filter with an empirically tuned stochastic modelling for nutation and polar motion and estimated repeatabilities on the 60–80 mu as level for nutation, and 100–130 mu as level for polar motion. The station position repeatabilities were evaluated to be 1.80 and 2.12 mm for the east and north components and 3.98 mm for the vertical, while the baseline length repeatabilities were estimated to be 4.22 mm at 6000 km. These results are promising with respect to the expected future VGOS performance, while increased attention should be paid to the celestial frame determination in the VGOS observing bands.Graphical

Performance of the IVS R1 and R4 sessions

The International VLBI Service for Geodesy and Astrometry (IVS) has observed the weekly IVS-R1 (R1) and IVS-R4 (R4) series of sessions since 2002. These regular series are generally stable in the sense that the networks were designed to be similar from week to week. The uniformity of these series has allowed researchers to conduct many scientific investigations. The IVS also observes with other networks that allow continued sampling of data from all VLBI stations, but the R1 and R4 observing sessions are a dominant part of overall VLBI observing accounting for 1841 sessions out of a total of 3129 24-hour sessions from 2002.0 to 2020.0 (where the last R1 and R4 in 2019 was on December 30 and December 26, respectively). In this paper, we investigate the evolution of these series in terms of their observing networks. We also discuss the construction of the R1 and R4 networks and the scheduling of these sessions. The performance of these networks in terms of the formal precision of polar motion have improved by factors of 2–3 over the period from 2002.0 to 2018.0. UT1 precision improved by a factor of about 1.2–1.5. The main reason for this improvement is the increased size of the networks. We also discuss the effect on this improvement arising from changes in the data rate and the number of observed sources. There is some degradation in performance after 2018 that is most likely due to a decline in the number of available network stations.

Evidence for large disturbances of the Ediacaran geomagnetic field from West Africa

Constraining the paleogeography of the Ediacaran is crucial for understanding the extensive tectonic, biological and geochemical changes that occurred during that epoch. Paleomagnetism is an essential tool for reconstructing the Ediacaran paleogeography but it is complicated because the paleomagnetic data of that age display unusually fast and large directional oscillations. Two main competing hypotheses have been proposed: the occurrence of very fast True Polar Wander (TPW) episodes, which correspond to the motion of the planetary spin axis relative to the solid Earth, or strong geomagnetic field disturbances that could potentially be dominated by an equatorial dipole field. Their implications for paleogeographic reconstructions are radically different as TPW would result in a major latitudinal shift of continents of up to ∼ 90°. In this study, we focus on one rapid paleomagnetic change recorded in pyroclastic rocks of the Ouarzazate Group in the Anti-Atlas Belt (Morocco) that has been interpreted to reflect an exceptionally fast episode of True Polar Wander between ∼ 575 and 565 Ma. To further test this hypothesis, tight constraints on the rate of the paleomagnetic directional change are needed, as TPW is speed-limited by mantle viscosity. Here, we present high-resolution Chemical Abrasion Isotope-Dilution Thermal Ionization Mass Spectrometry (CA-ID-TIMS) U-Pb dates on zircons from seven pyroclastic levels distributed stratigraphically below, in between and above the horizons where the large paleomagnetic change is observed. Based on these new data, we estimate the associated lower bound rate of the apparent polar motion related to this abrupt paleomagnetic change to be 11.6°/Myrs [5.5 – 17.9]. This value is much higher than the TPW speed limit estimated from numerical simulations, suggesting that this large paleomagnetic change cannot be explained by TPW. It could rather be associated with intense perturbations of the Ediacaran geomagnetic field potentially oscillating from an axial to an equatorial dipole. The paleomagnetic pole that we interpret as referring to the axial dipole field would imply that West Africa was located at high latitude during the mid-Ediacaran.