【作者】 雷湘鄂；

【导师】 许厚泽；

【作者基本信息】 中国科学院研究生院（测量与地球物理研究所） ， 固体地球物理学， 2003， 博士

【摘要】 本文的研究工作包括两个研究方向：上篇是液核自由章动常数的研究与检测，下篇是地球自由振荡的研究与检测。上篇首先是利用地球自转的欧拉方程分析了地球的自由摆动和受迫摆动，并以此为基础讨论了重力潮汐因子的液核共振效应，然后阐述了超导重力仪的观测原理和重力潮汐观测资料的调和分析及海潮负荷改正，最后论述了利用观测重力潮汐因子解算液核自由章动常数的三频谱线法及其解算结果。下篇首先推导了地球自由振荡所满足的常微分方程组，接着分析了环型自由振荡和球型自由振荡常微分方程组的数值积分，并利用瑞利原理和微扰理论分析了地球自由振荡的谱线分裂，然后讨论了地球自由振荡观测资料的寻找和预处理方法，最后阐述了所采用的谱分析方法及地球自由振荡谱的检测结果。本文获得的主要研究结果如下： （1）本文提出了解算液核自由章动常数的三频谱线法，这是研究该问题的新尝试。三频谱线法中的Awv（ob）和Bwv（ob）不仅有直观的几何意义，而且与之对应的幅谱线Awv（m1）和相频谱线Bwv（m1）也有明显的地球物理意义，并屏蔽了A^*对解算T_FCN和Q的影响。这利于我们清晰地分析观测资料与解算结果之间的相应关系。同时，我们提出ER（Akp）作为一种衡量观测资料优劣的相对客观的标准，使我们在解算前就舍弃一些不太合理的资料。这对于我们客观有效地提高解算质量是很有价值的。 （2）以往利用潮汐观测资料求取FCN常数的迭积法（Stacking mothed）的解算结果与VLBI的观测比较，T_FCN接近，而Q则相关较远了。本文外三频谱线法（Akp-Btk方法）的解算的FCN常数为：T_FCN=422.1±23.3（恒星日），Q=14781（Q＞434）与Herring等由VLBI观测获得的结果：T_FCN=433.2±2（恒星日），Q=16130±6600是吻合的。内三频谱线法（Awk-Bwk方法）的解算结果为：T_FCN=424.5±5.0（恒星日），Q=25994±1511，与外三频谱线法的结果一致的，而且与VLBI的观测结果也基本上是一致的。本文解算结果对于确定FCN常数这一地球物理参数具有较重要意义。 （3）在地球自由振荡信号的预处理中，我们提出一种多项式分段拟合重力潮汐信号的方法，而不是沿袭以往学者在去除重力潮汐时常采用的数字滤波法，通过对实际资料的细致分析表明：我们所提出的消除重力潮汐的预处理方法对于检测重要的低阶地球自由振荡振型更为有利。我们综合分析在2001年6月23日秘鲁8.2Ms地震期间国际上五个超导重力台站的6组重力潮汐观测资料，并采用残差迭积的傅氏分析和最大熵谱法进行谱分析，在国际上率先用超导重力仪检测到₀S₀～₀S₄₈的全部简正模系列。 （4）将本文检测的结果与先前发表的三组观测值和三组模型值进行比较，我们发现秘鲁地震激发的₀S₂振型与阿拉斯加地震激发的该振型之间存在约1.5‰额外相对偏差。利用已有自由振荡谱线分裂理论及其结果进一步讨论，我们认为两次地震激发的₀S₂振型的差别可能反映了地球内核的各向异性。另外，通过对₁S₂中国科学院测量与地球物理研究所博士学位论文振型分裂谱峰的讨论，本文还首次观测到自由振荡的谱线分裂不对称因子，进一步分析还表明自转方向和逆自转方向上的谱线分裂不对称因子可能是不同的，并且还差异较大。更多还原

【Abstract】 This paper includes in two sections: the first section is about the research and resolution of the parameters of the Earth’s liquid core free nutation, and the second section involves in the research and detection of the earth free oscillation. In the first section, we will analyze the free and forced wobble of the earth on the base of the Eular equation of the earth’s rotation, and discuss the earth liquid core resonance effect on the factors of diurnal gravity tides. Then, we will explain the observation principle of superconducting gravimeters and illustrate the harmonic analysis of gravity tidal data and the correction of ocean tide loading. At last, we will discuss the tri-frequency spectrum method and results for resolving the parameters of the earth’s free core nutation (FCN) by employing the observational factors of diurnal gravity tides. In the second section, we will infer the ordinary differential equation group satisfied by the earth free oscillations (EFO), and then we will give the discussion on the numerical integration of ordinary differential equation groups of torsional and spheroidal oscillations, and apply the Rayleigh principle and perturbation theory to analyze the spectral splitting of EFO. Later we will advise some simple method of looking for the signals of the earth free oscillation and illustrate the pretreatment of the observational data of EFO. Finally we will explain the methods of spectral analysis adopted in this section, and research the spectral analysis results of detecting the earth free oscillation. The main research results gained in this paper are summed up in the following lines:(1) We introduce the tri-frequency spectrum method for the resolution of FCN parameters, this is a new try in this geophysical field. In the tri-frequency spectrum method (TFSM), both the observational amplitude-frequency parameter (OAFP) Awv(ob) and the observational phase-frequency parameter (OPFP) Bwv(ob) have directly geometrical meaning, and both the amplitude-frequency spectrum (AFS) Awv(ml) and the phase-frequency spectrum (PFS) Bwv(ml) have clearly geophysical meaning. And A is shielded in the process of resolving TFCN and Q in TFSM, these help us to analyze the relationships between the resolution results and the observational tidal data distinctly. At the same time, we introduce the extended range of Akp(ob) value (ER(Akp)) as the relatively objective criterion of checking observational tidal data to get rid of those unreasonable data before resolving the FCN parameters, and it is very important for us to improve the quality of resolving FCN parameters objectively and effectively.(2) By comparing the resolution results of FCN parameters obtained by the stacking method from gravity tides with those from VLBI, we can find that TFCN values coming from gravity tides were close to TFCN value from VLBI, but Q values given by gravimetric observation were very different from that by VLBI. So there did not exist an affirmative observation value of FCN parameters before. The resolution values of FCN parameters in the external tri-frequency spectrum method (ETFSM) are TFCN=422.13 ± 23.34(sidereal days) and Q=14781(Q>433.76), which are identical with the observation values of FCN parameters: TFCN=433.1 ±2(sidereal days) and Q=16130±6600 from VLBI. The computational results of inner tri-frequency spectrum method (ITFSM) are TFCN=424.5 ± 5.03(sidereal days) and Q=25993.97 ± 1510.64, which are in agreement with FCN parameters provided by ETFSM and are basically accordant with FCN parameters by VLBI. So the resolution results for FCNparameters in whole tri-frequency spectrum method (TFM) will be relatively significant for the determination of the objective observation value of FCN parameters.(3) In the pretreatment of signals of the earth free oscillations (EFO), we don’t follow the digital filters that the former scholars often applied to get rid of gravity tides, but introduce a kind of polynomial fitting technique fragmentally to remove gravity tides更多还原