Pole Tide Research Articles

Anelasticity of the lower mantle inferred from the pole and lunar monthly tides using global DORIS coordinate time series

Global mantle anelasticity reflects the dissipation mechanism of Earth's interior structure. Nevertheless, there is still an ongoing debate regarding the anelastic properties of the lower mantle (660–2900 km depth). Advancements in data accuracy and record expansion have enabled geodetic technology to offer novel methods for determining the anelastic properties of the lower mantle. This study utilizes an optimal sequence estimation method to obtain tidal Love numbers based on Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS) coordinate time series. Love number h2,1 of pole tides at the 433-day Chandler wobble (CW) is 0.6280 (±0.0040) - 0.0127 (±0.0037)i. Love numbers h2,0 and l2,0 of zonal body tides at the 27.55-day Lunar month (Mm) are 0.6137 (±0.0034) - 0.0032 (±0.0035)i and 0.0886 (±0.0009) - 0.0015 (±0.0007)i, respectively. In light of these estimates, we infer the dispersion and dissipation parameters fr(ω) and fi(ω), respectively, by employing the power-law absorption band model with a reference period of 200 s and determine the weighted-mean value of the frequency exponent α as 0.210 ± 0.023 that links closely related to the effective viscosity. For comparison, we calculate the corresponding values from a laboratory-based extended Burgers model and show that the anelasticity parameter functions appear more compact but still support the conclusion that α varies between 0.1 and 0.3. Our results could serve as a practical constraint on the anelastic behavior of the lower mantle, contributing to a better understanding of the overall dynamics of the Earth's deep interior.

CryoSat Long-Term Ocean Data Analysis and Validation: Final Words on GOP Baseline-C

ESA’s Earth explorer mission CryoSat-2 has an ice-monitoring objective, but it has proven to also be a valuable source of observations for measuring impacts of climate change over oceans. In this paper, we report on our long-term ocean data analysis and validation and give our final words on CryoSat-2’s Geophysical Ocean Products (GOP) Baseline-C. The validation is based on a cross comparison with concurrent altimetry and with in situ tide gauges. The highlights of our findings include GOP Baseline-C showing issues with the ionosphere and pole tide correction. The latter gives rise to an east–west pattern in range bias. Between Synthetic Aperture Radar (SAR) and Low-Resolution Mode (LRM), a 1.4 cm jump in range bias is explained by a 0.5 cm jump in sea state bias, which relates to a significant wave height SAR-LRM jump of 10.5 cm. The remaining 0.9 cm is due to a range bias between ascending and descending passes, exhibiting a clear north–south pattern and ascribed to a timing bias of +0.367 ms, affecting both time-tag and elevation. The overall range bias of GOP Baseline-C is established at −2.9 cm, referenced to all calibrated concurrent altimeter missions. The bias drift does not exceed 0.2 mm/yr, leading to the conclusion that GOP Baseline-C is substantially stable and measures up to the altimeter reference missions. This is confirmed by tide gauge comparison with a selected set of 309 PSMSL tide gauges over 2010–2022: we determined a correlation of R = 0.82, a mean standard deviation of σ=5.7 cm (common reference and GIA corrected), and a drift of 0.17 mm/yr. In conclusion, the quality, continuity, and reference of GOP Baseline-C is exceptionally good and stable over time, and no proof of any deterioration or platform aging has been found. Any improvements for the next CryoSat-2 Baselines could come from sea state bias optimization, ionosphere and pole tide correction improvement, and applying a calibrated value for any timing biases.

Seismicity modulation by external stress perturbations in plate boundary vs. stable plate interior

Characterization of critically stressed seismogenic fault systems in diverse tectonic settings can be used to explore the stress/frictional condition of faults, along with its sensitivity for seismicity modulation by periodic stress perturbation. However, the process of seismicity modulation in response to external stress perturbation remains debated. In this paper, the characteristic difference in the seismicity modulation due to resonance destabilization phenomenon governed by rate-and-state friction is presented and validated with the globally reported cases of seismicity modulation in diverse tectonic settings. The relatively faster-moving plate boundary regions are equally susceptible for both shorter-period (e.g., semi-diurnal, diurnal, and other small tidal constituents) and long-period (e.g., semi-annual, annual, pole tide and pole wobble) seismicity modulation processes in response to stress perturbations from natural harmonic forcing, including tidal, semi-annual, annual, or multi-annual time scales. In contrast, slowly deforming stable plate interior regions and diffuse deformation zones appear to be more sensitive for long-period seismicity modulation of semi-annual, annual, or even multi-annual time scales but less sensitive for short-period seismicity modulation. This finding is also supported by the theoretical model predictions from the resonance destabilization process and worldwide documented natural observations of seismicity modulation in diverse types of tectonic settings.

The mean seasonal cycle in relative sea level from satellite altimetry and gravimetry

Satellite altimetry and gravimetry are used to determine the mean seasonal cycle in relative sea level, a quantity relevant to coastal flooding and related applications. The main harmonics (annual, semiannual, terannual) are estimated from 25 years of gridded altimetry, while several conventional altimeter “corrections” (gravitational tide, pole tide, and inverted barometer) are restored. To transform from absolute to relative sea levels, a model of vertical land motion is developed from a high-resolution seasonal mass inversion estimated from satellite gravimetry. An adjustment for annual geocenter motion accounts for use of a center-of-mass reference frame in satellite orbit determination. A set of 544 test tide gauges, from which seasonal harmonics have been estimated from hourly measurements, is used to assess how accurately each adjustment to the altimeter data helps converge the results to true relative sea levels. At these gauges, the median annual and semiannual amplitudes are 7.1 cm and 2.2 cm, respectively. The root-mean-square differences with altimetry are 3.24 and 1.17 cm, respectively, which are reduced to 1.93 and 0.86 cm after restoration of corrections and adjustment for land motion. Example outliers highlight some limitations of present-day coastal altimetry owing to inadequate spatial resolution: upwelling and currents off Oregon and wave setup at Minamitori Island.

The ocean pole tide loading and its effect on GPS position time-series

SUMMARY The changes in the centrifugal force induced by polar motion perturb the ocean, causing an ocean pole tide. The induced displacements due to the ocean pole tide, namely ocean pole tide loading (OPTL), previously ignored, raises the concerns in the GPS data processing with the increasing accuracy of Global Position System (GPS) technique. Though the amplitude of this effect is small, it is worth to demonstrate the magnitude and its impact on GPS solutions of the processing choices for correcting it from observations or onto estimated coordinates. For OPTL modelling, subdaily polar motion can introduce annual variations in OPTL with the small magnitudes in micrometres. The new secular pole model can cause OPTL vertical velocity difference up to 0.03 mm yr−1 compared with the mean pole model of International Earth Rotation and Reference System Service Conventions (2010). The OPTL deformation is dominated by the annual (∼365.25 d) and Chandler (∼433 d) periods, and the largest peak-to-peak variations can reach 0.70, 0.84 and 2.38 mm for East, North and Up components, respectively. We then investigate the effects of OPTL correction on GPS daily positions of 133 stations from 2014 to 2018. The root mean square of OPTL induced GPS daily displacements can reach submillimetre level. In most cases, a posteriori OPTL correction with daily averaged values applied onto the coordinates is acceptable considering the small deviation between the solution removing OPTL from coordinates and the solution correcting OPTL from observations. However, this does not hold when GPS coordinates have been aligned to a secular reference frame, as the annual/Chandler variations of OPTL would be biased. When reference frame alignment is required, either OPTL correction at observation level or a posteriori OPTL correction before reference frame alignment is recommended. Furthermore, we have demonstrated that the effects of OPTL on the annual variations of GPS position time-series can reach as much as 0.4 mm in the verticals. It has limited effect on the linear velocity and reduction of the residuals scatter (annual variations excluded), within Global Geodetic Observing System requirements for the future terrestrial reference frame at millimetre level.

On the influence of the method for estimating the parameters of the pole tide on the amplitude of the steady motion of the Earth’s pole

The steady-state Chandler wobble of the Earth’s pole is investigated for various choices of the pole tide model. The aim of the work is to estimate the parameters of the stationary Chandler wobble. The steady motion of the Earth’s pole is considered taking into account the pole tide, which depends both on the position and on the speed of the pole. The Chandler motion of the Earth’s pole is studied on the basis of the Euler-Liouville equations with a variable tensor of inertia. It is shown that both the choice of the pole tide model and the method of estimating the parameters of the chosen model significantly affect the parameters of the steady oscillatory process of the earth’s pole and the amplitude of the necessary disturbance to excite the observed Chandler wobble.

Assessment of degree-2 order-1 gravitational changes from GRACE and GRACE Follow-on, Earth rotation, satellite laser ranging, and models

We carry out a comprehensive analysis and assessment of degree-2 gravitational changes ΔC21, and ΔS21, estimated using the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GFO), satellite laser ranging (SLR), Earth Orientation Parameters (EOP), and geophysical models over the period April 2002–February 2020. The four independent estimates of ΔC21 and ΔS21 variations agree well over a broad band of frequencies. The GRACE/GFO Release 6 (RL06) solutions show major improvements over the previous RL05 solutions at both seasonal and intra-seasonal time scales, when compared with EOP and SLR estimates. Among the four independent estimates, highest correlation coefficients and smallest RMS residuals are found between GRACE/GFO and EOP estimates of ΔC21 and ΔS21 variations. GRACE/GFO and EOP ΔC21 and ΔS21 estimates exhibit slightly different trends, which are related to the implementation and interpretation of the pole tide correction in GRACE/GFO data processing. This study provides an important early validation of GFO ΔC21 and ΔS21 solutions, especially the new pole tide correction applied in GRACE/GFO RL06 solutions using independent estimates.

Refinement of the Rotational Deformation of the Viscoelastic Earth

Using a modal approach, this work determined the deformations caused by the pole tide for the axisymmetric model of a deformable Earth with a viscoelastic layer. We compared centrifugal moments of inertia variations with generally accepted expressions. The main properties of the theoretical pole tide are considered in comparison with those observed on the basis of processing high-precision measurements of the gravity acceleration.

Interrelations Between Temperature Variations in Oceanic Depths and the Global Atmospheric Oscillation

Using data on the distribution of temperatures in the Pacific, Indian, and Atlantic Oceans, large-scale structures of spatial and temporal variations of these temperatures are investigated. A structure is found which is almost identical to the spatial and temporal sea surface temperature (SST) structure that is characteristic of the recently found Global Atmospheric Oscillation. Variations in water temperature in a near-equatorial zone of the Pacific Ocean at depths up to about 150 m behave themselves in the same way as variations in sea surface height and SST. At even greater depths, variations in water temperature reveal a “striped” structure, which is, however, overall similar to that of SST variations. Variations of water temperature at depths in all three oceans spread from east to west along the equator with a period of 14 months. This makes it possible to think that the dynamics of these temperatures are controlled by the so-called Pole tides. The surface North Pacific Pole Tide was found previously responsible for excitation of El Nino. The deep Pole tides in the Southern Atlantic and Southern Indian Ocean appear to be triggers of the Atlantic El Nino and Indian Ocean Dipole (IOD). Thus, IOD manifests itself at the depth of the thermocline more clearly than on the surface of the Indian Ocean. The out-of-phase behavior of El Nino and IOD is explained by the 180° difference in the longitudes of these phenomena.

Is There an Influence of the Pole Tide on Volcanism? Insights From Mount Etna Recent Activity

AbstractWe investigate a possible link between polar motion and (i) seismic energy release and (ii) timing and intensity of eruptions at Mount Etna (Italy) for which a dense observational database is available. Our study suggests that the seismicity around Mount Etna increases during the largest excursions of the Earth rotation pole, which result from the constructive interference of the climate‐driven seasonal and Chandler wobbles. To a lesser extent, a similar link is detected between the pole tide and the erupted volume of magma. We infer that, by creating periodic changes in the state of stress in the crust through a variable centrifugal force and a periodic vertical displacement (pole tide), variations in polar motion influence eruption timing and magnitude and the rate of seismic energy release from volcanoes. This study provides new evidences on the sensitivity of volcanoes to external forcing.

Frequency dependence of the polar motion resonance

SUMMARY The nutation of the Celestial Intermediate Pole can be considered as a retrograde diurnal polar motion. As the common polar motion, it presents a resonance, but with period TPM and quality factor QPM differing from the ones characterizing the Chandler wobble (TCW = 430.2−431.6 d, QCW in the interval (56 255) according to Nastula & Gross): according to the nutation analysis presented in a separate paper, this period is about TPM = 380 d and the quality factor becomes −10. In this study, we aim to revisit the geophysical interpretation of this result. Two complementary factors account for the observed values: the non-equilibrium response of the ocean to the pole tide potential in the diurnal band, and the resonance of the solid Earth tide at the free core nutation period. This leads to a resonance of TPM in the vicinity of the free core nutation period, confirmed by estimates derived from nutation analysis.

THE PRESENCE OF GEOPHYSICAL LOADINGS IN GPS OBSERVATIONS USING GENERAL LEAST SQUARES APPROACHES

Abstract. The earth’s crust undergoes natural deformation due to the geophysical loadings that consist of the earth body tide, ocean tide loading, atmospheric pressure loading and pole tide. This periodic displacement is generated by the changes of the gravitational attraction between the moon and the sun acting upon the earth’s rotation, along with the temporal atmospheric changes and the variability of the ocean tide. The study of the geophysical loadings is important in the geodesy field as the magnitude of the signals is significant and can contribute to errors in space geodetic measurements such as Global Positioning System (GPS), Very-Long Baseline Interferometry (VLBI) and Altimeter. This study is conducted to evaluate the percentage of geophysical loadings in GPS observations by adopting general least square approaches. The presence of the geophysical loadings indicates that as many as 76% to 93% of the geophysical loadings signal are contained in the GPS time series. The findings reveal that earth body tide signals are more significant if compared to ocean tide loading signals because the magnitude of the earth body tide is greater than that of the ocean tide loading and it affects the coordinate system particularly at up component. Results illustrated the potential of GPS to provide the local parameters of the geophysical loadings that are beneficial for earth tidal modelling and that can be used to improve the quality of space geodetic measurements.

Optimal mathematical and statistical models to estimate vertical crustal movements using satellite altimetry and tide gauge data

AbstractKnowledge of vertical crustal movement is fundamental to quantify absolute sea level changes at tide gauge locations as well as for satellite altimetry calibration validations. While GPS measurements at collocated tide gauge stations fulfill this need, currently only few hundred tide gauge stations are equipped with GPS, and their measurements do not span a long period of time. In the past, several studies addressed this problem by calculating relative and geocentric trends from the tide gauge and satellite altimetry measurements respectively, and then difference the two trends to calculate the rate of changes at the tide gauge stations. However, this approach is suboptimal. This study offers an optimal statistical protocol based on themethod of condition equations with unknown parameters. An example solution demonstrates the proposed mathematical and statistical models’ optimality in estimating vertical crustal movement and its standard error by comparing them with the results of current methods. The proposed model accounts for the effect of autocorrelations in observed tide gauge and satellite altimetry sea level time series, adjusts observed corrections such as inverted barometer effects, and constraints tide gauge and satellite altimeter measurement to close. The new model can accommodate estimating other systematic effects such as pole tides that are not eliminated by differencing.

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.

Dynamic Analysis of Perturbed Chandler Oscillations of the Earth’s Pole

On the basis of the developed analytical model of the motion of a deformable Earth relative to the center of mass, the disturbed motion of the Earth’s pole is investigated. Taking into account the influence of the pole tide by linear and nonlinear dissipative terms, as well as disturbances at close to the Chandler frequency, corrections to the frequency and amplitudes of the Chandler oscillations depending on the dissipation coefficients were found in the equations of motion of the Earth’s pole.

Loading‐Induced Earth's Stress Change Over Time

AbstractWe establish a physical framework and build a preliminary database of stress changes on the Earth from 2000 to 2017 in a global scale and at various depths. We consider six loading forces that would generate stress changes on the Earth: hydrological loading, atmospheric pressure, ocean water (including tides and nontidal variation), solid lunisolar tides, pole tide, and postglacial rebound (PGR). The maximum amplitudes of normal deviatoric stress changes on the Earth's surface caused by hydrological loading, atmospheric pressure, and solid lunisolar tides reach 10−2 bar, those by pole tide 10−4–10−3 bar, and those by ocean tides 10−1 bar mostly in the coastal regions. The shear stress changes are about 1 order of magnitude smaller than the normal deviatoric stresses. The PGR‐induced stress rates are 10−3–10−2 bar/year. Stress variations caused by the different forces also exhibit different spatial patterns, with large hydro‐induced stresses mainly distributed in torrid and frigid zones, atmosphere‐induced stresses in temperate and frigid zones, and ocean‐induced stresses in coastlands and PGR‐induced stress rates in Greenland, north Europe, North America, and Antarctica. The hydro‐induced stresses exhibit significant seasonal variations in Amazon Basin, northern India, and central Africa and persistent increase/decrease in Antarctica, Greenland, and Alaska due to ice shelf melting. All loading‐induced stress changes exhibit significant depth variations. The stress database would provide a resource for better understanding the triggering mechanisms of various tectonic events, and the physical framework we establish to build the database could be useful for better studying properties and physical states of Earth's interior.

Assessment of radar altimetry correction slopes for marine gravity recovery: A case study of Jason-1 GM data

Marine gravity anomaly derived from satellite altimetry can be computed using either sea surface height or sea surface slope measurements. Here we consider the slope method and evaluate the errors in the slope of the corrections supplied with the Jason-1 geodetic mission data. The slope corrections are divided into three groups based on whether they are small, comparable, or large with respect to the 1 microradian error in the current sea surface slope models. (1) The small and thus negligible corrections include dry tropospheric correction, inverted barometer correction, solid earth tide and geocentric pole tide. (2) The moderately important corrections include wet tropospheric correction, dual-frequency ionospheric correction and sea state bias. The radiometer measurements are more preferred than model values in the geophysical data records for constraining wet tropospheric effect owing to the highly variable water-vapor structure in atmosphere. The items of dual-frequency ionospheric correction and sea state bias should better not be directly added to range observations for obtaining sea surface slopes since their inherent errors may cause abnormal sea surface slopes and along-track smoothing with uniform distribution weight in certain width is an effective strategy for avoiding introducing extra noises. The slopes calculated from radiometer wet tropospheric corrections, and along-track smoothed dual-frequency ionospheric corrections, sea state bias are generally within ±0.5 microradians and no larger than 1 microradians. (3) Ocean tide has the largest influence on obtaining sea surface slopes while most of ocean tide slopes distribute within ±3 microradians. Larger ocean tide slopes mostly occur over marginal and island-surrounding seas, and extra tidal models with better precision or with extending process (e.g. Got-e) are strongly recommended for updating corrections in geophysical data records.

Stress Models of the Annual Hydrospheric, Atmospheric, Thermal, and Tidal Loading Cycles on California Faults: Perturbation of Background Stress and Changes in Seismicity

AbstractStresses in the lithosphere arise from multiple natural loading sources that include both surface and body forces. The largest surface loads include near‐surface water storage, snow and ice, atmosphere pressure, ocean loading, and temperature changes. The solid Earth also deforms from celestial body interactions and variations in Earth's rotation. We model the seasonal stress changes in California from 2006 through 2014 for seven different loading sources with annual periods to produce an aggregate stressing history for faults in the study area. Our modeling shows that the annual water loading, atmosphere, temperature, and Earth pole tides are the largest loading sources and should each be evaluated to fully describe seasonal stress changes. In California we find that the hydrological loads are the largest source of seasonal stresses. We explore the seasonal stresses with respect to the background principal stress orientation constrained with regional focal mechanisms and analyze the modulation of seismicity. Our results do not suggest a resolvable seasonal variation for the ambient stress orientation in the shallow crust. When projecting the seasonal stresses into the background stress orientation we find that the timing of microseismicity modestly increases from an ~8 kPa seasonal mean‐normal‐stress perturbation. The results suggest that faults in California are optimally oriented with the background stress field and respond to subsurface pressure changes, possibly due to processes we have not considered in this study. At any time a population of faults are near failure as evident from earthquakes triggered by these slight seasonal stress perturbations.

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.

The pole tide/14-month oscillations in the Baltic Sea during the 19th and 20th centuries: Spatial and temporal variations

Sea level changes with a period of 14 months (P14) are usually associated with the pole tide, which is the oceanic response to the Chandler wobble in the Earth's axis of rotation. The amplitudes of these changes in the Baltic Sea are anomalously large, much larger than follows from the equilibrium pole tide theory. It appears that the oscillations are related to meteorological forcing rather than to pole motions. To examine the P14 properties, we used long-term (48–213 years) tide gauge records from 77 stations located in the Baltic Sea and adjacent area of the North Sea. High-resolution sea level spectra revealed a cluster of peaks with periods from 410 to 450 days. The temporal variations in the P14 sea level amplitudes and peak frequencies are found to be considerable and poorly correlated with the modulation of the Earth's pole motions. In contrast, our findings for 1871–2011 demonstrate strong resemblance between temporal (year-to-year) variations of the P14 peak and zonal wind, confirming earlier results of Ekman (1996) and O’Connor et al. (2000), who indicated the major role of the zonal wind in formation of the 14-month oscillations in the Baltic and North seas. The integral amplitudes of the P14 oscillations in the Baltic Sea gradually increase eastward from the entrance (the Danish straits) to the farthest ends of the sea with the largest amplitudes (up to 6.5cm) observed at the very head of the Gulf of Finland. Similar P14 amplification toward the west coast of Denmark is also observed along the south coast of the North Sea. The geographical distribution of the P14 in these two regions are almost the same as of the seasonal sea level oscillations, indicating presumably similar formation mechanisms. Extensive shallow-water areas in the Baltic Sea and southeastern part of the North Sea, combined with intense meteorological forcing, appear to be two key factors responsible for the formation of anomalously strong 14-month oscillations in these regions.