The Akp-Btk value method and the results for the retrieval of the parameters of the Earth's free core nutation

The rotation of the Earth's liquid core creates the Nearly Diurnal Free Wobble (NDFW). It is one of the problems of researching the Earth's liquid core for us to retrieve the parameters of the Earth's Free Core Nutation (FCN), from the Earth's liquid core resonance of gravity tide waves on the diurnal frequency band. Since 1987, some scientists in many different countries have come to calculate the parameters of FCN by using the observational data of gravity tide waves on the diurnal frequency band. They basically followed the Stacking method, which needed five diurnal waves for the resolution. In this paper, authors introduced the Akp-Btk value method with clearly geometrical meaning as a new method, which only requires three very high signal-noise-ratio waves O1, K1 and P1 for the resolution. Authors chose the observational data of the three superconducting gravimeter stations respectively located in Cantley of Canada, Wuhan of China and Brussels of Belgium, to compute the parameters of FCN. It was the first time that the observational results of the parameters of FCN obtained from gravitational tide were in accord with the parameters of FCN gained from VLBI since 1987.     

武汉台重力潮汐长期观测结果

采用武汉台超导重力仪(SG C032)14年多的长期连续观测资料,研究了固体地球对二阶和三阶引潮力的响应特征,精密测定了重力潮汐参数,系统研究了最新的固体潮模型和海潮模型在中国大陆的有效性.采用最新的8个全球海潮模型计算了海潮负荷效应,从武汉台SG C032的观测中成功分离出63个2阶潮汐波群和15个3阶潮汐波群信号,3阶潮波涵盖了周日、半日和1/3日三个频段.重力潮汐观测的精度非常高,标准偏差达到1.116 nm·s-2,系统反映了非流体静力平衡、非弹性地球对2阶和3阶引潮力的响应特征.结果表明,现有的武汉国际重力潮汐基准在半日频段非常精确,但在周日频段存在比较明显的偏差,需要进一步精化.对于中国大陆的大地测量观测,固体潮可以采用Dehant等考虑地球内部介质非弹性和非流体静力平衡建立的固体潮理论模型或Xu 等基于全球SG观测建立的重力潮汐全球实验模型作为参考和改正模型,海潮负荷效应应该采用Nao99作为改正模型.     

贝叶斯算法在拟合自由核章动参数中的应用

用高精度重力技术检测地球自由核章动(FCN)参数(包括周期和Q值等)的难点是资料观测信噪比低,传统的方法是使用最小二乘拟合,但是获得的FCN共振参数精度不理想.本文利用武汉国际潮汐基准站高精度超导重力仪和全球超导重力仪观测的时变重力资料,根据贝叶斯算法拟合地球自由核章动(FCN)参数.我们将贝叶斯拟合方法与传统最小二乘法实施了对比分析,研究了不同台站资料差异.讨论了潮波选择和不同海潮模型等因素对FCN参数的影响.结果表明用贝叶斯算法获得的FCN品质因子与空间大地测量VLBI结果吻合的更好,这说明贝叶斯算法可靠性高,为研究地球深内部构造参数(核幔边界粘滞系数等)提供了有效依据.     

Performance of superconducting gravimeters from long-period seismology to tides

The first phase (1997–2003) of the Global Geodynamics Project (GGP) has now been completed. Data from superconducting gravimeters (SGs) within GGP have shown great capabilities in a wide spectrum of geophysical applications from the tidal studies to the long-period seismology. Here, we compare the noise levels of the different contributing stations over the whole spectrum. We use three different processing procedures to evaluate the combined instrument-plus-site noise in the long-period seismic band (200–600 s), in the sub-seismic band (1–6 h) and in the tidal bands (12–24 h). The analysis in the seismic band has demonstrated that SGs are particularly well suited for the studies of the long-period normal modes and thus are complementary to long-period seismometers. In the sub-seismic band, the power spectral densities, computed over a period of 15 continuous days for every GGP station, cross the New Low Noise Model of Peterson from T = 16 min to T = 4.6 h. SG data are therefore appropriate for studying long-period seismic and sub-seismic modes. In the tidal bands, the noise comparison is realised by a least-squares fit to tides, local air pressure and instrumental drift, leading to gravity residuals where we estimate a standard deviation and average noise levels in different tidal frequency bands. Tidal gravity observations using SGs have also shown to be an independent validation tool of ocean tidal models, and they are therefore complementary to tide gauge and altimetric data sets. Knowledge of the noise levels at each station is important in a number of studies that combine the data to determine global Earth parameters. We illustrate it with the stacking of the data in the search for the gravity variations associated with the sub-seismic translational motions of the inner core, the so-called Slichter triplet.     

Free core nutation period inferred from the gravity measurements at Józefosław

The Free Core Nutation (FCN) is an important eigenmode which affects both Earth rotation and body tide. The FCN parameters, the resonance period and the quality factor are important for understanding the dynamics of the Earth at nearly diurnal periods. Those parameters are usually estimated either from the Very Long Baseline Interferometry (VLBI) observations of nutation, or from the tidal gravity measurements. In this paper we investigate the determination of the FCN parameters from gravity records covering a period of more than three years, collected with the use of a LaCoste&Romberg Earth Tide no. 26 gravimeter, located at Józefos?aw observatory near Warsaw. From the resonant enhancements of gravimetric factors and phases of diurnal tidal gravity waves, we could infer the FCN period to be equal to 430 sidereal days. This result is in very good agreement with previous gravimetric and VLBI nutation results, confirming the discrepancy in the dynamic flattening of the outer liquid core from its theoretical value based on the hydrostatic equilibrium assumption. The estimated FCN quality factor (Q ≈ 1300) is considerably smaller than the VLBI nutation result, which confirms that the local gravity measurements are more sensitive than VLBI global analyses to site-dependent phenomena (such as atmospheric and indirect ocean tidal effects). We also investigated the importance of gravimetric corrections in the FCN analysis, including numerical tests and simulations. This allowed us to estimate the uncertainty of FCN parameters due to improper or incomplete set of environmental corrections. We took also into account the impact of gravimetric factor errors and tidal wave selection on estimated FCN parameters. We demonstrated that despite relatively noisy measurements due to unfavorable gravimeter location, we were able to obtain very good results in case when proper correction and tidal wave selection were applied.     

Scientific achievements from the first phase (1997–2003) of the Global Geodynamics Project using a worldwide network of superconducting gravimeters

This paper aims to review the main scientific achievements which were obtained in the first phase (1997–2003) of the Global Geodynamics Project (GGP) consisting of a worldwide network of superconducting gravimeters (SG) of about 20 instruments. We show that the low noise levels reached by these instruments in various frequency bands allow us either to investigate new signals of very small amplitude or to better determine other signals previously seen. We first report new results in the long-period seismic band with special emphasis on the detection of the ₂S₁ normal mode and the splitting of the fundamental spheroidal mode ₂S₀ after the magnitude 8.4 Peru earthquake in 2001. We also discuss briefly the ‘hum’, which consists of a sequence of fundamental normal modes existing between 2 and 7 mHz even in the lack of any seismic excitation, and was first discovered on the Syowa (in Antarctica) instrument in 1998. We will comment on the search for the Slichter mode ₁S₁ of degree 1 which is associated with a translational motion of the inner core inside the liquid core. Atmospheric effects are reviewed from the local to the global scale and the improvement due to pressure loading computations on residual gravity signals is shown. An interesting study exhibiting the gravity consequence due to sudden rainfall and vertical mass motion in the atmosphere (without ground pressure change) is presented. The precision of the SGs leads to some convincing results in the tidal domain, concerning the fluid core resonance effect (free core nutation (FCN)) on diurnal tides or various loading effects (linear, non-linear) from the oceans. In particular, SGs gravity measurements are shown to be useful validating tools for ocean tides, especially if they are small and/or confined to coastal regions. The low instrumental drift of the SGs also permits to investigate non-tidal effects in time-varying gravity, especially of annual periodicity. Hydrology has also a signature which can be seen in SG measurements as shown by several recent studies. At even lower frequency, there is the Chandler motion of 435-day period which leads to observable gravity changes at the Earth's surface. We finally report on the progress done in the last years in the problem of calibrating/validating space satellite data with SG surface gravity measurements.     

Investigation of temporal gravity variations in SG-records

Not all of the gravity signals commonly observed in records of superconducting gravimeters have a physically significant meaning. Instrumental noise or signal components generated by specific processing techniques can have a strong effect. This paper analyzes selected case studies from gravity data acquired during the first period of GGP and tries to give an answer to the question of which signals are significant. It is focused on small amplitude variations in the time domain, which are compared with those of conventional spring-type gravimeters. Coherent atmospheric gravity signals due to atmospheric processes associated with strong vertical convection could be observed by different sensors. The second part deals with temporal variations of main tidal parameters, which can be seen clearly in the tidal analysis results from SG data. Synthetic case studies show that they are not strongly influenced by the analysis procedure and therefore mainly reflect ocean loading processes.     

Study on tidal gravity observations obtained at stations Zhongshan and Changcheng, Antarctic

IntroductionThe purpose of the studies on the tidal gravity observations on the Earth(s surface is to investigate the properties of the deformation and the tidal gravity variations of the Earth under the action of the luni-solar tidal force. These variations relate to the internal structure, shape and the medium(s rheology properties of the Earth (Wahr, 1981; Dehant, 1987). The theoretical studies and observations indicated that the amplitudes and the tidal parameters, including the amplitud…     

Temporal variations in free core nutation period

Based on the nearly diurnal resonance in the tidal gravity observations,the temporal variations in period of the Earth's free core nutation (FCN) are investigated by using the tidal gravity observations of 18-year duration recorded continu-ously with a superconducting gravimeter (SG) at Brussels. The effects of the global oceanic tide loading and local barometric pressure on the SG observations have been removed by using eleven high-precision global digital models of oceanic tides and barometric pressure me...     

Study of the Earth's free core nutation by tidal gravity data recorded with international superconducting gravimeters

By stacking high-precision tidal gravity observations obtained with superconducting gravimeters at six stations in China, Japan, Belgium, France, Germany and Finland, the local systematical discrepancies in the parameter fitting, caused by atmospheric, oceanic tidal loading and the other local environmental perturbations, are eliminated effectively. As a result, the resonance parameters of the Earth's free core nutation are accurately determined. In this study, the eigenperiod of free core nutation is given as 429.0 sidereal days, which is in agreement with those published in the previous studies. It is about 30 sidereal days less than those calculated in theoretical models (about 460 sidereal days), which confirms the real ellipticity of the fluid core of the Earth to be about 5% larger than the one expected in assumption of hydrostatic equilibrium. The quality factor (Q value) of free core nutation is given as about 9543, which, compared with those determined before based on the body tide observations, is much larger, but more close to those obtained using the VLBI observations. The complex resonance strength is also determined as (?6.10(10?4, ?0.01(10?4)(/h, which can principally describe the deformation characteristics of an anelastic mantle.     

Determination of the Earth＇s free core nutation parameters by using tidal gravity data

The Earth＇s free core nutation （FCN） is a retrograde eigenrnode which is attributed to the interaction between the solid mantle and the liquid core of the rotational elliptical Earth. This mode appears as an eigenmode of nearly diurnal free wobble （NDFW） in a terrestrial reference frame with a period of about one day （XU et al, 2001）. Therefore, the NDFW will lead to an obvious resonance enhancement in the diurnal tidal gravity observations, especially those of the tidal waves with frequencies closed to its eigenfrequency such as P1, K1, ψ1 and Ф1. The FCN resonance parameters can be retrieved accurately by high-precision tidal gravity observations, especially those recorded with the superconducting gravimeters （SG）. The Global Geodynamics Project （GGP） organized by IUGG took it as an important content for determining the FCN resonance parameters by using gravity data. However, the results are affected by many factors such as station location, background noise, the selection of the tide-generating potential tables, ocean tide models, data processing techniques and so on. In our study, the FCN parameters will be retrieved by using the SG observations at Wuhan, and the effects of the choices of various tide-generating potential tables, oceanic models and weight functions on the estimation of the FCN parameters will be discussed in detail,     

北京地区最新重力潮汐结果及其在检测液核共振效应中的应用

利用中国计量科学研究院北京昌平基地iGrav-012超导重力仪最新观测资料,对其作仔细地预处理,根据调和分析方法精密测定了重力潮汐参数,基于负荷理论与卷积积分技术获得了包含HAM11a,DTU10,EOT11a在内的14个全球海潮模型的重力海潮负荷效应,利用近周日频段内潮波振幅因子的共振效应求解了自由核章动（FCN）的本征参数.调和分析结果表明,重力潮汐的观测精度非常高,标准差达到1.184 nm·s^-2.基于加汉宁窗的快速傅里叶变换方法获得地震频段的地震噪声等级（SNM）为0.206,说明该台站是低背景噪声的.周日主波O₁和K₁经海潮模型作负荷效应改正的平均有效性分别为83%和85%;使用13个高精度海潮模型进行迭积计算获得的FCN本征周期为430.0（427.8,432.3）恒星日,品质因子Q值为-5137.

     

大气重力信号的理论计算及其检测

基于标准大气定律和大气圆柱体分布模型,本文引进了大气重力格林函数,用离散格积方法求得了大气对重力场观测的影响,对台站高程、周围地形和地表温度变化等因素的影响问题进行了讨论．结果说明台站近区气压变化是大气重力信号的主要贡献者,考虑大气质量负荷引起的弹性地球形变效应后,对距台站0．5°的区域积分获得的大气重力导纳值为—0．3603μGal／hPa,占全球大气变化引起的总信号的90％以上,这一理论模型结果与超导重力仪实测结果相吻合,并能较有效地用于消除重力观测中的气压干扰成分．     

大气重力信号的理论计算及其检测

基于标准大气定律和大气圆柱体分布模型,本文引进了大气重力格林函数,用离散格积方法求得了大气对重力场观测的影响,对台站高程、周围地形和地表温度变化等因素的影响问题进行了讨论．结果说明台站近区气压变化是大气重力信号的主要贡献者,考虑大气质量负荷引起的弹性地球形变效应后,对距台站0．5°的区域积分获得的大气重力导纳值为-0．3603μGal／hPa,占全球大气变化引起的总信号的90％以上,这一理论模型结果与超导重力仪实测结果相吻合,并能较有效地用于消除重力观测中的气压干扰成分．     

Time stability of spring and superconducting gravimeters through the analysis of very long gravity records

Long gravity records are of great interest when performing tidal analyses. Indeed, long series enable to separate contributions of near-frequency waves and also to detect low frequency signals (e.g. long period tides and polar motion). In addition to the length of the series, the quality of the data and the temporal stability of the noise are also very important. We study in detail some of the longest gravity records available in Europe: 3 data sets recorded with spring gravimeters in Black Forest Observatory (Germany, 1980–2012), Walferdange (Luxemburg, 1980–1995) and Potsdam (Germany, 1974–1998) and several superconducting gravimeters (SGs) data sets, with at least 9 years of continuous records, at different European GGP (Global Geodynamics Project) sites (Bad Homburg, Brussels, Medicina, Membach, Moxa, Vienna, Wettzell and Strasbourg). The stability of each instrument is investigated using the temporal variations of tidal parameters (amplitude factor and phase difference) for the main tidal waves (O1, K1, M2 and S2) as well as the M2/O1 factor ratio, the later being insensitive to the instrumental calibration. The long term stability of the tidal observations is also dependent on the stability of the scale factor of the relative gravimeters. Therefore we also check the time stability of the scale factor for the superconducting gravimeter C026 installed at the J9 Gravimetric Observatory of Strasbourg (France), using numerous calibration experiments carried out by co-located absolute gravimeter (AG) measurements during the last 15 years. The reproducibility of the scale factor and the achievable precision are investigated by comparing the results of different calibration campaigns. Finally we present a spectrum of the 25 years of SG records at J9 Observatory, with special attention to small amplitude tides in the semi-diurnal and diurnal bands, as well as to the low frequency part.     

利用全球超导重力仪数据检测长周期核模

采用全球地球动力学计划观测网中13台超导重力仪长期连续观测资料,探讨了长周期核模检测的可能性。采用相同的方法剔除了所有13个观测序列中的重力潮汐信号、仪器漂移和大气重力信号,估计了各个序列的功率谱密度及其积谱密度,估计并分析了非潮汐不同频段背景噪声。结果表明,在两个潮汐间频段（0.047~0.075cph和0.089~0.117cph)和亚潮汐频段(0.172~0.333cph),全球超导重力仪的平均噪声水平分别为0.0649,0.0350nm/s2和0.0138nm/s2,可以检测到的全球谐信号幅度极限分别为0.0416,0.0231nm/s2和0.0098nm/s2,表明全球超导重力仪观测资料基本可以识别长周期核模信号.在全球超导重力观测中,在潮汐间频段发现周期分别16.55,15.79,11.00h和10.09h的全球谐信号谱峰,可能来自于液核长周期振荡;在亚潮汐频段没有Smylie 1992年发现的Slichter模信号,但存在8个全球谐信号的谱峰,参考现有的理论模拟结果,Slichter模是这些信号可能的来源之一.     

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．     

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.     

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．     

Study of the Earth’s free core nutation by tidal gravity data recorded with international superconducting gravimeters

By stacking high-precision tidal gravity observations obtained with superconducting gravimeters at six stations in China, Japan, Belgium, France, Germany and Finland, the local systematical discrepancies in the parameter fitting, caused by atmospheric, oceanic tidal loading and the other local environmental perturbations, are eliminated effectively. As a result, the resonance parameters of the Earth’s free core nutation are accurately determined. In this study, the eigenperiod of free core nutation is given as 429.0 sidereal days, which is in agreement with those published in the previous studies. It is about 30 sidereal days less than those calculated in theoretical models (about 460 sidereal days), which confirms the real ellipticity of the fluid core of the Earth to be about 5% larger than the one expected in assumption of hydrostatic equilibrium. The quality factor (Q value) of free core nutation is given as about 9543, which, compared with those determined before based on the body tide observations, is much larger, but more close to those obtained using the VLBI observations. The complex resonance strength is also determined as (−6.10×10⁻⁴, −0.01 ×10⁻⁴)°/h, which can principally describe the deformation characteristics of an anelastic mantle.