利用小波分析重力的长期变化

运用小波滤波方法估算Chandler和周年项的潮汐因子.本文分析了四个台站(Brussels, Boulder, Membach以及Strasbourg)的观测记录,运用合成潮方法得到重力残差后,用Daubechies小波带通滤波器滤波残差,得到256～512 d时间尺度上的序列,根据标准差最小原则确定观测极潮周年和Chandler项的周期,然后利用最小二乘法估算它们的潮汐因子,同时给出未经模型改正的周年重力.由于高阶Daubechies小波构造的滤波器具有良好的频率响应,且能压制信号中的高阶异常成分,使滤波的信号更加光滑,因此计算结果具有更小的均方差,更加可靠.     

基于集合经验模态分解法的重力极潮提取与研究

重力极潮,即极移引起的重力变化,是地球由于惯性离心力变化导致地球形变的综合反映,其观测和研究有助于了解地球在长周期频段的响应,约束地球形变、地球内部构造和物理参数.区别于以往研究,本文采用了集合经验模态分解方法（Ensemble Empirical Mode Decomposition,EEMD）从全球5个超导重力仪台站连续重力观测资料中提取重力极潮、消除仪器漂移及极潮频段以外的大部分噪声信号,该方法所用的基函数是基于自身信号获得的;在此基础上,利用最小二乘匹配法分离极潮中的周年项和Chandler项,估算Chandler周期的极潮潮汐因子.结果表明,基于EEMD得到的极潮潮汐因子与前人基于其他消除仪器漂移方法（数学模型或小波分析）得到的结果相符合,精度相当,但由于这种方法是自适应的,因此本文结果更能反映实际物理过程.     

El Niño Impact on Polar Motion Prediction Errors

The polar motion prediction is computed as a least-squares extrapolation of the polar motion data. The least-squares model consists of a Chandler circle with constant or variable amplitude, annual and semiannual ellipses, and a bias. The model with constant amplitude of the Chandler oscillation is fit to the last three years of polar motion data and the model with variable amplitude of the Chandler oscillation is fit to the whole time series ranging from 1973.0 to 2001.1. The variable amplitude of the Chandler oscillation is modeled from the envelope of the Chandler oscillation filtered by the Fourier transform band pass filter from the long-term IERS EOPC01 polar motion series. The accuracy of the polar motion prediction depends mostly on the phase variation of the annual oscillation, which is treated as a constant in the least-squares adjustment. There were two significant changes of the annual oscillation phase of the order of 30° before the two El Niño events in 1982/83 and 1997/98.     

Free Wobble of the Triaxial Earth: Theory and Comparisons with International Earth Rotation Service (IERS) Data

Earth’s free wobble is often referred to as the Euler wobble (for the rigid case) or the Chandler wobble for the real case. In this study, we investigate the theory of the free wobble of the triaxial Earth and demonstrate that: (1) the Euler period should actually be expressed by the complete elliptic integral of first kind, and (2) the trace of the free polar motion is elliptic, with the orientations of its semi-minor and major axes being approximately parallel to the Earth’s principal axes A and B, respectively. Numerical calculations show that, due to the triaxiality of the Earth, the spin rate ω ₃ fluctuates with the semi-Euler/Chandler period, although its amplitude (about 10⁻¹⁹ rad/s) is rather small and beyond the present measurement accuracy; the tilt of the instantaneous spin axis (or the amplitude of the free wobble), θ, has a fluctuation whose amplitude is around 0.34 milli-arcsecond (mas), which could be detected by present observations. Thus, we conclude that the Earth’s triaxial nature has little impact on ω ₃, but has an influence on the polar motion which should not be ignored. On the other hand, our study shows that there is a mechanism of frequency–amplitude modulation in the Chandler wobble which might be a candidate to explain the correlation between the amplitude and period of the Chandler wobble. We compare the theoretical polar parameters (m ₁, m ₂) with the observed values for the Chandler components obtained from the data EOP (IERS) C 04, and find that they coincide with each other quite well, especially for recent years. In addition, a polar wander towards 76.7°W, which is in agreement with previous results given by other scientists, is also obtained.     

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.     

Some critical factors for engineering and environmental microgravity investigations

The gravity method is one of the geophysical tools used for engineering and environmental investigations where the detection of cavities, karst phenomena, subsoil irregularities, or landfills is essential. In many cases, deep or small-scale heterogeneities generating low-amplitude anomalies have to be detected and the reliability of further interpretation requires highly accurate measurements, carefully corrected for any quantifiable disturbing effects. The purpose of this study is to investigate the factors likely to limit measurement quality and how to make improvements.Calibrations of a Scintrex gravimeter were made between French relative and absolute base stations, and the relative uncertainties on the calibration factors were estimated for these links. Ranging from 10⁻³, for calibration on an old gravity net, to 10⁻⁴, for a high amplitude absolute base line, this accuracy will be generally sufficient for microgravity surveys.Continuous gravity recordings of Scintrex gravimeters, installed at the same stable site, enabled the estimation of the stability and accuracy of the instruments and revealed that some of the time variations of g measurements, such as instrumental drift, tidal effects and seismic noise, are not entirely removed by standard processing procedures. The accuracy of corrected gravity measurements is mainly limited by inadequate corrections of tidal effects and by a poor estimation of ocean loading effects. In comparison with residual defaults in tidal corrections, instrumental and seismic noises are taken more properly into account by statistical data processing.In field operation, residual tidal effects are generally integrated into an experimental terrain drift estimated on the basis of frequent repeated measurements. A differential gravity approach, based on a fixed gravimeter reference whose recordings are used to correct measurements made with a mobile gravimeter, has also been investigated at a test site. Compared to standard processing, this method can help improve repeatability of gravity measurements.Microgravity surveys in the urban environment require effective and accurate consideration of the effects of infrastructures, nearby buildings and basements, as well as those of topography, in the vicinity of a gravity station. Correction procedures, applied at the same experimental site, where gravity points are located close to buildings, walls and basement slope, appear to have almost totally eliminated these disturbances.     

利用超导重力仪观测资料检测地球近周日共振

简要介绍了地球近周日摆动（ＮＤＦＷ）及其在周日重力潮汐中共振的理论背景,利用武汉和Ｂｒｕｓｓｅｌｓ两台站超导重力仪的潮汐观测结果,采用造积方法（Ｓｔａｃｋｉｎｇｍｅｔｈｏｄ）检测ＮＤＦＷ,根据ＮＤＦＷ在４个周日潮波的共振,得到近周日摆动的本征频率和品质因子．考虑ＮＤＦＷ,可精化地球模型,更客观的理解和分析固体潮观测值和其它一些地球物理现象．     

Probabilistic analysis of the data on atmospheric angular momentum for January 1, 1980 to March 27, 2003

The data series of the International Earth Rotation and Reference Systems Service and National Centers for Environmental Prediction () for 1982–2003 are analyzed. It is shown that the atmospheric component of polar motion can be treated as the anisotropic Markov process with discrete time, and the torque exerted by the atmosphere on the solid Earth, as the white noise. The intensity and characteristic correlation time of the process are estimated. The efficiency of the atmospheric mechanism in the excitation of the Chandler wobble is estimated in the context of the probabilistic model.     

The Chandler annual resonance and its possible geophysical significance

The secular decrease of the earth's rotation rate has caused the Chandler and annual modes of the earth's wobble to resonate in the past. The physics of the resonance is discussed as well as its thermal impact on the mantle. Energy of the order of 10²⁶ erg/year were dissipated in the upper mantle during the resonance. Estimates of the epoch and duration of the resonance place them at about 185 m.y. ago and about 10 m.y., respectively. The possibility of a causal connection between the resonance and the onset of continental drift is suggested.     

鄂尔多斯块体北缘台站水管仪观测质量及同震响应对比分析

针对仪器运行状况和外界环境等影响观测质量的因素,以及台站所处地质构造不同对台站影响的问题,采用位于鄂尔多斯块体北缘的乌加河台、包头台、乌海台2015～2017年DSQ水管倾斜仪的观测资料,对比分析3个台站的年零漂、相对噪声水平M_1、M2波潮汐因子γ值均方差等特征参数,并进行同震响应分析。研究表明,包头台水管仪的观测质量优于其它台站,主要是体现在零漂小、精度高、稳定性好,研究结果为评定水管仪观测质量提供了科学依据。同震响应的延迟时间与震中距相关,最大振幅与震级间呈正相关,与震中距间呈负相关。     

Annual variation detected by GPS,GRACE and loading models

Most GPS coordinate time series, surface displacements derived from the Gravity Recovery and Climate Experiment (GRACE), and loading models display significant annual signals at many regions. This paper compares the annual signals of the GPS position time series from the Crustal Dynamics Data Information System (CDDIS), estimates of loading from GRACE monthly gravity field models calculated by three processing centers (Center of Spatial Research, CSR; Jet Propulsion Laboratory, JPL; GeoForschungsZentrum, GFZ) and three geophysical fluids models (National Center for Environmental Prediction, NCEP; Estimating the Circulation and Climate of the Ocean, ECCO; Global Land Data Assimilation System, GLDAS) for 270 globally distributed stations for the period 2003-2011. The results show that annual variations derived from the level-2 products from the three GRACE product centers are very similar. The absolute difference in annual amplitude between any two centers is never larger than 1.25 mm in the vertical and 0.11 mm in horizontal displacement. The mean phase differences of the GRACE results are less than ten days for all three components. When we correct the GPS vertical coordinate time series using the GRACE annual amplitudes using the products from three GRACE analysis centers, we find that we are able to reduce the GPS annual signal in the vertical at about 80% stations and the average reduction is about 47%. In the north and the east, the annual amplitude is reduced on 77% and 72% of the stations with the average reduction 32% and 33%. We also compare the annual surface displacement signal derived from two environmental models; the two models use the same atmospheric and non-tidal ocean loading and differ only in the continental water storage model that we use, either NCEP or GLDAS. We find that the model containing the GLDAS continental water storage is able to better reduce the annual signal in the GPS coordinate time series.     

Results from 44 months of observations with a superconducting gravimeter at Moxa/Germany

Results for more than 42 months of observations with the superconducting gravimeter CD-034 at the Geodynamic Observatory Moxa are discussed. Moxa observatory is one of the newer stations within the ‘Global Geodynamics Project’ (GGP). A special feature of the gravimeter at Moxa is its dual sensor system; differences in the results obtained from the two sensor recordings are generally well within the standard deviations of the tidal analysis. One significant difference concerns the slightly different drift rates of 31 and 49.5 nm/s² per year for upper and lower sensor; both sensor drifts can be fitted by a linear function. We find that the noise levels are close to the ‘New Low Noise Model’ for the seismic-modes and are also low in the tidal bands. Due to this low noise, Moxa is a station well suited to search for small geodynamic signals. The long-period variation in the gravity residuals correlates well with the polar motion.The difference signal between the two sensor recordings has a peak-to-peak amplitude of about 6 nm/s² and shows systematic variations. Its spectrum is characterised by instrumental noise between 0.2 and 0.4 cph. The noise level of the difference and of the sum of the two residual datasets are clearly lower, respectively, higher than the noise contents of the gravity residuals themselves. This is a strong indication for the existence of broadband signals common to the two residual datasets, leading to the conjecture that the reduction of environmental effects is still not sufficient.Our results once more emphasize the necessity to correct the data for barometric pressure effects when analyzing the data for seismic modes. The reduction visibly increases the signal-to-noise ratio in the low frequencies of the mode band and helps to avoid misinterpreations of peaks. Besides the well known barometric pressure influence we can establish hydrological effects in the data which are probably caused by soil moisture and groundwater table variations as well as by batch-wise water movement within the weathering layer. As the major part of the observatory surroundings is above gravimeter level, an anticorrelation between hydrological and gravity changes is observed. In addition, it can be shown that global hydrological effects reach an order of magnitude that makes it necessary to consider these effects when analyzing long-period signals like polar motion. Vice versa these effects are large enough to be detectable in the gravity data. A first joint analysis of five datasets from the GGP network shows no indications for signals related to the Slichter triplet or core modes.     

Tilt effects on GWR superconducting gravimeters

The superconducting gravimeters (SGs) are the most sensitive and stable gravity sensors currently available. The low drift and high sensitivity of these instruments allow to investigate several geophysical phenomena inducing small- and long-period gravity changes. In order to study such topics, any kind of disturbance of instrumental origin has to be identified and possibly modelled. A critical point in gravity measurement is the alignment of the gravimeter to the local vertical. In fact a tilt of the instrument will lead to an apparent gravity change and can affect the instrumental drift. To avoid these drawbacks, SGs are provided with an “active tilt feedback system” (ATFS) designed to keep the meter aligned to the vertical. We analyse tilt and environmental parameters collected near Strasbourg, France, since 1997 to study the source of the tilt changes and check the capability of the ATFS to compensate them. We also present the outcomes of a calibration test applied to the ATFS output to convert the Tilt Power signals into angles. We find that most of the observed signal has a thermal origin dominated by a strong annual component of about 200 μrad. Nevertheless, our analysis shows that even the tilt due to different geophysical phenomena, other than the thermal ones, can be detected. A clear tidal signal of about 0.05 μrad is detectable thanks to the large data stacking (>11 years). We conclude that (i) the ATFS device compensates the tilt having a thermal origin or coming from any sources and (ii) no significant tilt changes alter the gravity signal, except for the high frequency (>1 mHz) perturbations.     

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.     

Low-Frequency Variations, Chandler and Annual Wobbles of Polar Motion as Observed Over One Century

Polar motion data are available from the mid-19th century to the present. Basedon time series with a variety of sampling intervals (monthly, 0.05-year, 5-day anddaily), we have separated the low-frequency terms by low-pass filtering and theChandler and annual terms by recursive band-pass filtering of the pole coordinates.Using a simple unweighted least-squares fit to the filtered low-frequency terms, thelinear trends of the rotation pole were estimated. Assessing the estimates based onintercomparisons, the most reliable trend estimate was found. Using a Fast FourierTransform, we have computed the prograde, retrograde and total amplitude spectraof the low-frequency part of polar motion in order to reveal the long-periodic signals.The characteristics and time evolution of the Chandler and annual wobbles aredescribed by changes in their parameters (radii, directions and period lengths) overone century.     

Observation of recent tectonic movements by extensometers in the Pannonian Basin

In Hungary four extensometric observatories were established in the last two decades. The extensometers were installed primarily for observations of Earth tides. A 15-year continuous data series (1991–2005) was recorded at the Sopronbánfalva station and a 7-year record (1993–1999) was obtained at the Pécs station. The length of the measured continuous data series at the two other stations (Bakonya and Budapest) is only a few years. The long-term data records were also applied to the investigation of long-periodic deformations caused by recent tectonic movements. To get an insight into the present day tectonic processes on the margin of the Pannonian Basin, the measurement results of two additional stations (Vyhne in Slovakia and Beregovo in Ukraine) were also included into the investigations. The seasonal variations in the long data series due to temperature and air pressure effects were eliminated. The residual curve – after the correction of the seasonal effects and filtering the “high frequency” components (e.g. earthquakes, Earth tides, etc.) – contains the instrumental drift. It is impossible to determine this curve mathematically. It can be diminished by special instrumental solutions and by regular calibration of the instruments. This paper shows methods and possible solutions how the instrumental drift was investigated and eliminated in order to get the most reliable data for studying recent tectonic movements. The reliability of the extensometric measurements was tested by the tidal evaluation of the data series. The results of the observations show that the Pannonian Basin is under compressive stress. The strain rates measured by extensometers on the margin of the basin are about three orders of magnitude higher than the intra-plate strains obtained by GPS measurements. The reason for this large difference arises from the interaction between the plate boundary and intra-plate forces and from the different measurement techniques. Investigations showed that the rate of the tectonic movements varies, and depends on the local geographical and topographical conditions.     

Long-term crustal deformation monitored by gravity and space techniques at Medicina, Italy and Wettzell, Germany

Series of gravity recordings at the stations Medicina (Italy) and Wettzell (Germany) are investigated to separate seasonal gravity variations from long-term trends in gravity. The findings are compared to height variations monitored by continuous GPS observations. To study the origin of these variations in height and gravity the environmental parameters at the stations are included in the fact finding. In Medicina, a clear seasonal signal is visible in the gravity and height data series, caused by seasonal fluctuations in the atmosphere including mass redistribution, the ocean, groundwater but also by geo-mechanical effects such as soil consolidation and thermal expansion of the structure supporting the GPS antenna. In Wettzell, no seasonal effect could be clearly identified, and the long-term trend in gravity is mainly caused by ground water variations. The successful combination of height and gravity series with the derived ratio of gravity to height changes indicates that the long-term trends in height and gravity are most likely due to mass changes rather than to tectonic movements.     

纬度变化和地极运动

远在1687年,牛顿已说到地球自转轴的运动,欧拉在1790年指出:由于地球转动的主要动力矩的方向,并不和地球惯性椭球的短轴方向相重合,将使地球的自转轴发生沿着一个圆锥面的摆动.假定地球为一个刚体时,可以从地球惯性椭球的扁率（或称力学椭率,或动力学扁率）算出地球自转轴运动的周期.     

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

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