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.     

解算液核自由章动常数的三频谱线法

地球液核自由章动(FCN)常数是比较重要的地球物理参数. Sosao等人, Wahr和 Bergen等人给出了FCN常数的理论估值. Gwinn等人首先利用甚长基线干涉测量获得FCN常数的观测值, 同年Neuberg等人开始采用重力潮汐观测资料解算FCN常数, 并引入了此后进行类似研究的学者所普遍采用的迭积法, 其他学者的研究都基本与Neuberg等人的结果相似, 但其结果与VLBI的观测结果不吻合, FCN常数的观测值一时无定论. 现提出了有直观地球物理意义的三频谱线法, 采用3个超导重力台站的资料进行解算, 获得的FCN常数与VLBI的观测基本吻合, 这对于确定FCN常数的观测值具有较重要意义.     

利用国际超导重力仪观测资料研究地球自由核章动

采用不同区域分布的6台国际超导重力仪高精度重力潮汐观测资料的迭积, 有效地消除了大气、海洋和台站周围环境因素引起的参数拟合的区域性系统偏差, 精密确定了地球自由核章动(FCN)的共振参数. FCN的本征周期为429.0 d1), 与以前的同类研究结果相吻合, 和理论模拟结果相比则偏小约30 d, 证实了液核的真实动力学椭率比流体静力平衡假设下动力学椭率大约5%的结论. 品质因子为9543, 与早期利用固体潮观测资料获得的相应结果相比, 更接近于利用VLBI观测资料得到的结果. 所测定的复共振强度为(-6.10×10-4, -0.01×10-4)°/h, 基本反映了非弹性地幔的形变特征.     

核幔耦合对地球自由核章动的激发影响

地球自由核章动（FCN）是地幔与液核相互作用的重要动力学现象,其激发机制涉及地表流体层、地幔和地核等圈层之间的耦合,此前研究多利用地表流体层角动量数据单独研究其对FCN的激发,对核幔耦合的影响考虑不足.本文基于角动量守恒理论分析了核幔耦合对FCN周期及振幅的影响,并结合多个大气及海洋角动量函数时间序列首次估算了核幔耦合在FCN激发过程中的贡献.结果表明核幔耦合对FCN周期产生的固定和时变影响对FCN激发的作用均不可忽视,尤其时变影响可达几十个微角秒,对于进一步解释FCN时变特征非常重要;核幔耦合对FCN振幅的直接影响是地表流体层的激发与实测FCN不相符的主要原因,黏滞、电磁和地形等耗散耦合的存在对地表流体的激发振幅有67%左右的减弱效果.     

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.     

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.     

解算液核自由章动常数Akpem>-Btkem>方法及其结果

地球液核旋转产生近周日晃动（NDFW）．利用周日波的液核共振效应解算液核自由章动（FCN）常数是液核研究的一个方面．1987年以来一些国家的学者相继开展了由潮汐资料解算FCN常数的研究,他们基本上都采用了5个周日波参与解算的迭积法(stackingmethod)．本文提出了一种有直观几何意义的Akp-Btk方法,仅用信噪比最高的3个周日波就可完成FCN常数的解算,并选用3个超导重力台站Cantley（北美洲）、武汉（亚洲）和布鲁塞尔（欧洲）的资料进行计算．解算的液核自由章动常数（TFCN和Q）与VLBI的观测结果基本一致,这在十几年来尚属首次．      

利用潮汐重力资料检测地球自由核章动

地球的自由核章动(free core nutation,简称FCN)是由于旋转椭球地球的固态地幔与液态地核之间的相互作用而产生的一个逆向自由章动本征模,在地固参考系中表现为近周日自由摆动(nearly diurnal free wobble,简称NDFW)(徐建桥等,2001).     

内核地球自转动力学理论的研究进展(Ⅰ)-理论基础

地球固体内核(SIC)和地球其余部分之间的引力和压力的耦合作用引起了一个力矩,从而对地球的章动运动产生影响.由于SIC的转动惯量和整体地球转动惯量相比是非常小的,因此可以认为SIC的动力学效应只是导致一个新的章动本征模,其频率与自由核章动(FCN)相差不太远,且对地球章动产生了一个微弱的共振影响.本文在文献[1]理论的基础上,对内核地球自转动力学理论进行了更加深入和详细的研究,顾及到高阶引潮力位的影响,介绍了研究内核地球自转的基本假设和定义,引潮力位的复数球函数表示,复数矢量球函数的基本理论等.     

内核地球自转动力学理论的研究进展(Ⅰ)

地球固体内核（SIC）和地球其余部分之间的引力和压力的耦合作用引起了一个力矩，从而对地球的章动运动产生影响.由于SIC的转动惯量和整体地球转动惯量相比是非常小的，因此可以认为SIC的动力学效应只是导致一个新的章动本征模，其频率与自由核章动（FCN）相差不太远，且对地球章动产生了一个微弱的共振影响.本文在文献〔1〕理论的基础上，对内核地球自转动力学理论进行了更加深入和详细的研究，顾及到高阶引潮力位的影响，介绍了研究内核地球自转的基本假设和定义，引潮力位的复数球函数表示，复数矢量球函数的基本理论等.     

Investigation of the time variability of diurnal tides and resonant FCN period

The time variability of diurnal tides was investigated by analyzing gravity observations from global superconducting gravimeter (SG) stations with running time intervals. Through least-square and Bayesian approaches, FCN resonance parameters were estimated for each data section after obtaining the tidal parameters of mainly diurnal tidal waves. The correlation of the time variation in diurnal tidal waves and FCN period was discussed. For comparison, a similar method was used to analyze VLBI observations to study the time variability of nutation terms and FCN period. The variation trend of the FCN period totally depends on the Ψ1 wave in tidal gravity and on the retrograde annual term in nutation. We observed a similar variation trend in the FCN periods obtained from different SG stations worldwide and VLBI observations. The relation between diurnal tides and LOD variations is discussed and the possible mechanisms of the decadal variation in FCN periods were discussed.     

Tri-frequency spectrum method and results for resolving the parameters of Earth's liquid core free nutation

The parameters of Earth free core nutation (FCN) are two relatively significant geophysical parameters. Sasao et al. (1980) and Wahr and Bergen (1986) provided the theoretical estimation values of FCN parameters. Gwinn, Herring and Shapiro (1987) first obtained the observational values of FCN parameters by very long base Interference (VLBI) at Cambridge University. In the same year, Neuberg and Zürn in former West Germany and Hinderer in France began to retrieve FCN parameters by the observation of gravity tides and introduced the stacking method. The other scholars who researched into the same geophysical problems by applying the data of gravity tides basically followed the stacking method. The results they reached were similar to the observational result of FCN parameters given by Neuberg et al. in 1987. But the observational results of FCN parameters gained from gravity tides were not identical with those from VLBI, mainly because of the large difference of quality of FCN. So there was not an affirmative observational result of FCN parameters since then. In this paper, The authors firstly introduce the tri-frequency spectrum method with clearly geometrical and geophysical meaning for the resolution of FCN parameters, and the observational results of FCN parameters obtained from tide data at three superconducting gravity stations were accordant with those from VLBI, which will be relatively important to arriving at a certain observational result of FCN parameters.     

Tri-frequency spectrum method and results for resolving the parameters of Earth’s liquid core free nutation

The parameters of Earth free core nutation (FCN) are two relatively significant geophysical parameters. Sasao et al. (1980) and Wahr and Bergen (1986) provided the theoretical estimation values of FCN parameters. Gwinn, Herring and Shapiro (1987) first obtained the observational values of FCN parameters by very long base Interference (VLBI) at Cambridge University. In the same year, Neuberg and Zürn in former West Germany and Hinderer in France began to retrieve FCN parameters by the observation of gravity tides and introduced the stacking method. The other scholars who researched into the same geophysical problems by applying the data of gravity tides basically followed the stacking method. The results they reached were similar to the observational result of FCN parameters given by Neuberg et al. in 1987. But the observational results of FCN parameters gained from gravity tides were not identical with those from VLBI, mainly because of the large difference of quality of FCN. So there was not an affirmative observational result of FCN parameters since then. In this paper, The authors firstly introduce the tri-frequency spectrum method with clearly geometrical and geophysical meaning for the resolution of FCN parameters, and the observational results of FCN parameters obtained from tide data at three superconducting gravity stations were accordant with those from VLBI, which will be relatively important to arriving at a certain observational result of FCN parameters.     

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.     

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.     

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...     

Effects of inner core viscosity on gravity changes and spatial nutations induced by luni-solar tides

In this paper, we investigate the perturbations induced by the nearly-diurnal luni-solar tidal potential on the surface gravity changes and on the spatial nutations. The effects of the magnetic friction at the inner core boundary (ICB) and on the inner core viscosity at this time scale are studied. We show that very precise very long baseline interferometry (VLBI) observations of the in-phase and out-of-phase components of some nutations can give information on the Earth’s deep interior, especially on the effective viscosity of the inner core and on the amplitude of the radial component of the magnetic field at the ICB.     

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,