Earth tides

The main geometrical characteristics and mechanical properties of bodily tides are described, using the convenient elastic parameters of Love. The problem of the Earth's deformation is a problem of spherical elasticity of the sixth order. The importance of Earth tides in astronomy and geophysics is emphasized by their relation to the precession-nutation and tesseral tidal problems, the secular retardation of the Earth's speed of rotation due to the dissipation of energy in sectorial tides, the periodic variations of the speed of rotation due to zonal tides, the satellite orbit perturbations due to the Earth's potential variation, and the radial deformations in laser distance measurements. The possibility that dynamical effects would be produced in the Earth's liquid core was pointed out by Poincaré and developed by Jeffreys, Vicente, and Molodensky. An experimental confirmation is presented here. The role of the Earth tide phenomenon in gravimetry and oceanography is also described, as are the perturbing effects due to regional tectonic features. Instrumental developments are critical in the acquisition of precise data; the calibration problem is fundamental for a correct comparison with Earth models.     

Earth tides observed by gravity and GPS in southeastern Alaska

We analyzed gravity data obtained in Juneau and global positioning system (GPS) data obtained from three PBO sites in southeastern Alaska (SE-AK), which are part of a US research facility called ‘EarthScope’, and we compared the obtained tidal amplitudes and phases with those estimated from the predicted tides including both effects of the body tide and ocean tide. Global tide models predict the ocean tides in this region of complex coastline and bathymetry. To improve the accuracy of prediction, we developed a regional ocean tide model in SE-AK.Our comparison results suggest: (1) by taking into account the ocean tide effect, the amplitude differences between the observation and the predicted body tide is remarkably reduced for both the gravity and displacement (e.g. for the M₂ constituent, 8.5–0.3 μGal, and 2.4–0.1 cm at the AB50 GPS site in Juneau in terms of the vector sum of three components of the north–south, east–west and up–down), even though the ocean tide loading is large in SE-AK. (2) We have confirmed the precise point positioning (PPP) method, which was used to extract the tidal signals from the original GPS time series, works well to recover the tidal signals. Although the GPS analysis results still contain noise due to the atmosphere and multipath, we may conclude that the GPS observation surely detects the tidal signals with the sub-centimeter accuracy or better for some of the tidal constituents. (3) In order to increase the accuracy of the tidal prediction in SE-AK, it is indispensable to improve the regional ocean tide model developed in this study, especially for the phase.     

Earth tides observed by gravity and GPS in southeastern Alaska

We analyzed gravity data obtained in Juneau and global positioning system (GPS) data obtained from three PBO sites in southeastern Alaska (SE-AK), which are part of a US research facility called ‘EarthScope’, and we compared the obtained tidal amplitudes and phases with those estimated from the predicted tides including both effects of the body tide and ocean tide. Global tide models predict the ocean tides in this region of complex coastline and bathymetry. To improve the accuracy of prediction, we developed a regional ocean tide model in SE-AK.Our comparison results suggest: (1) by taking into account the ocean tide effect, the amplitude differences between the observation and the predicted body tide is remarkably reduced for both the gravity and displacement (e.g. for the M₂ constituent, 8.5–0.3 μGal, and 2.4–0.1 cm at the AB50 GPS site in Juneau in terms of the vector sum of three components of the north–south, east–west and up–down), even though the ocean tide loading is large in SE-AK. (2) We have confirmed the precise point positioning (PPP) method, which was used to extract the tidal signals from the original GPS time series, works well to recover the tidal signals. Although the GPS analysis results still contain noise due to the atmosphere and multipath, we may conclude that the GPS observation surely detects the tidal signals with the sub-centimeter accuracy or better for some of the tidal constituents. (3) In order to increase the accuracy of the tidal prediction in SE-AK, it is indispensable to improve the regional ocean tide model developed in this study, especially for the phase.     

A global experimental model for gravity tides of the Earth

The long-term, continuous and high-quality tidal gravity data, recorded with the superconducting gravimeters (SGs) at 19 stations in the Global Geodynamics Project (GGP), were simultaneously used to investigate the global pattern of the tidal gravity variations. The atmospheric effects were removed from the gravity observations by using the simultaneous pressure records at the stations. A total of six global co-tidal models were employed to remove the loading effects of oceanic tides. The resonance parameters of the Earth's free core nutation (FCN), as well as the spheroidal constant components in the gravimetric factors of waves O₁ and M₂, were accurately retrieved. As a result, a global experimental model for gravity tides (GEMGT) was developed, considering the nearly diurnal resonance and the latitude-dependence of the gravimetric amplitude factors. The final results indicate that the mean discrepancy of the four main tidal waves (i.e. O₁, K₁, M₂ and S₂) between the GEMGT and SG observations is less than 0.2% on average. The GEMGT is in good agreement with the theoretical models based on the inelastic non-hydrostatic equilibrium Earth models [Dehant, V., Defraigne, P., Wahr, J., 1999. Tides for a convective Earth. J. Geophys. Res. 104, 1035–1058; Mathews, P.M., 2001. Love numbers and gravimetric factor for diurnal tides. J. Geodetic Soc. Jpn. 46 (4), 231–236] with a mean discrepancy less than 0.15%. However, the GEMGT is in closer accordance with the theoretical model given by Mathews [Mathews, P.M., 2001. Love numbers and gravimetric factor for diurnal tides. J. Geodetic Soc. Jpn. 46 (4), 231–236] for the diurnal tides while it is in closer agreement with one obtained by Dehant et al. [Dehant, V., Defraigne, P., Wahr, J., 1999. Tides for a convective Earth. J. Geophys. Res. 104, 1035–1058] for the semi-diurnal tides.     

True polar wander in the Earth system

True polar wander(TPW), or planetary reorientation, is the rotation of solid Earth(crust and mantle) about the liquid outer core in order to stabilize Earth’s rotation due to mass redistribution. Although TPW is well-documented on Earth presently with satellites and for multiple planets and moons in the Solar System, the prevalence of TPW in Earth history remains contentious. Despite a history of controversy, both the physical plausibility of TPWon Earth and an empirical basis for it are now und...     

Influence of mantle anelasticity on the phase and amplitude of Earth tides

The effect of the anelasticity of the mantle on the phase and amplitude of Earth tides is calculated for recent models of the internal structure of the Earth and its rheological characteristics. The anelastic properties of the mantle are modelled by the Maxwell and Knopoff-Lomnitz rheological bodies. For numerical calculations two different methods of solution are used. Results indicate that the effect of mantle anelasticity on tidal amplitudes is practically zero. For both types of rheological models the phase shifts of the functions characterizing solid tides are small, none of them exceeding values of some minutes of arc. These phase shifts have a very weak dependence on the variation of attenuation and viscosity within the mantle. The present study is closely related to an important problem: what proportion of the observed tidal friction arises not in the ocean but is due to the anelasticity of the mantle? The results suggest that dissipation by solid friction at present is an insignificant, almost negligible component of tidal energy sink.     

Estimating aquifer properties from the water level response to Earth tides

Water level fluctuations induced by tidal strains can be analyzed to estimate the elastic properties, porosity, and transmissivity of the surrounding aquifer material. We review underutilized methods for estimating aquifer properties from the confined response to earth tides. The earth tide analyses are applied to an open well penetrating a confined carbonate aquifer. The resulting range of elastic and hydraulic aquifer properties are in general agreement with that determined by other investigators for the area of the well. The analyses indicate that passive monitoring data from wells completed in sufficiently stiff, low porosity formations can provide useful information on the properties of the surrounding formation.     

Determination of polar motion from satellite observations

Doppler observations of U.S. Navy Navigation Satellites have been used to determine the Earth's pole position for the period 1967 to July 1972. Recent results are competitive in accuracy with astronomic results and exhibit about 0".02 agreement with astronomic pole positions. The differences are no larger than those between independent calculations of pole positions based on astronomic data (BIHvs. ILS). For a two-day span of observations made by 18 Doppler stations the uncertainty in computed pole position corresponding to random errors in observation is 0".002. However, the results have systematic errors with various frequencies which are primarily due to uncertainties in the gravity coefficients. Since these errors are independent of those producing systematic errors in astronomic results, the two techniques are complementary. Recent results of computation of polar motion based on laser observations of artificial Earth satellites have also produced results having accuracies comparable to Doppler and astronomic results. The analysis of the laser observations is based on the effect of pole position on the apparent inclination of satellite orbits; on the other hand, since the Doppler observations are made on polar orbiting satellites, they are more sensitive to errors in the component of pole position which lies in the orbit plane. As a result of this difference, biases in Doppler and laser results may be different in size or character.     

Influence of dynamic shear modulus on the amplitude and phase of Earth tides

The effect of the frequency-dependent (dynamic) shear modulus on the amplitude and phase of Earth tides is calculated. It is shown that dynamic shear modulus corrections to the tidal phases are completely negligible. A practically reasonable increase of accuracy of tidal measurements, however, would detect the influence of dynamic shear modulus on the amplitude of gravity tide.     

极移振幅主要周期分量的时变特征

用JPL近年发布的地极坐标序列求得1893―1998年间极移的振幅序列,用最大熵谱分析方法求得了该资料序列包含的一些周期的参数,并利用小波变换方法分析讨论了其中的主要周期的变化.结果表明,极移振幅变化中存在着约6.5年和约40年的主要周期,且它们均具有一定程度的时变性.因此,在研究讨论极移与一些地球物理现象和自然灾害现象的关系时,应特别注意极移振幅中主要周期的时变特征.     

Relationship between polar motion and key hydrological elements at multiple scales

Science China Earth Sciences - Changes in the elements of the Earth system are closely related. Finding the key factors linked with hydrological changes is significant for in-depth analysis of...     

天文观测极移运动周期变化的原因解析

宋贯一（1991,2006）相继发现日-地之间存在一种奇特的能量（动量）相耦合的自然现象:当太阳辐射光压作用于地表之后,地球表面物质的特殊物理性质会自然地把太阳辐射光压立刻分解为两部分,即P₁和P₂.其中P₁为全球各纬度带内单位海洋和陆地表面接收到的等值光压（P₁为随时间和纬度而变化的变量）.在一个回归年的时段内,由P₁在北、南两半球上的不平衡分布激发自转轴摆动,引起转动惯量的变化（该变化是目前所了解到的地球转动惯量的最大变化）并产生极移,该项极移运动的周期为12个月左右.由于P₁在北、南半球上的分布相对赤道是基本对称的和规则的,P₁对自转轴摆动的激发可称谓“规则性激发”;P₂为全球各纬度带内单位陆地和海洋表面接收到的光压值之差（P₂为随时间和纬度而变化的变量）.在一个回归年的时段内,由 P₂在北、南两半球上的不平衡分布激发自转轴摆动而产生的极移运动周期为14个月附近.由于P₂在北、南两半球上的分布相对赤道是不对称和不规则的, P₂对自转轴摆动的激发可称谓“不规则性激发”.这种天然存在的力源,恰恰是近百年来世界各国研究地球自转的地球物理学家渴望寻找的那种既能激发自转轴产生自由章动、又使其摆动含有两个不同周期（12个月和14个月）的激发力源.正是这一奇特自然现象的发现,才使长期以来困扰地球物理学领域内的极移、极移所包含两个周期的涨落变化及由此引起的地球自转速度变化等自然之谜得以破解成为可能. 本文作者仅对天文观测的极移运动周期及其极移运动所包含的两个周期分量在一定的范围内变化的成因作出了详细的解析,并得出如下结论： （1）极移运动主要是由太阳光压P₁ 和P₂共同激发引起的.天文观测的极移摆动周期的涨落变化是太阳光压（P₁＋P₂）激发自转轴摆动过程中,在空间上自转轴的摆动中心相对自转轴中心（地心）移动造成的,涨落范围在395～403±2天之间,即天文观测的极移运动的实际计算周期应在13.0～13.3个月之间变化.（2）极移所含的周年期摆动是由太阳光压P₁激发的.天文观测的周年期摆动周期涨落很小,变化于365.24～365.53天之间.在一个回归年内,由于日-地间距离的变化,使地球表面接受到的太阳辐射光能产生微小差异则是造成观测的周年摆动周期稍有拖长的原因.（3）极移所含的钱德勒摆动周期是由太阳光压P₂激发的.天文观测的钱德勒周期涨落较大,变化于426～437±2天之间,即实际计算周期应在14.0～14.4个月之间变化.观测的钱德勒摆动周期的变化是太阳光压P₂激发自转轴摆动过程中,在空间上自转轴的摆动中心相对自转轴中心（地心）移动造成的.上述的定量解析数据均得到实际观测资料的验证,为极移光压成因理论的正确性提供了具体详实的证据.     

Secular polar motion,crustal movements,and international latitude service observations

Summary The latitude variations observed by optical astrometry at five International Latitude Service (ILS) stations since the beginning of the century are analyzed to estimate the secular motion of the pole and the correction of the proper motions of the observed stars. The geophysical model of tectonic plate motions NUVEL-1 is used to correct the observed latitude drifts, thus referring the derived secular polar motion to the "no net rotation" terrestrial reference system. It is shown that one of the ILS stations, Ukiah (near the U.S. west coast), very probably exhibits an anomalous drift which differs significantly from the motion of both the Pacific and North American plates.     

Storage in confined aquifer: Spectral analysis of groundwater in responses to Earth tides and barometric effect

Dilatation of aquifer and associated water level fluctuation in groundwater well is known to be driven periodically from lunar, solar, or other tidal forces. Time‐dependent variables in groundwater system, such as water level, can be converted to power spectra in the frequency domain using Fourier transform to evaluate significant fluctuation. The major innovation of this research is to develop spectral representation in frequency domain for the groundwater system that the storage in confined aquifer can be determined considering dilatation affected by Earth tides and barometric effect. In order to verify applicability of the evolved method, time series of Earth tides and barograph are collected; aquifer storage is then determined inversely by selecting significant semidiurnal and diurnal components in spectra computation. It suggests that to discover groundwater storage using groundwater level with barograph and tidal potential of Earth in frequency domain becomes accessible and feasible.     

Assessment of terrestrial water contributions to polar motion from GRACE and hydrological models

The hydrological contribution to polar motion is a major challenge in explaining the observed geodetic residual of non-atmospheric and non-oceanic excitations since hydrological models have limited input of comprehensive global direct observations. Although global terrestrial water storage (TWS) estimated from the Gravity Recovery and Climate Experiment (GRACE) provides a new opportunity to study the hydrological excitation of polar motion, the GRACE gridded data are subject to the post-processing de-striping algorithm, spatial gridded mapping and filter smoothing effects as well as aliasing errors. In this paper, the hydrological contributions to polar motion are investigated and evaluated at seasonal and intra-seasonal time scales using the recovered degree-2 harmonic coefficients from all GRACE spherical harmonic coefficients and hydrological models data with the same filter smoothing and recovering methods, including the Global Land Data Assimilation Systems (GLDAS) model, Climate Prediction Center (CPC) model, the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis products and European Center for Medium-Range Weather Forecasts (ECMWF) operational model (opECMWF). It is shown that GRACE is better in explaining the geodetic residual of non-atmospheric and non-oceanic polar motion excitations at the annual period, while the models give worse estimates with a larger phase shift or amplitude bias. At the semi-annual period, the GRACE estimates are also generally closer to the geodetic residual, but with some biases in phase or amplitude due mainly to some aliasing errors at near semi-annual period from geophysical models. For periods less than 1-year, the hydrological models and GRACE are generally worse in explaining the intraseasonal polar motion excitations.     

北京站重力潮汐分析及海潮负荷效应

采用引潮势和海潮潮族作为输入函数,对北京实测的重力潮汐进行了响应分析,将频率相同的引潮力产生的重力天文(引力)潮和海洋潮汐负荷效应产生的重力负荷潮分离开.再对重力天文潮和负荷潮进行调和分析,得到北京重力天文潮和负荷潮的平均变幅分别为121.5和7.5微伽.海洋潮汐的负荷影响为北京重力天文潮的6.2%.     

Ocean tides and resonance

Tidal currents and surface amplitudes are calculated globally for the dominating diurnal and semidiurnal constituents using an established tidal model under a range of altered bathymetry. The purpose is to evaluate if the well-known amplification of the global tides during the Last Glacial Maximum (LGM) is related to changed propagation properties for the tidal wave or to changed damping due to removal of shelf seas. The response of the tides and tidal dissipation to future sea-level rise is also discussed. The tides in the present and LGM oceans were simulated first, followed by runs where the present day bathymetry was used but the shelf seas removed by the introduction of vertical walls or where sea level is allowed to rise. Previously reported results regarding tidal amplitudes and dissipation rates are reproduced in the control runs. The runs without shelf seas show significantly enhanced tidal amplitudes in the North Atlantic, whereas sea-level rise of 5 m above present levels show a significant shift in the amphidromic points on a local and regional scale but had a limited effect on the open ocean tides. Simulations with very large sea-level rise show a significantly decreased global tidal dissipation, whereas experiments without friction in present-day shallow water display results similar to those with no shelf seas. The results all point towards changing damping properties due to the removal of shelf seas as being the mechanism behind the LGM amplification, and they imply the importance of implementing future sea-level changes properly in tidal simulations.