地球液核动力学效应的研究和检测
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摘要
综合分析、处理了包括武汉台超导重力仪在内的全球地球动力学计划(GGP)观测网中多台超导重力仪长期连续观测资料及相应的台站气压观测资料，围绕地球液核动力学效应的研究与检测，着重介绍了全球超导重力仪观测资料在该领域研究的重要作用，开展了观测资料预处理、固体地球形变特征、地球近周日自由摆动、液核长周期自由振荡和固体内核平动振荡等方面的研究工作，主要结果如下：
1．研究了地球在日月引潮力和表面负荷作用下的形变特征，数值计算结果表明，在固体内核中的形变很小，由于在长周期核模本征频率附近的共振，液核中低阶(n＜10)位移随半径的变化非常复杂，当负荷阶数超过10时，地核中的形变和扰动位都很小，地球的响应主要表现为弹性地幔中的径向位移，且随深度增加急剧减弱，地表负荷Love数与信号频率的依赖关系很弱，给出了体潮Love数计算的一种有效的近似处理方案。
2．以内部负荷Love数描述了地球固体部分对液核动力学效应的形变响应，严密推导了内部负荷Love数的一般表达式，研究了内部负荷Love数的空间和频率依赖特征。数值计算结果表明，内部负荷Love数随阶数的增加迅速减小，且与扰动频率，特别是相对较高的接近于地球自由振荡本征频率的扰动频率之间存在很强的依赖性。
3．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的影响，精密确定了地球自由核章动(FCN)的共振参数，结果表明，FCN的本征周期为429.0恒星日，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恒星日，进一步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约大5％的结论；品质因子为9543，更接近于利用空间大地测量手段(如VLBI)观测资料得到的相应结果；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。
4．以武汉台超导重力仪观测资料为例，研究了海潮负荷对FCN共振参数拟合的影响和重力潮汐观测中近周日共振的区域性特征。结果表明，不同海潮模型对拟合的FCN周期和共振强度实部影响甚微，差异主要表现在品质因子和共振强度虚部的拟合，通过不同海潮模型改正后重力潮汐观测资料的迭积，可减小海潮模型不确定性的影响，获得FCN共振参数。考虑近周日共振的区域性特征，获得了基于武汉国际重力潮汐基准值的区域性重力潮汐模型，还可以为海潮负荷重力效应的反演提供很好的约束。
5．采用位移场的变分方法研究了地球椭球分层、非粘性、可压缩自转流体外核的自由振荡(内部重力／惯性波或核模)问题，充分考虑了固体弹性地幔和内核(包括CMB和ICB)的形变以及幔固系和内核自转变化(摆动或相对摆动)的影响，通过内部负荷Love数将地表自由边界条件和地心正则条件引入液核运动方程之中，经严密推导获得了液核自由振荡运动的变分泛函和用于有限元数值计算的最终计算公式。
6．采用国际GGP观测网中14台超导重力仪21个长期、稳定、连续的高质量重
！1 中国科学院测量七地球物理研究所埋学博卜学位论义
力潮汐观测序列研究了地球固体内核的平动振荡．采用相同的预处理和调和分祈川主，
精密确定并剔除了重力潮汐信号、大气重力信号和仪器长期漂移，获得了相应的重力
残差序列，引入并估计了重力残差序列的“积谱密度”．初步分析结果表明，在积谱密
度估计中没有 Smylie（1992），Smylie等（1993）和 Courtier等（2000）发现的与内核小
动振荡有关的共振信号，但存在与某些未知的全球地球物理或地球动力学效应介关的8
个重要的明显公共谱峰，估计了在这些谱峰附近的重力共振参数，其中三个谱峰的中
。L’周期与 Smith（1976）理论预测的固体内核 Slichter模的本征周期符合得非常好，－
者之间的差异分别仅为0．4％，－1．4％和1刀％．实际观测与理论模拟的这种非常灯地－－敖
性意昧着这三个谱峰可能勺地球固体内核的平动振荡有关，与然，要得到史确切的引
论还必而进一步的证据支持．
The long-term,continuous gravity data,recorded with superconducting gravimeters (SCO) at the Global Geodynamics Project (GGP) observatories including one at Wuhan,and the corresponding station atmospheric pressure records have been comprehensively processed and analyzed. Based on the study and detection on the geodynamical effects of the Earth's fluid outer core,the roles of the SCG distributed globally are especially emphasized on. We have investigated the data pre-processing,the deformation characteristics of the solid Earth,the Earth's nearly diurnal free wobble,the free oscillations of the fluid outer core and the translational oscillations of the solid inner core. The main results are listed as following:
1. The Earth's deformation under the luni-solar tidal force and surface loads is investigated. The numerical results indicate that the deformation within the solid inner core is very small. However,in the fluid outer core,the changes of the displacement with relatively low spherical harmonic degree (n<10) is very complicated via the radius,due to the resonance near the eigenfrequenies of the core long-period oscillations. While the spherical harmonic degree of the loading is larger than 10,the deformation and the gravitational perturbation in the core are very small,and the Earth's deformation response is dominantly represented as the radial displacement in the elastic mantle. The displacement decreases sharply with the depth increasing. The surface load Love numbers weakly depend upon the signal frequencies. An acceptable approximate procedure for the body tide Love number calculation is developed in this dissertation.
2. The internal load Love numbers,expressed as a general form in this dissertation,are employed to describe the deformation response of the Earth's solid parts to the dynamical behaviors of the fluid outer core. The spatial distribution and frequency-dependence characteristics of the internal load Love numbers are also investigated. The numerical results indicate that the internal load Love numbers decrease quickly with the spherical harmonic degree enhancement,and depend strongly upon the perturbation frequencies,especially upon relatively high those closed to the eigenfrequencies of the Earth's free oscillations.
3. By stacking the high-precision tidal gravity observations recorded with international SCG at six stations located on different area,the influences of the barometric pressure,ocean tides and the local environmental perturbations around the stations are eliminated effectively,and lead to an accurate determination of the resonance parameters of the Earth's free core nutation (FCN). The final results indicate that the FCN period is about 429.0 sidereal days,in closed agreement with the corresponding results in the previous studies,and about 30 sidereal days less than one expected theoretically. It confirms that the real dynamical ellipticity of the fluid core is about 5% larger than one expected on assumption of the hydrostatic equilibrium. The quality factor is about 9543,which,compared with those determined based on the tidal gravity observations in the previous studies,more closes to those obtained by using the VLBI data. The complex resonance strength is (-6.10X10-4,-0.01X10-4). It can principally descr
ibe the deformation characteristics of an anelastic mantle.
4. The tidal gravity observations,recorded with a SCG at Wuhan,are employed to investigate the influences of the ocean tide loading on the fitted FCN parameters and the
local characteristics of the nearly diurnal resonance on the tidal gravity observations. It is found that the influence of different co-tides on the fitted eigenperiod and the real part of the resonance strength of the FCN is very small. The discrepancies are less than 1.5% for the eigenperiod and 7.7% for the real part of the resonance strength. Meanwhile,the fitted qualify factor Q and the imaginary part of the resonance strength of the FCN depends obviously on the chosen co-tides,and the influence of different co-tides on the fittin
1．研究了地球在日月引潮力和表面负荷作用下的形变特征，数值计算结果表明，在固体内核中的形变很小，由于在长周期核模本征频率附近的共振，液核中低阶(n＜10)位移随半径的变化非常复杂，当负荷阶数超过10时，地核中的形变和扰动位都很小，地球的响应主要表现为弹性地幔中的径向位移，且随深度增加急剧减弱，地表负荷Love数与信号频率的依赖关系很弱，给出了体潮Love数计算的一种有效的近似处理方案。
2．以内部负荷Love数描述了地球固体部分对液核动力学效应的形变响应，严密推导了内部负荷Love数的一般表达式，研究了内部负荷Love数的空间和频率依赖特征。数值计算结果表明，内部负荷Love数随阶数的增加迅速减小，且与扰动频率，特别是相对较高的接近于地球自由振荡本征频率的扰动频率之间存在很强的依赖性。
3．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的影响，精密确定了地球自由核章动(FCN)的共振参数，结果表明，FCN的本征周期为429.0恒星日，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恒星日，进一步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约大5％的结论；品质因子为9543，更接近于利用空间大地测量手段(如VLBI)观测资料得到的相应结果；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。
4．以武汉台超导重力仪观测资料为例，研究了海潮负荷对FCN共振参数拟合的影响和重力潮汐观测中近周日共振的区域性特征。结果表明，不同海潮模型对拟合的FCN周期和共振强度实部影响甚微，差异主要表现在品质因子和共振强度虚部的拟合，通过不同海潮模型改正后重力潮汐观测资料的迭积，可减小海潮模型不确定性的影响，获得FCN共振参数。考虑近周日共振的区域性特征，获得了基于武汉国际重力潮汐基准值的区域性重力潮汐模型，还可以为海潮负荷重力效应的反演提供很好的约束。
5．采用位移场的变分方法研究了地球椭球分层、非粘性、可压缩自转流体外核的自由振荡(内部重力／惯性波或核模)问题，充分考虑了固体弹性地幔和内核(包括CMB和ICB)的形变以及幔固系和内核自转变化(摆动或相对摆动)的影响，通过内部负荷Love数将地表自由边界条件和地心正则条件引入液核运动方程之中，经严密推导获得了液核自由振荡运动的变分泛函和用于有限元数值计算的最终计算公式。
6．采用国际GGP观测网中14台超导重力仪21个长期、稳定、连续的高质量重
！1 中国科学院测量七地球物理研究所埋学博卜学位论义
力潮汐观测序列研究了地球固体内核的平动振荡．采用相同的预处理和调和分祈川主，
精密确定并剔除了重力潮汐信号、大气重力信号和仪器长期漂移，获得了相应的重力
残差序列，引入并估计了重力残差序列的“积谱密度”．初步分析结果表明，在积谱密
度估计中没有 Smylie（1992），Smylie等（1993）和 Courtier等（2000）发现的与内核小
动振荡有关的共振信号，但存在与某些未知的全球地球物理或地球动力学效应介关的8
个重要的明显公共谱峰，估计了在这些谱峰附近的重力共振参数，其中三个谱峰的中
。L’周期与 Smith（1976）理论预测的固体内核 Slichter模的本征周期符合得非常好，－
者之间的差异分别仅为0．4％，－1．4％和1刀％．实际观测与理论模拟的这种非常灯地－－敖
性意昧着这三个谱峰可能勺地球固体内核的平动振荡有关，与然，要得到史确切的引
论还必而进一步的证据支持．
The long-term,continuous gravity data,recorded with superconducting gravimeters (SCO) at the Global Geodynamics Project (GGP) observatories including one at Wuhan,and the corresponding station atmospheric pressure records have been comprehensively processed and analyzed. Based on the study and detection on the geodynamical effects of the Earth's fluid outer core,the roles of the SCG distributed globally are especially emphasized on. We have investigated the data pre-processing,the deformation characteristics of the solid Earth,the Earth's nearly diurnal free wobble,the free oscillations of the fluid outer core and the translational oscillations of the solid inner core. The main results are listed as following:
1. The Earth's deformation under the luni-solar tidal force and surface loads is investigated. The numerical results indicate that the deformation within the solid inner core is very small. However,in the fluid outer core,the changes of the displacement with relatively low spherical harmonic degree (n<10) is very complicated via the radius,due to the resonance near the eigenfrequenies of the core long-period oscillations. While the spherical harmonic degree of the loading is larger than 10,the deformation and the gravitational perturbation in the core are very small,and the Earth's deformation response is dominantly represented as the radial displacement in the elastic mantle. The displacement decreases sharply with the depth increasing. The surface load Love numbers weakly depend upon the signal frequencies. An acceptable approximate procedure for the body tide Love number calculation is developed in this dissertation.
2. The internal load Love numbers,expressed as a general form in this dissertation,are employed to describe the deformation response of the Earth's solid parts to the dynamical behaviors of the fluid outer core. The spatial distribution and frequency-dependence characteristics of the internal load Love numbers are also investigated. The numerical results indicate that the internal load Love numbers decrease quickly with the spherical harmonic degree enhancement,and depend strongly upon the perturbation frequencies,especially upon relatively high those closed to the eigenfrequencies of the Earth's free oscillations.
3. By stacking the high-precision tidal gravity observations recorded with international SCG at six stations located on different area,the influences of the barometric pressure,ocean tides and the local environmental perturbations around the stations are eliminated effectively,and lead to an accurate determination of the resonance parameters of the Earth's free core nutation (FCN). The final results indicate that the FCN period is about 429.0 sidereal days,in closed agreement with the corresponding results in the previous studies,and about 30 sidereal days less than one expected theoretically. It confirms that the real dynamical ellipticity of the fluid core is about 5% larger than one expected on assumption of the hydrostatic equilibrium. The quality factor is about 9543,which,compared with those determined based on the tidal gravity observations in the previous studies,more closes to those obtained by using the VLBI data. The complex resonance strength is (-6.10X10-4,-0.01X10-4). It can principally descr
ibe the deformation characteristics of an anelastic mantle.
4. The tidal gravity observations,recorded with a SCG at Wuhan,are employed to investigate the influences of the ocean tide loading on the fitted FCN parameters and the
local characteristics of the nearly diurnal resonance on the tidal gravity observations. It is found that the influence of different co-tides on the fitted eigenperiod and the real part of the resonance strength of the FCN is very small. The discrepancies are less than 1.5% for the eigenperiod and 7.7% for the real part of the resonance strength. Meanwhile,the fitted qualify factor Q and the imaginary part of the resonance strength of the FCN depends obviously on the chosen co-tides,and the influence of different co-tides on the fittin
引文
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