液核自由章动常数和地球自由振荡的研究与检测
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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_0S_0～_0S_(48)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_0S_2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_0S_2振型的差别可能反映了地球内核的各向异性。另外，通过对_1S_2
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。
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 o
n 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 FCN
parameters 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
(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_0S_0～_0S_(48)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_0S_2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_0S_2振型的差别可能反映了地球内核的各向异性。另外，通过对_1S_2
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。
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 o
n 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 FCN
parameters 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
引文
1．钱伟长，叶开源，1980，弹性力学，北京：科学出版社
2．傅承义，陈运泰，祁贵仲，1985，地球物理学基础．北京：科学出版社
3．方俊，1984，固体潮，北京：科学出版社
4．方俊，1986a，地球自由振荡，测量与地球物理集刊，7：65-83
5．方俊，1986b，地球自由振荡(续)，测量与地球物理集刊，8：53-69。
6．许厚泽，蒋福珍，张赤军，1999，我国动力大地测量学进展，动力大地测量学研究进展论文集：1-8
7．许厚泽，王广运，1989，动力大地测量学—研究地球动态变化的学科，科学发展与研究，(4)：9-15。
8．许厚泽，张赤军，1997，我国大地重力学和固体潮研究进展，地球物理学报，40(sup)：192-205。
9．孙和平，许厚泽，1997，国际地球动力学合作项目的实施和展望，地球科学进展，12(2)：152-157。
10．张赤军，1995，大地测量与地球动力学—兼述它与地球物理学的联系，地球物理学进展，10(4)：48-56
11．韩大仲，1986，旋转椭球地球的潮汐响应，测量与地球物理集刊，7：103-107
12．周蕙兰，1990，地球内部物理，北京：地震出版社
13．孙和平，许厚泽，Ducarme．B等，1998，中比法三国超导重力仪潮汐观测资料综合对比分析与研究，科学通报，43(13)：1438-1443
14．孙和平，许厚泽，罗少聪，1999，用超导重力仪的潮汐观测资料研究海潮模型，测绘学报，28(2)：115-120。
15．孙和平，许厚泽，徐建桥，柳林涛，2000，重力场的潮汐变化观测及其研究，地球科学进展，15(1)：53-57。
16．许厚泽、陈振帮、杨怀冰，1982，海洋潮汐对重力潮汐观测的影响，地球物理学报，25(2)：120-129。
17．许厚泽，毛伟健，1988，中国大陆的海洋负荷潮汐改正模型，中国科学(B辑)，25(9)：984-994．
18．许厚泽，孙和平，1998，我国重力固体潮实验研究进展，地球科学进展，13(5)：415-421。
19．许厚泽，孙和平，徐建桥等，2000，武汉国际重力潮汐基准研究，中国科学(D辑)，30(5)：549-553。
20．徐建桥，许厚泽，孙和平等，1999，利用超导重力仪观测资料检测地球近周日共振，地球物理学报，42(5)：599-608。
21．徐建桥，郝兴华，孙和平，1999，武汉基准台气压对重力潮汐观测的影响，测绘学报，28(1)：75-79。
22．徐建桥，孙和平，罗少聪，2001，利用国际超导重力仪研究地球自由核章动，中国科学(D辑)，31(9)：719-726
23．柳林涛，许厚泽，孙和平，郝兴华，2000，重力潮汐参数精密确定的小波分析方法，中国科学(D辑)，30(4)：442-448
24．罗少聪，孙和平，2000，大气压力变化对武汉台站重力场观测的影响，测绘学报，29(sup)：181-187．
25．丁月蓉，1998，天文数据处理方法．南京：南京大学出版社
26．孙和平，1997，大气重力格林函数．科学通报，42(5)：1640-1646
27．徐建桥，郝兴华，孙和平，1999，武汉基准台气压对重力潮汐观测的影响．测绘学报，28(1)：21-27
28．管泽霖、宁津生，1981，地球形状及其外部重力场(上册)，北京：测绘出版社
29．管泽霖、宁津生，1983，地球形状及其外部重力场(下册)，北京：测绘出版社
30．维尼狄柯夫，对任意长度的固体潮记录资料进行分析的方法，郭寿铃等译，1980，固体潮译文集，北京：科学出版社
31．梅尔基奥尔、著，杜品仁、吴庆鹏、陈益惠、刘克人译，行星地球的固体潮，1984，北京：科学出版社
32．李瑞浩，1988，重力学引论，北京：地震出版社
33．郭俊义，1994，物理大地测量学基础，武汉：武汉测绘科技大学出版社
34．郭俊义，2001，地球物理学基础，北京：测绘出版社
35．郗庆文，1982，固体潮汐理论值计算，地球物理学报，25(增刊)：632-643
36．郗庆文、侯天航，1986，固体潮汐与引潮常数，中国地震，2(2)：30-41
37．刘钦圣，1989，最小二乘问题计算方法，北京：北京工业大学出版社
38．南京大学数学系计算数学专业，1978，数值逼近方法(计算数学讲义一)，北京：科学出版社
39．南京大学数学系计算数学专业，1978，常微分方程数值解法(计算数学讲义三)，北京：科学出版社
40．Aki，K．，Rieherds，EG．，(著)，李钦祖、邹其嘉等(译)，傅承义(校)，1986，定量地震学(第一卷)，理论和方法，北京：地震出版社
41．邹鲲、彭俊泉、龚享铱，2002，MATLAB 6.X信号处理，北京：清华大学出版社
42．姚天任，孙洪，2000，现代数学信号处理，武汉：华中理工大学出版社
43．孙和平，陈晓东，许厚泽，王勇，2001，GWR超导重力仪潮汐观测标定因子的精密测定，地震学报，23(6)：651-658
44．陈晓东，孙和平，2002，一种新的重力潮汐数据预处理和分析方法，大地测量与地球动力学，22(3)：83-87
45．周华，1988，液核近周日共振的检测，[硕士论文]，武汉：中科院测量与地球物理研究所
46．方明，1991，地球自由振荡—正演、反演理论中若干问题的研究，[博士论文]，武汉：中科院测量与地球物理研究所
47．陈晓东，2003，武汉九峰台超导动仪固体潮观测资料的预处理和分析结果，中国科学院研究生院[硕士论文]，武汉：中国科学院测量与地球物理研究所
48．周江存，2002，利用最近海潮模型研究地球物理场中的负荷效应问题，中国科学院研究生院[硕士论文]，武汉：中国科学院测量与地球物理研究所
49．徐建桥，2002，地球液核动力学效应的研究和检测，中国科学院研究生院[博士论文]，武汉：中国科学院测量与地球物理研究所
50．罗少聪，2003，大气负荷效应问题研究，中国科学院研究生院[博士论文]，武汉：中国科学院测量与地球物理研究所
51．雷湘鄂，1998，液核共振参数的值算法及其结果，中国地震局[硕士论文]，武汉：中国地震局地震研究所
52．雷湘鄂，贾民育，李辉，2000，解算液核自由章动常数的Akp-Btk方法及其结果，地震学报，22(3)：319-326
53．雷湘鄂，许厚泽，2001，解算液核自由章动常数的三频谱线法，中国科学(D辑)，31(9)：727-734
54．雷湘鄂，许厚泽，孙和平，2002，利用超导重力观测资料检测地球自由振荡．科学通报，47(18)：1432-1436
55. Bullen. K. E. 1942, The density var of the earth's central core, Bull. Seismol. (32):19
56. Marriam, J. B., 1992, An ephemeris for gravity tide predictions at then Gal level, Geophys. J. Int., 108:415-422
57. Oldham, R. D., 1906, The Constitution of the Interior the Earth, as Revealed by Earthquakes, Quarterly Journal, Geological Society, 62: 456-475.
58. Gutenberg, B, 1913, ü ber die Konstitution des Erdinnem, Erschlossen aus Erdbebenbeobachtungen, Phys. Zeits, 14: 1217-1218.
59. Jefferys, H, 1939, The times of the core waves (second paper). M.N.R.A.S., Geophys. Suppl.,4: 594-615.
60. Lehman.n, I, P, 1936, Publ, Bur.Cent. Assoc. Int. Seismol, A.14:87-115.
61. Driewonski, A.M., & Gilbert, F.,1971, Solidity of the inner core of the Earth inferred from hormal mode observations, Nature, 234: 465-466.
62. Bullen, K. K., 1946, A hypothesis on compressibility at pressure of the order of a million atmospheres, Nature, 157: 405-406.
63. Teffreys, H., & Vicente, R.O.,1957,The theory of nutationd Var of lat., Mon. Not., Roy. Ast. Sot., Vol.117(2)
64. Tamura. Y.1981, A harmonic development of the tidal generating potential, Marees Terrestres Bulletin d'Information, 99:6813-6855.
65. Venedikov, A.P., 1966, Use method pour I'analyse des marees terrestres a partir d'enr gistrements de longuer arbitrative, Observatiire Royal de Belgiqe Serie Geophysique, 17: 463-485.
66. Sato. T., 1991, Fluid Core resonances measured by quartz tube extensometers at the Esashi Earth tide station, In: Kakkuri. J. ed. Pro.11th Int.Sympos. On Earth Tides, Stuttgart: 573-582.
67. Sasao.T., Okubo. S., Saito. M., 1980, A simple theory on the dynamical effects of a stratified fluid core upon nutational motion of the Earth, In: Proc. IAU Symp, 78: 165-183.
68. Wahr J.M., 1981, A normal mode expansion for the forced response of a rotating earth, Geophys.J.R. astr., Soc(64): 651-675.
69. Wahr.J.M., 1981, Body tides on an elliptical, rotating, elastic and oceanless earth. Geophys. J. R. astr., soc(64): 677-703.
70. Wahr.J.M., Sasao. T., 1981, A diurnal resonance in the ocean tide and in the Earth's load response due to the resonant free core nutation', Geophys, J. R. astr. Soc(64):747-750.
71. Wahr.J.M., Sosao. T., Smith. M. L., 1981, Effect of the fluid on changes in the length of day due to long period tides. Geophys. J. R. astr. Soc(64): 635-650.
72. Wahr,J.M., Bergen. Z., 1986, The effects of mantle anelasticity on nutation, Earth's tides, and tidal variations in rotation rate, Geophy. J.R.,(64): 633-668.
73. Gwinn, C.R., Herring, T.A., Shapiro, I.I., 1986, Geodesy by radio interferometry: studies of the forced nutation of the earth, 2.Interpretation, J.Geophys, Res, 91(B35):4755-4765
74. Herring, T.A., Gwinn, C.R., Shapiro, I.I., 1986, geodesy by radio interferonetry: Studies of the forced nutation of the earth, I, Data analysis, 91(B5): 4745-4754.
75. Liu, L.T., Hsu, H.T., 1998, Harmonic analysis of Wuhan tidal gravity with wavelets, In: Ducarme B. ed. Proc. 13th Int. Sympos. On Earth tides. Brussds: 495-502.
76. Liu, L.T., et al, 2000, Wavelet method for the harmonic analysis of the Earth tides, Scienre in
China(D).43(2).
77. Longman, I.M., 1962, A Green's function for determining the deformation of the Earth under Surface mass loads I, Theory, J.Geophys. Res, 67: 845-850.
78. Longman, I.M., 1963, A Green's function for determining the deformation of the Earth under surface mass loads, 2. Computation and numerical results, J.Geophys, Res, 68:485-498.
79. Farrell, W.E., 1972, Deformation of the Earth by surface loads. Rev, Geophys, Space phys, 10(3): 761-797.
80. Cummins, P.R., Wahr, J.M., 1993, A study of the Earth's free core nutation using international deloyment of accelerometers graity data, J.Geophys, Res., 98(B2): 2-91-2103.
81. Defraigne, P., Dehant, V., Hinderer, J., 1994, Stacking gravity tide measurements and nutation observations in order to determine the complex eigen frequency of nearly diurnal free wobble, J. Geophys. Res., 99(B5): 9203-9213.
82. Driewonski, A.M, Anderson, D.L., 1981, Preliminary reference Earth model, Phys Earth planet. Inter., (25):297-356.
83. Hinderer. J., Legros. H., Amalvict. M., 1982, A search for chandler and nearly diurnal free wobble using Liouville equations, Geophys, J.R. astr. Soc(71): 303-332.
84. Hinderer, J., Zürn, W., Legros, H., 1991, Interpretation of the strength of the "nearly diurnal free wobble"-resonance from stacked gravity tide observation, In: Kakuri J ed. Proc. 11th Int. Sympos. On Earth Tides, Helsinki: 549-555.
85. Sun H.P., 1992, Comprehensive researches for the effect of the ocean loading on gravity observations in the Western Pacific eara. Bull. Dinformation de Marrees Terrestres, 113: 8271-8292.
86. Sun H.P., Ducarme. B., Dehant, V, 1993, Correction of the atmospheric pressure on gravity measurements recorded by a super conducting gravimeter at gravity measurements recorded by a super conducting gravimeter at Brussels, In: Hsu H-T ed. Proc. 12th Int. Sympos, on Earth Tides, Beijing: 317-330.
87. Sun H.P., 1997, Atmospheric gravity Green function, Chinese Science Bulletin, 42(15): 1640-1646.
88. Sun H.P., Xu Houze, Ducarme B, et al, 1999, Comprehensive comparison and analysis of tidal gravity observations obtained with superconducting gravimeters at stations in Chian, Belgium and France, Chinese Science Bulletin, 44(8): 750-755.
89. Sun H.P., Xu J.Q., Ducarme B., Preliminary Results of the Free lore Nutation Eigenperiod Obtained by Stacking SG observations at GGP Stations, Third Workshop of the Global Geodynamics Project (GGP) on Super conducting Gravimetry and Meeting of the ETC-Working Group 7 on Analysis of Environmental Data for the Interpretation of Gravity Measurements Jena, German, March 11-15, 2002.
90. Xu H.Z., Sun H.P., Xu J.Q., et al, 2000, International tidal gravity reference values at Wuhan station, Science in China, (Series D), 43(1):77-83
91. Lei, X.E., Jia, M.Y., Li, H., 2000, The Akp-Btk value method and the results for the retrieval of the parameters of the Earth's free core nutation, Acta Seismologia Sinica, 13(3):342-350
92. Lei, X.E., Xu, H.Z., 2002, Tri-frequency spectrum method and results for resolving the parameters of the Earth's liquid core free nutation, Science in China (Series D), 45(4):325-336
93. Garland G D. 1979, Introduce to Geophysics (Mantle, Core and Crust). 2nded., Toronto: W.B. Saunders Company. 123-133
94. Benioff H., Press E, Smith S., 1961, Excitation of the free oscillations of the earth by earthquake. J. Geophys. Res., 66(2): 605-619
95. Ness N.R., Harrison C.T., Slichter L.B., 1961, Observation of the free oscillation of the earth. J. Geophys. Res., 66(2): 621-629
96. Van Camp M.,1999, Measuring Seismic normal modes with-the GWR C021 Superconducting gravimeter. Phys. Earth and Plan Int., (116): 81-92
97. Neumeyer J., Bathelmes F., Combrinck L., et al., 2002, Analysis results from the SG registration with the dual sphere superconducting gravimeter at SAGOS (South Africa). Bull D'infor Marees Terrestres, 135:10607-10616
98. Lei X.E., Xu H.Z., Sun H.P., 2002, Preliminary results of the Earth's free oscillations after Peru earthquake observed using a SG in China, Bull D'infor Marees Terrestres, 135:10713-10715
99. Lei,X.E., Xu,H.Z., Sun,H.P., 2002, Check of free oscillation signals with SG data, Chinese Science Bulletin, 47(18): 1573-1578
100. Poupinet G., Pillet R., Souriau A., 1983, Possible heterogeneity of the Earth's core deduced from PKIKP travel times. Nature, (305): 204-206
101. Masters G., Gilbert F., 1981, Structure of the inner core inferred from observations of its spheroidal shear modes. Geophys. Res. Lett., (8): 569-571
102. Morrelli A., Dziewonski A.M., Woodhouse J.H., 1986, Anisotropy of inner core inferred from PKIKP travel times. Geophys. Res. Lett., (13): 1545-1548
103. Woodhouse J.H.Giardini D. Li X.D., 1986, Evidence for inner core anisotropy from free oscillations. Geophys. Res. Lett., (13): 1549-1552
104. Banka D., Jentzsch G., Crossley D., 1998, Investigations of superconducting gravimeter records in the frequency range of the free oscillations of the Earth—the noise magnitude. Proc. 13th Symp. Earth Tides, Brussels: 641-648
105. Derr J.S., 1969, Internal structure of the earth inferred from free oscillations. J. Geophys. Res.,74(22): 5202-5220
106. Dziewonski A., Gilbert F., 1972, Observations of normal modes from 84 recordings of the Alaskan earthquake of 1964 March 28. Geophys. J. R. astr. 27:293-446
107. Haddpn R.A., Bullen K.E., 1969, An earth model incorporating free earth oscillation data. Phys. Earth and Plan. Int., (2): 35-46
108. Jordan T.H., Anderson D.L., 1974, Earth structure from free oscillations and travel times. Geophys.J.R.astr., 36:411-459
109. Crossley D.J., Hinderer J., 1995, Global Geodynamics Project-GGP: status report 1994. Proceeding of the workshop on Non-tidal Gravity changes (ed. Poitevin, C.,), Luxembourg: via Conseil de L'Europe Cahiers du Centre Européen de Géodynamique et de Séismologie, 11: 244-269
110. Birch F., 1964, Density and composition of mantle and core. J.Geophys.Res., 69:4377-4388
111. Anderson O.L.,1995, Mineral physics of iron and of the core. Rev. Geophys., (suppl): 429-441
112. Stixrude L., Cohen R.E., 1995, High-pressure elasticity of iron and anisotropy of Earth's inner core. Science, 267:1972-1975
113. Greager K.C., 1992, Anisotropy of the inner core from differential travel times of the phases PKP and PKIK.P. Nature, 356:309-314
114. Shearer P.M., 1994Constraints on inner core anisotropy from PKP(DF) travel-times. J. Geophys. Res., 99:19647-19657
115. Shearer P.M., Masters G., 1990, The density and shear velocity contrast at the inner core boundary. Geophys.J.Int., 102:491-498
116. Song X.D., Helmberger D.V., 1995, Depth dependence of anisotropy of Earth's inner core. J. Geophys. Res.,100:9805-9816
117. Durek J.J.,Romanowicz B., 1999, Inner core anisotropy inferred by direct inversion of normal mode spectra. Geophys. J. Int., 139:599-622
118. Backus G.E., Gilbert J.F., 1961, The rotational splitting of the free oscillations of the earth. Proc. Natn. Acad. Sci., 47:362-371
119. MacDonald G., Ness N., 1961, A study of the free oscillations of the Earth. J. Geophys. Res., 66:1865-1911
120. Pekeris C.L., Alterman Z., Jarosch H., 1961, Rotational multiplets in the spectrum of the Earth. Phys.Rev., 122:1692-1700
121. Caputo M., 1963, Free modes of layered oblate planets. J. Geophys. Res., 68:497-503
122. Dahlen F.A., 1968, The normal modes of a rotating, elliptical earth. Geophys. J.R. astr. (16): 329-367
123. Dahlen F.A., 1969, The normal modes of a rotating, elliptical earth-Ⅱ near-resonance multiplet coupling. Geophys. J. R. astr. 18:397-436
124. 东敏傅, 1995, Simaltaneous observations of time change of Gravity by Means of Two Superconducting Gravitymeters at Kyoto Japan, Journal of Geodectic Society of Japan, 41(3):227-237
125. Florsch, N., Chambat, F., Hinderer, J., Legros, H., 1991, A Simple method to retrieve the complex eigenfrequency of the earth's nearly diurnal-free wobble; application to the Strasbourg super conducting gravimeter data, Geophys, J.Int., 116:53-63
126. Neuberg, J., Hinderer, J., Züm, W., 1987, stacking gravity tide observations in central Europe for the retrieval of the complex eigenfrequency of the hearly diumal free wobble, Geophy. J.K. astr., 91:853-868
127. Merriam, J.B.,1992, The atmospheric pressure and gravity, Geophys, J.Int., 109:488-500
128. Merriam, J.B.,1994, The nearly diurnal free wobble resonance in gravity measured at Cantley, Quebec, Geophys, J.Int.,119:369-380
129. Florsch, N., chambat,F., Hinderer, J., Legros, H., 1991, A simple method to retrieve the complex eigenfrequency of the Earth's nearly diumall-free wobble: application to strassbourg superconduction gravimeter data, Geophys, J.Int., 116:53-63
130. Dziewonski, A., and Landisman, M., 1970, Great circle Rayleigh and Love wave dispersion from 100 to 900 second, Geophys, J., 19:37-91
131. Stoneley, R., 1931, On deep-focus earthquake Beitr, Geophys, 29:417-432
132. Vauterin, P., 1998, Tsoft: Graphical & Interative Software for the Analysis of Earth Tide Data, Proc. 13th Int. Sympos. On Earth tides, Brussels, Observatoire Royal de Belgique, Série Gé ophysique. 481-486
133. Hartmann, T., Wenzel, H. G., 1995, The HW95 Tidal Potential Catalogue. Geophysical Research Letters, 22(24):3553-3556
134. Nakai, S., 1979, Preproeessing of tidal data, Marees Terrestres Bulletin d'Information, Vol(75)
135. Ducarme, B., 1975, The computation procedures at the international center for earth tides (ICET), Marees Terrestres Bulletin d'information, vol, 72
136. Marriam, J.B., 1992, An ephemeris for gravity tide predictions at then Gal level, Geophys. J. Int., 108:415-422
137. Doodson A.T., 1922, The harmonic development of the tide-generating potential, Proc.Roy.Soc.London, A100:305-329
138. Ishiguro M., Tamura T., 1985, BAYTAP-G in TIMSAC-84, Comp.Sci.Mono., 22:56-11
139. Ishiguro M., 1981, A Bayesian approach to the analysis of the data of crustal movements, J.Geod.Soc.Japan.,27:256-262
140. Agnew E.,1983, Conservation of mass in tidal loading computations, Geophys.J.astr., Soc.72
141. Wenzel H.G.,1996, The Nanogal Software: Earth Tide Data Processing Package Etema3.30, Bulletin d'information de Marees Terrestres, 124:9425-9439
142. Wenzel H.G.,1994, PRETERNA-a preprocessor for digitally recorded tidal data, Bulletin d'information Marees Terrestres, 118:8722-8734
143. Dehant V., 1987, Tidal parameters for an elastic earth, Phys.Earth.Planet.Int.,49:97-116
144. Wahr J.M., 1981, Discussion to: A nearly diurnal resonance in the ocean load tide, New York: Proc 9th Int Sympos, on Earth Tides.
145. Matumoto T., Sato Y., 1954, on the vibration of an elastic globe with one layer, Bull. Earthq.Int.,32:247-258
146. Jobert N., 1956, Evalution de la periode d'ocillation d'une phere elastique heterogene, par application du principle de Rayleigh, Computes Rendus, 243:1230-1232
147. Takeuchi H., 1959, Torsional oscillations of the earth and some related problems, Geophys.J., 2:89-100
148. Backus G.E., Gilbert F., 1961, The rotational splitting of the free oscillations of the earth, Proc.Nat.Acad.Sci., 47:362-371
149. MacDonald G.J.F., Ness N.F., 1961, A study of the free oscillations of the earth, J.Geophy.Res., Soc.66
150. Legros H., Amalvict M., 1985, Rotation of a deformable earth with dynamical superficial fluid layer and liquid core-part1: Fundamental equations, Ann,Geophysics., 3(5): 655-670
151. McSweeney T.J., Creager K.C., Merrill R.T., 1997, Depth extent of inner-core seismic anisotropy and implications for geomagnetism, Phys.Earth Planet. Inter., 101: 131-156
152. Su W.J., Dziewonski A.M., 1995, Inner core anisotropy in three dimensions, J.Geophys.Res., 102:24729-24739
153. Vinnik L., Romanowicz B., Breger L., 1994, Anisotropy in the center of the irmer core, Geophys.Res.Lett.,21:1671-1674
154. Higashi T.,1995, Simultaneous observations of time change of gravity by means of two superconducting gravimeters at Kyoto, J.Geode.Soc.Japan.,41(3):227-237
155. Neumeyer J., Dittfed H.J., 1997, Results of three year observation with a superconducting gravimeter at the geoForchungs zentrum Potsdam, Journal of Geodesy Spring., 71: 97-102
156. Flach D., Commlich G., Jentzsch G., 1993, Three years of experiences with a movable superconducting gravimeter at the underground installation site in the salt mine ASSE in North.Germany, Bull d'infor Marees Terreatres, 117:8639-8654
157. Merriam J.B., 1993, A Comparison of recent tide catalogues and the consequences of catalogue error for tidal analysis, Bull d'infor Marees Terrestres, 115:8515-8635
158. Alterman Z.S., Jarosh H., Pekeris C.L., 1959, Oscillation of the earth, Proc.Roy.Soc., A 252:80-95
159. Jefferys H., Jefferys B.S., 1956, Methods of Mathmetical Physics, 3rd ed., Camb.Uni.Press.
160. Lapwood E.R., Usami T., 1981, Free Oscillation of the Earth, Camb.Uni.Press.
161. Pekeris C.L., Jarosch H., 1958, the free oscillations of the Earth, London: Pergamon Press, Contributions in Geophysics ed Benioff H., pp:171-192
162. Sato Y., Usami T., 1962a, Basic study on the oscillation of a homogeneous elastic sphere Ⅰ. Frequency of free oscillation, Geophys.Mag., 31:15-24
163. Sato Y., Usami T., 1962b, Basic study on the oscillation of a homogeneous elastic sphere Ⅱ. Distribution of displacement, Geophys.Mag.,31:25-47
164. Sato Y., Usami T., 1964, Propogation of spherical disturbances on an elastic sphere with a homogeneous mantle and core, Bull.Earthq.Res.Inst.,42:407-425
165. Takeuchi H., Saito M., 1972, Seismic surface waves, New York: Acad Press, Methods in Computational Physics. Ed, Bolt B.A. et al., Vol.11:217-295
166. Chandrasekhar S., Lebovitz N.R.,1962, on the oscillations and the stability of rotating gaseous masses,Astrophys.J.,135:248-260
167. Cowling T.G.,Newing R.A., 1949, the oscillations of a rotating star, Astrophys.J., 109:149-158
168. Ledoux P., 1951, the non-radial oscillations of gaseous stars and the problem of Beta Canis Majoris, Astrophys.J.,114:373-384
169. Haddon R.A.W., Bullen K.E., An earth model incorporating free earth oscillation data, Phys Earth and Plan Int, 1969(2): 35-42
170. Züm W., Widmer R., On noise reduction in vertical seismic records below 2 mHz using local barometricpressure, Geophys Res.Let., 1995(22): 3537-2540
171．雷湘鄂，许厚泽，孙和平，由五个国际超导重力仪台站资料检测到的秘鲁8.2级大地震所激发的球型自由振荡现象，中国科学(D辑)，(2003年4月已被采用)
172. Lei, X. E., Xu, H. Z., Sun, H. P., Detection of spheriodal free oscillation excited by Peru 8.2Ms earthquake with five international;Superconducting gravimeter data, Science in China (Series D), (accepted on April, 2003)
2．傅承义，陈运泰，祁贵仲，1985，地球物理学基础．北京：科学出版社
3．方俊，1984，固体潮，北京：科学出版社
4．方俊，1986a，地球自由振荡，测量与地球物理集刊，7：65-83
5．方俊，1986b，地球自由振荡(续)，测量与地球物理集刊，8：53-69。
6．许厚泽，蒋福珍，张赤军，1999，我国动力大地测量学进展，动力大地测量学研究进展论文集：1-8
7．许厚泽，王广运，1989，动力大地测量学—研究地球动态变化的学科，科学发展与研究，(4)：9-15。
8．许厚泽，张赤军，1997，我国大地重力学和固体潮研究进展，地球物理学报，40(sup)：192-205。
9．孙和平，许厚泽，1997，国际地球动力学合作项目的实施和展望，地球科学进展，12(2)：152-157。
10．张赤军，1995，大地测量与地球动力学—兼述它与地球物理学的联系，地球物理学进展，10(4)：48-56
11．韩大仲，1986，旋转椭球地球的潮汐响应，测量与地球物理集刊，7：103-107
12．周蕙兰，1990，地球内部物理，北京：地震出版社
13．孙和平，许厚泽，Ducarme．B等，1998，中比法三国超导重力仪潮汐观测资料综合对比分析与研究，科学通报，43(13)：1438-1443
14．孙和平，许厚泽，罗少聪，1999，用超导重力仪的潮汐观测资料研究海潮模型，测绘学报，28(2)：115-120。
15．孙和平，许厚泽，徐建桥，柳林涛，2000，重力场的潮汐变化观测及其研究，地球科学进展，15(1)：53-57。
16．许厚泽、陈振帮、杨怀冰，1982，海洋潮汐对重力潮汐观测的影响，地球物理学报，25(2)：120-129。
17．许厚泽，毛伟健，1988，中国大陆的海洋负荷潮汐改正模型，中国科学(B辑)，25(9)：984-994．
18．许厚泽，孙和平，1998，我国重力固体潮实验研究进展，地球科学进展，13(5)：415-421。
19．许厚泽，孙和平，徐建桥等，2000，武汉国际重力潮汐基准研究，中国科学(D辑)，30(5)：549-553。
20．徐建桥，许厚泽，孙和平等，1999，利用超导重力仪观测资料检测地球近周日共振，地球物理学报，42(5)：599-608。
21．徐建桥，郝兴华，孙和平，1999，武汉基准台气压对重力潮汐观测的影响，测绘学报，28(1)：75-79。
22．徐建桥，孙和平，罗少聪，2001，利用国际超导重力仪研究地球自由核章动，中国科学(D辑)，31(9)：719-726
23．柳林涛，许厚泽，孙和平，郝兴华，2000，重力潮汐参数精密确定的小波分析方法，中国科学(D辑)，30(4)：442-448
24．罗少聪，孙和平，2000，大气压力变化对武汉台站重力场观测的影响，测绘学报，29(sup)：181-187．
25．丁月蓉，1998，天文数据处理方法．南京：南京大学出版社
26．孙和平，1997，大气重力格林函数．科学通报，42(5)：1640-1646
27．徐建桥，郝兴华，孙和平，1999，武汉基准台气压对重力潮汐观测的影响．测绘学报，28(1)：21-27
28．管泽霖、宁津生，1981，地球形状及其外部重力场(上册)，北京：测绘出版社
29．管泽霖、宁津生，1983，地球形状及其外部重力场(下册)，北京：测绘出版社
30．维尼狄柯夫，对任意长度的固体潮记录资料进行分析的方法，郭寿铃等译，1980，固体潮译文集，北京：科学出版社
31．梅尔基奥尔、著，杜品仁、吴庆鹏、陈益惠、刘克人译，行星地球的固体潮，1984，北京：科学出版社
32．李瑞浩，1988，重力学引论，北京：地震出版社
33．郭俊义，1994，物理大地测量学基础，武汉：武汉测绘科技大学出版社
34．郭俊义，2001，地球物理学基础，北京：测绘出版社
35．郗庆文，1982，固体潮汐理论值计算，地球物理学报，25(增刊)：632-643
36．郗庆文、侯天航，1986，固体潮汐与引潮常数，中国地震，2(2)：30-41
37．刘钦圣，1989，最小二乘问题计算方法，北京：北京工业大学出版社
38．南京大学数学系计算数学专业，1978，数值逼近方法(计算数学讲义一)，北京：科学出版社
39．南京大学数学系计算数学专业，1978，常微分方程数值解法(计算数学讲义三)，北京：科学出版社
40．Aki，K．，Rieherds，EG．，(著)，李钦祖、邹其嘉等(译)，傅承义(校)，1986，定量地震学(第一卷)，理论和方法，北京：地震出版社
41．邹鲲、彭俊泉、龚享铱，2002，MATLAB 6.X信号处理，北京：清华大学出版社
42．姚天任，孙洪，2000，现代数学信号处理，武汉：华中理工大学出版社
43．孙和平，陈晓东，许厚泽，王勇，2001，GWR超导重力仪潮汐观测标定因子的精密测定，地震学报，23(6)：651-658
44．陈晓东，孙和平，2002，一种新的重力潮汐数据预处理和分析方法，大地测量与地球动力学，22(3)：83-87
45．周华，1988，液核近周日共振的检测，[硕士论文]，武汉：中科院测量与地球物理研究所
46．方明，1991，地球自由振荡—正演、反演理论中若干问题的研究，[博士论文]，武汉：中科院测量与地球物理研究所
47．陈晓东，2003，武汉九峰台超导动仪固体潮观测资料的预处理和分析结果，中国科学院研究生院[硕士论文]，武汉：中国科学院测量与地球物理研究所
48．周江存，2002，利用最近海潮模型研究地球物理场中的负荷效应问题，中国科学院研究生院[硕士论文]，武汉：中国科学院测量与地球物理研究所
49．徐建桥，2002，地球液核动力学效应的研究和检测，中国科学院研究生院[博士论文]，武汉：中国科学院测量与地球物理研究所
50．罗少聪，2003，大气负荷效应问题研究，中国科学院研究生院[博士论文]，武汉：中国科学院测量与地球物理研究所
51．雷湘鄂，1998，液核共振参数的值算法及其结果，中国地震局[硕士论文]，武汉：中国地震局地震研究所
52．雷湘鄂，贾民育，李辉，2000，解算液核自由章动常数的Akp-Btk方法及其结果，地震学报，22(3)：319-326
53．雷湘鄂，许厚泽，2001，解算液核自由章动常数的三频谱线法，中国科学(D辑)，31(9)：727-734
54．雷湘鄂，许厚泽，孙和平，2002，利用超导重力观测资料检测地球自由振荡．科学通报，47(18)：1432-1436
55. Bullen. K. E. 1942, The density var of the earth's central core, Bull. Seismol. (32):19
56. Marriam, J. B., 1992, An ephemeris for gravity tide predictions at then Gal level, Geophys. J. Int., 108:415-422
57. Oldham, R. D., 1906, The Constitution of the Interior the Earth, as Revealed by Earthquakes, Quarterly Journal, Geological Society, 62: 456-475.
58. Gutenberg, B, 1913, ü ber die Konstitution des Erdinnem, Erschlossen aus Erdbebenbeobachtungen, Phys. Zeits, 14: 1217-1218.
59. Jefferys, H, 1939, The times of the core waves (second paper). M.N.R.A.S., Geophys. Suppl.,4: 594-615.
60. Lehman.n, I, P, 1936, Publ, Bur.Cent. Assoc. Int. Seismol, A.14:87-115.
61. Driewonski, A.M., & Gilbert, F.,1971, Solidity of the inner core of the Earth inferred from hormal mode observations, Nature, 234: 465-466.
62. Bullen, K. K., 1946, A hypothesis on compressibility at pressure of the order of a million atmospheres, Nature, 157: 405-406.
63. Teffreys, H., & Vicente, R.O.,1957,The theory of nutationd Var of lat., Mon. Not., Roy. Ast. Sot., Vol.117(2)
64. Tamura. Y.1981, A harmonic development of the tidal generating potential, Marees Terrestres Bulletin d'Information, 99:6813-6855.
65. Venedikov, A.P., 1966, Use method pour I'analyse des marees terrestres a partir d'enr gistrements de longuer arbitrative, Observatiire Royal de Belgiqe Serie Geophysique, 17: 463-485.
66. Sato. T., 1991, Fluid Core resonances measured by quartz tube extensometers at the Esashi Earth tide station, In: Kakkuri. J. ed. Pro.11th Int.Sympos. On Earth Tides, Stuttgart: 573-582.
67. Sasao.T., Okubo. S., Saito. M., 1980, A simple theory on the dynamical effects of a stratified fluid core upon nutational motion of the Earth, In: Proc. IAU Symp, 78: 165-183.
68. Wahr J.M., 1981, A normal mode expansion for the forced response of a rotating earth, Geophys.J.R. astr., Soc(64): 651-675.
69. Wahr.J.M., 1981, Body tides on an elliptical, rotating, elastic and oceanless earth. Geophys. J. R. astr., soc(64): 677-703.
70. Wahr.J.M., Sasao. T., 1981, A diurnal resonance in the ocean tide and in the Earth's load response due to the resonant free core nutation', Geophys, J. R. astr. Soc(64):747-750.
71. Wahr.J.M., Sosao. T., Smith. M. L., 1981, Effect of the fluid on changes in the length of day due to long period tides. Geophys. J. R. astr. Soc(64): 635-650.
72. Wahr,J.M., Bergen. Z., 1986, The effects of mantle anelasticity on nutation, Earth's tides, and tidal variations in rotation rate, Geophy. J.R.,(64): 633-668.
73. Gwinn, C.R., Herring, T.A., Shapiro, I.I., 1986, Geodesy by radio interferometry: studies of the forced nutation of the earth, 2.Interpretation, J.Geophys, Res, 91(B35):4755-4765
74. Herring, T.A., Gwinn, C.R., Shapiro, I.I., 1986, geodesy by radio interferonetry: Studies of the forced nutation of the earth, I, Data analysis, 91(B5): 4745-4754.
75. Liu, L.T., Hsu, H.T., 1998, Harmonic analysis of Wuhan tidal gravity with wavelets, In: Ducarme B. ed. Proc. 13th Int. Sympos. On Earth tides. Brussds: 495-502.
76. Liu, L.T., et al, 2000, Wavelet method for the harmonic analysis of the Earth tides, Scienre in
China(D).43(2).
77. Longman, I.M., 1962, A Green's function for determining the deformation of the Earth under Surface mass loads I, Theory, J.Geophys. Res, 67: 845-850.
78. Longman, I.M., 1963, A Green's function for determining the deformation of the Earth under surface mass loads, 2. Computation and numerical results, J.Geophys, Res, 68:485-498.
79. Farrell, W.E., 1972, Deformation of the Earth by surface loads. Rev, Geophys, Space phys, 10(3): 761-797.
80. Cummins, P.R., Wahr, J.M., 1993, A study of the Earth's free core nutation using international deloyment of accelerometers graity data, J.Geophys, Res., 98(B2): 2-91-2103.
81. Defraigne, P., Dehant, V., Hinderer, J., 1994, Stacking gravity tide measurements and nutation observations in order to determine the complex eigen frequency of nearly diurnal free wobble, J. Geophys. Res., 99(B5): 9203-9213.
82. Driewonski, A.M, Anderson, D.L., 1981, Preliminary reference Earth model, Phys Earth planet. Inter., (25):297-356.
83. Hinderer. J., Legros. H., Amalvict. M., 1982, A search for chandler and nearly diurnal free wobble using Liouville equations, Geophys, J.R. astr. Soc(71): 303-332.
84. Hinderer, J., Zürn, W., Legros, H., 1991, Interpretation of the strength of the "nearly diurnal free wobble"-resonance from stacked gravity tide observation, In: Kakuri J ed. Proc. 11th Int. Sympos. On Earth Tides, Helsinki: 549-555.
85. Sun H.P., 1992, Comprehensive researches for the effect of the ocean loading on gravity observations in the Western Pacific eara. Bull. Dinformation de Marrees Terrestres, 113: 8271-8292.
86. Sun H.P., Ducarme. B., Dehant, V, 1993, Correction of the atmospheric pressure on gravity measurements recorded by a super conducting gravimeter at gravity measurements recorded by a super conducting gravimeter at Brussels, In: Hsu H-T ed. Proc. 12th Int. Sympos, on Earth Tides, Beijing: 317-330.
87. Sun H.P., 1997, Atmospheric gravity Green function, Chinese Science Bulletin, 42(15): 1640-1646.
88. Sun H.P., Xu Houze, Ducarme B, et al, 1999, Comprehensive comparison and analysis of tidal gravity observations obtained with superconducting gravimeters at stations in Chian, Belgium and France, Chinese Science Bulletin, 44(8): 750-755.
89. Sun H.P., Xu J.Q., Ducarme B., Preliminary Results of the Free lore Nutation Eigenperiod Obtained by Stacking SG observations at GGP Stations, Third Workshop of the Global Geodynamics Project (GGP) on Super conducting Gravimetry and Meeting of the ETC-Working Group 7 on Analysis of Environmental Data for the Interpretation of Gravity Measurements Jena, German, March 11-15, 2002.
90. Xu H.Z., Sun H.P., Xu J.Q., et al, 2000, International tidal gravity reference values at Wuhan station, Science in China, (Series D), 43(1):77-83
91. Lei, X.E., Jia, M.Y., Li, H., 2000, The Akp-Btk value method and the results for the retrieval of the parameters of the Earth's free core nutation, Acta Seismologia Sinica, 13(3):342-350
92. Lei, X.E., Xu, H.Z., 2002, Tri-frequency spectrum method and results for resolving the parameters of the Earth's liquid core free nutation, Science in China (Series D), 45(4):325-336
93. Garland G D. 1979, Introduce to Geophysics (Mantle, Core and Crust). 2nded., Toronto: W.B. Saunders Company. 123-133
94. Benioff H., Press E, Smith S., 1961, Excitation of the free oscillations of the earth by earthquake. J. Geophys. Res., 66(2): 605-619
95. Ness N.R., Harrison C.T., Slichter L.B., 1961, Observation of the free oscillation of the earth. J. Geophys. Res., 66(2): 621-629
96. Van Camp M.,1999, Measuring Seismic normal modes with-the GWR C021 Superconducting gravimeter. Phys. Earth and Plan Int., (116): 81-92
97. Neumeyer J., Bathelmes F., Combrinck L., et al., 2002, Analysis results from the SG registration with the dual sphere superconducting gravimeter at SAGOS (South Africa). Bull D'infor Marees Terrestres, 135:10607-10616
98. Lei X.E., Xu H.Z., Sun H.P., 2002, Preliminary results of the Earth's free oscillations after Peru earthquake observed using a SG in China, Bull D'infor Marees Terrestres, 135:10713-10715
99. Lei,X.E., Xu,H.Z., Sun,H.P., 2002, Check of free oscillation signals with SG data, Chinese Science Bulletin, 47(18): 1573-1578
100. Poupinet G., Pillet R., Souriau A., 1983, Possible heterogeneity of the Earth's core deduced from PKIKP travel times. Nature, (305): 204-206
101. Masters G., Gilbert F., 1981, Structure of the inner core inferred from observations of its spheroidal shear modes. Geophys. Res. Lett., (8): 569-571
102. Morrelli A., Dziewonski A.M., Woodhouse J.H., 1986, Anisotropy of inner core inferred from PKIKP travel times. Geophys. Res. Lett., (13): 1545-1548
103. Woodhouse J.H.Giardini D. Li X.D., 1986, Evidence for inner core anisotropy from free oscillations. Geophys. Res. Lett., (13): 1549-1552
104. Banka D., Jentzsch G., Crossley D., 1998, Investigations of superconducting gravimeter records in the frequency range of the free oscillations of the Earth—the noise magnitude. Proc. 13th Symp. Earth Tides, Brussels: 641-648
105. Derr J.S., 1969, Internal structure of the earth inferred from free oscillations. J. Geophys. Res.,74(22): 5202-5220
106. Dziewonski A., Gilbert F., 1972, Observations of normal modes from 84 recordings of the Alaskan earthquake of 1964 March 28. Geophys. J. R. astr. 27:293-446
107. Haddpn R.A., Bullen K.E., 1969, An earth model incorporating free earth oscillation data. Phys. Earth and Plan. Int., (2): 35-46
108. Jordan T.H., Anderson D.L., 1974, Earth structure from free oscillations and travel times. Geophys.J.R.astr., 36:411-459
109. Crossley D.J., Hinderer J., 1995, Global Geodynamics Project-GGP: status report 1994. Proceeding of the workshop on Non-tidal Gravity changes (ed. Poitevin, C.,), Luxembourg: via Conseil de L'Europe Cahiers du Centre Européen de Géodynamique et de Séismologie, 11: 244-269
110. Birch F., 1964, Density and composition of mantle and core. J.Geophys.Res., 69:4377-4388
111. Anderson O.L.,1995, Mineral physics of iron and of the core. Rev. Geophys., (suppl): 429-441
112. Stixrude L., Cohen R.E., 1995, High-pressure elasticity of iron and anisotropy of Earth's inner core. Science, 267:1972-1975
113. Greager K.C., 1992, Anisotropy of the inner core from differential travel times of the phases PKP and PKIK.P. Nature, 356:309-314
114. Shearer P.M., 1994Constraints on inner core anisotropy from PKP(DF) travel-times. J. Geophys. Res., 99:19647-19657
115. Shearer P.M., Masters G., 1990, The density and shear velocity contrast at the inner core boundary. Geophys.J.Int., 102:491-498
116. Song X.D., Helmberger D.V., 1995, Depth dependence of anisotropy of Earth's inner core. J. Geophys. Res.,100:9805-9816
117. Durek J.J.,Romanowicz B., 1999, Inner core anisotropy inferred by direct inversion of normal mode spectra. Geophys. J. Int., 139:599-622
118. Backus G.E., Gilbert J.F., 1961, The rotational splitting of the free oscillations of the earth. Proc. Natn. Acad. Sci., 47:362-371
119. MacDonald G., Ness N., 1961, A study of the free oscillations of the Earth. J. Geophys. Res., 66:1865-1911
120. Pekeris C.L., Alterman Z., Jarosch H., 1961, Rotational multiplets in the spectrum of the Earth. Phys.Rev., 122:1692-1700
121. Caputo M., 1963, Free modes of layered oblate planets. J. Geophys. Res., 68:497-503
122. Dahlen F.A., 1968, The normal modes of a rotating, elliptical earth. Geophys. J.R. astr. (16): 329-367
123. Dahlen F.A., 1969, The normal modes of a rotating, elliptical earth-Ⅱ near-resonance multiplet coupling. Geophys. J. R. astr. 18:397-436
124. 东敏傅, 1995, Simaltaneous observations of time change of Gravity by Means of Two Superconducting Gravitymeters at Kyoto Japan, Journal of Geodectic Society of Japan, 41(3):227-237
125. Florsch, N., Chambat, F., Hinderer, J., Legros, H., 1991, A Simple method to retrieve the complex eigenfrequency of the earth's nearly diurnal-free wobble; application to the Strasbourg super conducting gravimeter data, Geophys, J.Int., 116:53-63
126. Neuberg, J., Hinderer, J., Züm, W., 1987, stacking gravity tide observations in central Europe for the retrieval of the complex eigenfrequency of the hearly diumal free wobble, Geophy. J.K. astr., 91:853-868
127. Merriam, J.B.,1992, The atmospheric pressure and gravity, Geophys, J.Int., 109:488-500
128. Merriam, J.B.,1994, The nearly diurnal free wobble resonance in gravity measured at Cantley, Quebec, Geophys, J.Int.,119:369-380
129. Florsch, N., chambat,F., Hinderer, J., Legros, H., 1991, A simple method to retrieve the complex eigenfrequency of the Earth's nearly diumall-free wobble: application to strassbourg superconduction gravimeter data, Geophys, J.Int., 116:53-63
130. Dziewonski, A., and Landisman, M., 1970, Great circle Rayleigh and Love wave dispersion from 100 to 900 second, Geophys, J., 19:37-91
131. Stoneley, R., 1931, On deep-focus earthquake Beitr, Geophys, 29:417-432
132. Vauterin, P., 1998, Tsoft: Graphical & Interative Software for the Analysis of Earth Tide Data, Proc. 13th Int. Sympos. On Earth tides, Brussels, Observatoire Royal de Belgique, Série Gé ophysique. 481-486
133. Hartmann, T., Wenzel, H. G., 1995, The HW95 Tidal Potential Catalogue. Geophysical Research Letters, 22(24):3553-3556
134. Nakai, S., 1979, Preproeessing of tidal data, Marees Terrestres Bulletin d'Information, Vol(75)
135. Ducarme, B., 1975, The computation procedures at the international center for earth tides (ICET), Marees Terrestres Bulletin d'information, vol, 72
136. Marriam, J.B., 1992, An ephemeris for gravity tide predictions at then Gal level, Geophys. J. Int., 108:415-422
137. Doodson A.T., 1922, The harmonic development of the tide-generating potential, Proc.Roy.Soc.London, A100:305-329
138. Ishiguro M., Tamura T., 1985, BAYTAP-G in TIMSAC-84, Comp.Sci.Mono., 22:56-11
139. Ishiguro M., 1981, A Bayesian approach to the analysis of the data of crustal movements, J.Geod.Soc.Japan.,27:256-262
140. Agnew E.,1983, Conservation of mass in tidal loading computations, Geophys.J.astr., Soc.72
141. Wenzel H.G.,1996, The Nanogal Software: Earth Tide Data Processing Package Etema3.30, Bulletin d'information de Marees Terrestres, 124:9425-9439
142. Wenzel H.G.,1994, PRETERNA-a preprocessor for digitally recorded tidal data, Bulletin d'information Marees Terrestres, 118:8722-8734
143. Dehant V., 1987, Tidal parameters for an elastic earth, Phys.Earth.Planet.Int.,49:97-116
144. Wahr J.M., 1981, Discussion to: A nearly diurnal resonance in the ocean load tide, New York: Proc 9th Int Sympos, on Earth Tides.
145. Matumoto T., Sato Y., 1954, on the vibration of an elastic globe with one layer, Bull. Earthq.Int.,32:247-258
146. Jobert N., 1956, Evalution de la periode d'ocillation d'une phere elastique heterogene, par application du principle de Rayleigh, Computes Rendus, 243:1230-1232
147. Takeuchi H., 1959, Torsional oscillations of the earth and some related problems, Geophys.J., 2:89-100
148. Backus G.E., Gilbert F., 1961, The rotational splitting of the free oscillations of the earth, Proc.Nat.Acad.Sci., 47:362-371
149. MacDonald G.J.F., Ness N.F., 1961, A study of the free oscillations of the earth, J.Geophy.Res., Soc.66
150. Legros H., Amalvict M., 1985, Rotation of a deformable earth with dynamical superficial fluid layer and liquid core-part1: Fundamental equations, Ann,Geophysics., 3(5): 655-670
151. McSweeney T.J., Creager K.C., Merrill R.T., 1997, Depth extent of inner-core seismic anisotropy and implications for geomagnetism, Phys.Earth Planet. Inter., 101: 131-156
152. Su W.J., Dziewonski A.M., 1995, Inner core anisotropy in three dimensions, J.Geophys.Res., 102:24729-24739
153. Vinnik L., Romanowicz B., Breger L., 1994, Anisotropy in the center of the irmer core, Geophys.Res.Lett.,21:1671-1674
154. Higashi T.,1995, Simultaneous observations of time change of gravity by means of two superconducting gravimeters at Kyoto, J.Geode.Soc.Japan.,41(3):227-237
155. Neumeyer J., Dittfed H.J., 1997, Results of three year observation with a superconducting gravimeter at the geoForchungs zentrum Potsdam, Journal of Geodesy Spring., 71: 97-102
156. Flach D., Commlich G., Jentzsch G., 1993, Three years of experiences with a movable superconducting gravimeter at the underground installation site in the salt mine ASSE in North.Germany, Bull d'infor Marees Terreatres, 117:8639-8654
157. Merriam J.B., 1993, A Comparison of recent tide catalogues and the consequences of catalogue error for tidal analysis, Bull d'infor Marees Terrestres, 115:8515-8635
158. Alterman Z.S., Jarosh H., Pekeris C.L., 1959, Oscillation of the earth, Proc.Roy.Soc., A 252:80-95
159. Jefferys H., Jefferys B.S., 1956, Methods of Mathmetical Physics, 3rd ed., Camb.Uni.Press.
160. Lapwood E.R., Usami T., 1981, Free Oscillation of the Earth, Camb.Uni.Press.
161. Pekeris C.L., Jarosch H., 1958, the free oscillations of the Earth, London: Pergamon Press, Contributions in Geophysics ed Benioff H., pp:171-192
162. Sato Y., Usami T., 1962a, Basic study on the oscillation of a homogeneous elastic sphere Ⅰ. Frequency of free oscillation, Geophys.Mag., 31:15-24
163. Sato Y., Usami T., 1962b, Basic study on the oscillation of a homogeneous elastic sphere Ⅱ. Distribution of displacement, Geophys.Mag.,31:25-47
164. Sato Y., Usami T., 1964, Propogation of spherical disturbances on an elastic sphere with a homogeneous mantle and core, Bull.Earthq.Res.Inst.,42:407-425
165. Takeuchi H., Saito M., 1972, Seismic surface waves, New York: Acad Press, Methods in Computational Physics. Ed, Bolt B.A. et al., Vol.11:217-295
166. Chandrasekhar S., Lebovitz N.R.,1962, on the oscillations and the stability of rotating gaseous masses,Astrophys.J.,135:248-260
167. Cowling T.G.,Newing R.A., 1949, the oscillations of a rotating star, Astrophys.J., 109:149-158
168. Ledoux P., 1951, the non-radial oscillations of gaseous stars and the problem of Beta Canis Majoris, Astrophys.J.,114:373-384
169. Haddon R.A.W., Bullen K.E., An earth model incorporating free earth oscillation data, Phys Earth and Plan Int, 1969(2): 35-42
170. Züm W., Widmer R., On noise reduction in vertical seismic records below 2 mHz using local barometricpressure, Geophys Res.Let., 1995(22): 3537-2540
171．雷湘鄂，许厚泽，孙和平，由五个国际超导重力仪台站资料检测到的秘鲁8.2级大地震所激发的球型自由振荡现象，中国科学(D辑)，(2003年4月已被采用)
172. Lei, X. E., Xu, H. Z., Sun, H. P., Detection of spheriodal free oscillation excited by Peru 8.2Ms earthquake with five international;Superconducting gravimeter data, Science in China (Series D), (accepted on April, 2003)