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.     

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.     

Parameters of the fluid core resonance inferred from superconducting gravimeter data

We have estimated the parameters of fluid core resonance (FCR) due to the nearly diurnal free wobble of the Earth's core based on the superconducting gravimeter (SG) data obtained at the following four observation sites; Esashi and Matsushiro in Japan, Canberra in Australia and Membach in Belgium. By fitting the tidal admittances normalized with the O1 wave at each site to a model of the damped harmonic oscillator, we obtained values of 429.66 ± 1.43 sidereal days, 9350–10,835, −4.828E−4 ± 3.4E−6, −3.0E−5 ± 4.5E−6 for the eigenperiod, the Q-value and the real and imaginary parts of the resonance strength, respectively. Our values obtained from only using the gravity data are very consistent with those inferred from the VLBI nutation data. Our study strongly indicates that the systematic difference between two estimations from the gravity and the nutation in particular for the Q-value, which has been shown in previous works, is mainly caused by the inaccurate correction for the ocean tide effects. The error in the ocean tide correction is discussed based on the comparison among four global ocean tide models; Schwiderski model (1980), NAO.99b (Matsumoto et al., 2000), CSR4.0 (Eanes and Bettadpur, 1994) and GOT99.2b (Ray, 1999).     

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1.184nm·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.     

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.     

深内部地球结构对内核平动振荡本征周期的影响

地球固态内核的平动振荡是地球的基本简正模之一,又称Slichter模,其本征周期大约为几个小时,与地球内部结构密切相关.为了研究影响内核平动振荡的本征周期与内部结构的依赖关系,本文利用球对称、非自转、弹性和各向同性地球模型（SNREI）,通过自由振荡运动方程的数值积分,以地球模型PREM为基础,理论上系统研究了地球内部介质（包括密度、地震波速等）分布异常对Slichter模本征周期的影响.数值结果表明,Slichter模周期随着内外核边界（ICB）密度差的增加以类似于双曲线的特征显著减小,当ICB密度差从597 kg·m^-3减小到200 kg·m^-3时,周期增大66.44%,当ICB密度差从597 kg·m^-3增大到1000 kg·m^-3时,周期减小21.48%;Slichter模周期随着核幔边界（CMB）密度差的增大而缓慢增大;相对于PREM,地球模型1066A在ICB和CMB的密度差分别相差45.321%和1.132%,内部地震波速度和密度梯度也存在差异,但是,当密度差减小到1066A模型提供的数值时,得到的Slichter模周期与基于1066A获得的结果（4.599 h）非常接近,差异分别只有3.762%和0.037%;表明Slichter模本征周期与地球内部介质的精细结构关系不大,而对ICB的密度差非常敏感.内、外核P波波速分布异常对Slichter模周期的影响基本相当,当内核和外核P波波速均增加5%时,Slichter周期分别减小1.02%和1.69%,P波波速分别减小5%时,Slichter模周期分别增加1.27%和1.847%,内核S波波速分布异常比P波波速分布异常对Slichter模周期的影响小1个量级;与地核相比,地幔中的地震波速异常对Slichter模本征周期的影响小1~2个量级;表明地核中地震波速异常对Slichter模周期的影响很小,目前有关Slichter模周期理论计算的差异主要来自于所采用的地球模型中内核边界的密度差的差异,本文结果可以为Slichter模的研究、探测及其对地球深内部结构的约束提供理论依据.     

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．     

地球重力场的精细频谱结构及其应用

综述了近年内在全球地球动力学合作观测和研究网络框架下开展的重力场观测、频谱结构和应用研究方面的成果. 内容涉及精密大气、海潮负荷信号检测, 重力潮汐和自由核章动参数测定, 海潮模型和重力固体潮模型有效性检验, 重力潮汐实验模型构制, 地球球型基频和低阶震型谱峰分裂现象和地球Chandler摆动等方面. 文章还介绍了综合现代大地测量技术, 全球超导重力仪的长期、连续观测在地表水循环、同震和震后形变、地球慢形变和地壳垂直运动等方面将发挥重要作用的情况.     

基于旋转微椭地球模型的内核平动振荡三重谱线理论模拟与实验探测

本文基于旋转微椭地球模型,采用简正模理论计算了地球内核平动振荡三重谱线的本征周期,理论上系统研究了地球内部介质(包括密度、地震波速等)分布异常对三重谱线本征周期的影响,计算了不同的内外核密度差和地核中的不同的P/S波速对应的内核平动振荡理论三重谱线周期;利用全球分布的9个超导台站,迭积每个台站长达54个月的高精度超导重力仪数据,在亚潮汐频段(0.162~0.285cph)检测内核平动振荡三重谱线.结果发现,三重谱线本征周期对内外核边界的密度跳跃非常敏感,随着密度差的增加,以类似于双曲线的特征减小;无论是采用地球质量不变的方法还是采用浮力频率为常数的方法,计算得到的三重谱线本征周期结果相差较小,且随着内外核密度差的增大,差距逐渐减小;内、外核P波波速分布异常对三重谱线周期的影响基本相当,内核S波波速分布异常比P波波速分布异常对三重谱线周期的影响小1个量级;探测到一组信噪比较高且满足谱峰分裂特征的三重谱线的信号(0.19281,0.21456和0.24151cph),有极大的可能是来自于内核平动振荡.基于探测结果可以推断实际的地球模型其内外核密度差应该介于PREM模型和1066A地球模型之间,更接近于1066A模型.     

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.     

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...     

Determination of the long period tidal waves in the GGP superconducting gravity data

Several results about the long period (LP) tidal waves are obtained by the analysis of series of superconducting gravity data, provided by the Global Geodynamics Project (GGP). The most important result is the determination of a single group called LPMF, composed by all LP tides but representing accurately the parameters of the M_f wave. As the LP tidal generating potential is vanishing at latitudes ±35°15′52″ we cannot determine accurate tidal amplitude factors for the stations located between ±40° and ±30°. However, it is still possible to obtain tidal residual vectors and compare them with oceanic tidal loading computations. For 15 stations the NAO99 oceanic model is giving a coherent picture. For nine stations with M_f amplitude larger than 3 μgal (1 μgal = 10 nm s⁻²) a global analysis is obtained by introducing the loading effect of the ocean directly in the observation equations. The mean amplitude factor obtained for LPMF is larger than expected from the models and there is a significant phase lag, showing the imperfection of the tidal oceanic models for M_f. Other new result is the first separate estimation of the parameters of the LP tides, generated by the tidal potential of third degree, dominated by a Lunar declinational monthly wave, called here 3M_md. Due to their small amplitudes (under 1 μgal) these waves are practically hidden by the noise. Nevertheless, the quality of the data and the flexibility of the VAV analysis method [Venedikov, A.P., Arnoso, J., Vieira, R., 2001. Program VAV/2000 for tidal analysis of unequally spaced data with irregular drift and colored noise. J. Geodetic Soc. Jpn. 47 (1), 281–286; Venedikov, A.P., Arnoso, J., Vieira, R., 2003. VAV: a program for tidal data processing. Comput. Geosci. 29, 487–502.] allow getting significant results, in agreement with the theory of the Earth deformation by the tidal potential of third degree.     

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,     

On the Mechanism of the Secular Tidal Acceleration of the Solid Inner Core and the Viscosity of the Liquid Core

As is known, the secular deceleration of the Earth's diurnal rotation is explained mainly by the tidal friction in the ocean. Below we consider this mechanism in some detail, taking into account also elastic deformations of the mantle under the action of ocean loading and the interaction between the tide-generating body, ocean tidal wave, liquid outer core, and solid inner core. It is shown that elastic displacements of the core-mantle boundary under the action of ocean loading are of about the same amplitude and phase as the elastic loading displacements of the Earth's outer surface. As a result, side by side with the mechanism of secular deceleration of diurnal rotation of the mantle, there are also (1) the opposite mechanism of secular acceleration of diurnal rotation of the outer liquid core and of the solid inner core and (2) the mechanism of excitation of differential rotation in the liquid core. Taking these effects into account, we compare theoretical and modern observed data on the eastward drift of the solid inner core. It is shown that the best agreement may be obtained if the turbulent viscosity of the liquid core is about 2 × 10 ³ Poise     

液核地球的周日固体潮响应

本文研究了液核地球对日月引潮力位球谐函数项的变形响应,即周日固体潮。作为数值结果,计算了1066A地球模型的周日潮汐勒夫数。所建立的周日固体潮理论模型改进了Molodensky液核动力学理论模型。为了比较两者之间的差异,还根据Molodensky理论模型计算了1066A地球模型的周日潮汐勒夫数。     

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.     

International tidal gravity reference values at Wuhan station

The international tidal gravity reference values at Wuhan station are determined accurately based on the comprehensive analysis of the tidal gravity observations obtained from 8 instruments. By comparing these with those in the tidal models given by Dehant (1997) while considering simultaneously (i) the global satellite altimeters tidal data, and (ii) the Schwiderski global tidal data and the local ones along the coast of China, it is found that the average discrepancy of the amplitude factors and of the phase differences for four main waves are given as 5.2% and 3.6% and as 0.16° and 0.08° respectively. They are improved evidently compared to those determined in early stage, indicating the important procedures in improving the Wuhan international tidal gravity reference values when including the long-series observations obtained with a superconducting gravimeter, and when considering the influence of the ocean loading and of the nearly daily free wobble of the Earth’s core.     

Time Variations In Gravity And Inferences On The Earth's Structure And Dynamics

This paper reviews how the study of the surface gravity changes is able to provide useful information on the Earth's structure and global dynamics. The spectral range which is observable with superconducting gravimeters is broad and goes from the seismic frequency band to periods longer than one year. We first investigate the seismic and sub-seismic bands with a special attention paid to the gravity detection of core modes in the liquid core and to the Slichter mode of translation of the solid inner core. In the tidal bands, we show how accurate measurements allow us to infer constraints on various phenomena such as mantle (an-)elasticity, as well as ocean and atmospheric loading. The observation of the Free Core Nutation resonance in the diurnal frequency band is reviewed and indirectly suggests an increase in the ellipticity of the core-mantle boundary with respect to its hydrostatic value. A similar resonance is also theoretically predicted in the diurnal band for the rotation of the solid inner core (Free Inner Core Nutation) but we show that its detection is much more difficult because of the small amplitude and lack of a nearby tidal frequency. Oceanic and atmospheric loading mechanisms induce gravity changes over a wide spectral range and we present some recent progress in this field. Finally, because superconducting gravimeters have high calibration stability and small long-term instrumental drift, they can easily measure longperiod gravity variations due to polar motion and hydrogeology.     

基于分层结构参数变化的地球自由振荡简正模研究

大地震激发导致的地球自由振荡可为获得地球深部结构提供重要手段,通过理论计算自由振荡简正模的本征周期,并与实测结果进行比较,可为地球深内部结构和新地球模型的研究提供有效约束.采用微分方程数值积分技术和G-D1066A地球模型,本文计算了0~48阶的187个球型自由振荡简正模的本征周期,将计算结果与Gilbertt和Dziewonski等3组模型理论结果及Ness等4组观测结果进行比较,相对偏差在0.3%以内.分析说明由于考虑了地幔、外核和内核等不同分层密度和拉梅参数变化的影响,获得了较高精度的地球自由振荡简正模周期.本文提供的理论计算结果可为修正真实地球内部参数提供有效参考.     

超导重力技术在探讨核幔边界黏性特征中的初步应用

旋转椭球型地球的固体地幔与液态地核间相互作用而产生的逆向本征模通常称之为地球自由核章动,自由核章动的品质因子（Q值）能有效反映核幔边界层能量耗散特征,与核幔边界的黏滞度密切相关.本文首次利用全球地球动力学计划网络23个台站27组高密度采样的高精度超导重力仪器观测数据,采用迭积技术,确定了自由核章动参数Q值,进而计算了核幔边界的黏滞系数.数值结果说明获得的核幔边界动力学黏滞系数达到10³ Pa·s量级,与加拿大科学家Smylie等利用VLBI观测资料获得的最新结果一致,这说明重力技术是有效应用于研究地球深内部结构的重要手段之一.