三轴形变地球自转的自由摆动的理论研究
|
摘要
地球是人类的家园。地球的自转运动以及其绕太阳的公转运动是地球运动的重要形式,与人类的生活休戚相关。地球自转是天文学与地球科学相互交叉、相互渗透的一个分支学科。对它的研究除了具有重大理论意义外,还具有明显的实用意义,例如:对地球自转速率变化和地极移动或地极摆动(极移)的研究,关系到确定地面观测站在宇宙空间的精确位置,以及地球参考系在准惯性空间的指向,这是地面精密测绘和空间飞行器跟踪所需要的参数;板块运动和断层位移,则是大地测量和地震监测所需要的资料。
地球自转在受到外部天体(月球、太阳和行星)影响的同时,也受到地球本身(包括大气、海洋、地壳、地幔、液体外核(FOC)和固体内核(SIC)等)的各种复杂物质形态和运动形式的影响。因此,影响地球自转的力学机制主要包括:地球内部结构的物理性质和物质运动,如液体外核与地幔、地幔与地壳的相互作用;地球磁场和重力场的精细结构及其变化;地球水圈和大气圈的大规模物质运动;地球所在的宇宙空间中的引力场和电磁场的作用以及地球和太阳系的起源和演化等。历史上许多著名的天文学家和地球物理学家都对地球自转的研究做出过重要的贡献。但直到目前为止关于地球自转还有很多悬而未决的问题,仍然吸引着天文学和地球科学的学者,充分显示了这一学科领域的强大生命力。
本文的主要工作表现在:在查阅当前国内外相关文献的基础之上,研究了三轴整体形变地球自转的动力学理论;给出了顾及高阶引潮力位影响的岁差章动力矩表达式,以及在地球自由摆动情况下的地球自转轴和任一天球参考轴(极)之间的理论关系式;对液核三轴整体地球自转的自由长期摆动进行了理论上的解算。最后针对测量地球自转的不同技术进行了归纳总结。
The Earth is a celestial body that which we live on. Since the Earth rotation is the most important component of the motion of the Earth which is associated with our lives closely. The earth rotation is a branch subject of the murual infiltration and cross-link of astronomy and earth science. So the research of the Earth rotation is of great theoretical significance and practical value. Such as the research on the change of earth rotation, pole motion and pole oscillation, which is associated with the accurate position of the observation stations of terrestrial reference frame in the astrospace, and the direction of the terrestrial reference frame in the inertial space, all of this are called for ground precise surveying and mapping, also called for the tracking of the spacecraft. The research on the tetonic processes and fault displacement is also called for the geodesy and the earthpuake monitoring.
The earth rotation is not only influenced by the external celestial body (the moon, the sun and planets), but also influenced by the different layers of the earth (atmosphere, ocean, crust and mantle, FOC and SIC). So these mechanical mechanism influenced the earth rotation just inculed: the physical properties and the material movement of the inner earth, like the interaction between the FOC and the crust, the interaction between the mantle and crust; the large-scale material movement for the hydrosphere and atmosphere. Many astronomers and geophysicist have made great contributions to the earth rotation, but there are some problems to be solved yet.
The primary work of this paper as following: After referring to many of currently correlative literature from foreign and home, this paper considering the influence of high step tidal generating potential to the moment of precession and nutation; theoretical relationship between any celestial reference pole and instantaneous rotational pole of the Earth; established the rotational dynamical equation of the triaxial Earth; induction and summarization on Earth Rotation Measurement Techniques.
地球自转在受到外部天体(月球、太阳和行星)影响的同时,也受到地球本身(包括大气、海洋、地壳、地幔、液体外核(FOC)和固体内核(SIC)等)的各种复杂物质形态和运动形式的影响。因此,影响地球自转的力学机制主要包括:地球内部结构的物理性质和物质运动,如液体外核与地幔、地幔与地壳的相互作用;地球磁场和重力场的精细结构及其变化;地球水圈和大气圈的大规模物质运动;地球所在的宇宙空间中的引力场和电磁场的作用以及地球和太阳系的起源和演化等。历史上许多著名的天文学家和地球物理学家都对地球自转的研究做出过重要的贡献。但直到目前为止关于地球自转还有很多悬而未决的问题,仍然吸引着天文学和地球科学的学者,充分显示了这一学科领域的强大生命力。
本文的主要工作表现在:在查阅当前国内外相关文献的基础之上,研究了三轴整体形变地球自转的动力学理论;给出了顾及高阶引潮力位影响的岁差章动力矩表达式,以及在地球自由摆动情况下的地球自转轴和任一天球参考轴(极)之间的理论关系式;对液核三轴整体地球自转的自由长期摆动进行了理论上的解算。最后针对测量地球自转的不同技术进行了归纳总结。
The Earth is a celestial body that which we live on. Since the Earth rotation is the most important component of the motion of the Earth which is associated with our lives closely. The earth rotation is a branch subject of the murual infiltration and cross-link of astronomy and earth science. So the research of the Earth rotation is of great theoretical significance and practical value. Such as the research on the change of earth rotation, pole motion and pole oscillation, which is associated with the accurate position of the observation stations of terrestrial reference frame in the astrospace, and the direction of the terrestrial reference frame in the inertial space, all of this are called for ground precise surveying and mapping, also called for the tracking of the spacecraft. The research on the tetonic processes and fault displacement is also called for the geodesy and the earthpuake monitoring.
The earth rotation is not only influenced by the external celestial body (the moon, the sun and planets), but also influenced by the different layers of the earth (atmosphere, ocean, crust and mantle, FOC and SIC). So these mechanical mechanism influenced the earth rotation just inculed: the physical properties and the material movement of the inner earth, like the interaction between the FOC and the crust, the interaction between the mantle and crust; the large-scale material movement for the hydrosphere and atmosphere. Many astronomers and geophysicist have made great contributions to the earth rotation, but there are some problems to be solved yet.
The primary work of this paper as following: After referring to many of currently correlative literature from foreign and home, this paper considering the influence of high step tidal generating potential to the moment of precession and nutation; theoretical relationship between any celestial reference pole and instantaneous rotational pole of the Earth; established the rotational dynamical equation of the triaxial Earth; induction and summarization on Earth Rotation Measurement Techniques.
引文
[1]金文敬,李东明,夏一飞等.近10年我国天体测量的发展[J].天文学进展, 2004, 22(2): 15-121.
[2] Johnson, T.J., W. Kosek, M. Kalarus, et al., 2005, Recent advancements in the determination of Earth orientation combination solutions and prediction, AGU 2005 Fall Meeting, San Francisco, California.
[3]金文敬,唐正宏,黄剩利,王叔和.国际地球自转服务IERS简评[J].天文学进展, 2003, 21(1):26-32.
[4]张捍卫,许厚泽,柳林涛.动力大地测量学中的地球自转理论[M].北京:中国科学技术出版社, 2006.
[5]郭俊义.地球物理学基础[M].北京:测绘出版社, 2001.
[6]魏子卿.地球主惯性矩[J].测绘学报, 2005, 34: 7–13.
[7] Vondrák, J., C. Ron, R. Weber, Combined VLBI/GPS series of precession-nutation and comparison with IAU2000 model[J], Astronomy and Astrophysics, 2003, 397: 771–776.
[8] Dehant V, F. Arias, Ch. Bizouard, et al., Considerations concerning the non-rigid Earth nutation theory[J], Celestial Mechanics and Dynamical Astronomy, 1999, 72: 245–310.
[9] Wang, W-J(王文均), Decadal free polar motion of triaxial Earth[J], Geophysical Journal International, 2004, 158:1-15.
[10]许厚泽.地球各圈层相互作用的大地测量研究和检测[J].大地测量与地球动力学, 2002, 22(4):1-5.
[11] Mathews, P. M., T. A. Herring, and B. A. Buffett, Modeling of nutation-precession: New nutation series for nonrigid Earth, and insights into the Earth's interior[J], Journal of Geophysical Research, 2002, 107(B4):10.1029 /2001JB000390.
[12]高布锡.天文地球动力学原理[M].北京:科学出版社, 1997.21-125
[13] Merriam JB (1980) Zonal tides and changes in the length of day. [J] Geophysical Journal of the Royal Astronomical Society 62: 551–561.
[14] Wahr JM (1981) The forced nutations of an elliptical, rotating, elastic and oceanless earth. [J]Geophysical Journal of the Royal Astronomical Society 64: 705–727.
[15] Dahlen FA (1976) The passive influence of the oceans upon the rotation of the Earth. [J]Geophysical Journal of the Royal Astronomical Society 46: 363–406.
[16] Wahr JM (1983) The effects of the atmosphere and oceans on the Earth’s wobble and on the seasonal variations in the length of day—II. Results. [J] eophysical Journal of the Royal Astronomical Society 74: 451–487.
[17] Dickman SR (2003) Evaluation of‘‘effective angular momentum function’’formulations with respect to core–mantle coupling. [J] Journal of Geophysical Research 108(B3): 2150 (doi:10.1029/2001JB001603).
[18] Wilson CR and Vicente RO (1990) Maximum likelihood estimates of polar motion parameters. In: McCarthy DD and Carter WE (eds.) Variations in Earth Rotation, American Geophysical Union Geophysical Monograph Series, vol. 59, pp. 151–155.
[19] Smith ML and Dahlen FA (1981) The period and Q of the Chandler wobble. Geophysical Journal of the Royal Astronomical Society 64: 223–281.
[20] Sovers OJ, Fanselow JL, and Jacobs CS (1998) Astrometry and geodesy with radio interferometry: Experiments, models, results. Reviews of Modern Physics 70(4): 1393–1454.
[21] Goldstein H (1950) Classical Mechanics. Reading, MA: Addison-Wesley. Greff-Lefftz M (2004) Upwelling mantle plumes, superswells, and true polar wander. Geophysical Journal International 159: 1125–1137.
[22] Gross RS (1992) Correspondence between theory and observations of polar motion. Geophysical Journal International 109: 162–170.
[23] Brzezinski A (1992) Polar motion excitation by variations of the effective angular momentum function: Considerations concerning deconvolution problem. Manuscripta Geodaetica 17: 3–20.
[24] Brzezinski A and Capitaine N (1993) The use of the precise observations of the celestial ephemeris pole in the analysis of geophysical excitation of Earth rotation. Journal of Geophysical Research 98(B4): 6667–6675.
[25] Capitaine N (2000) Definition of the celestial ephemeris pole and the celestial ephemeris origin. In: Johnston KJ, McCarthy DD, Luzum BJ, and Kaplan GH (eds.) Towards Models and Constants for Sub-Microarcsecond Astrometry, Proc. IAU Colloquium 180, US Naval Obs, pp. 153–163. Washington, DC: US Naval Observatory.
[26] Seidelmann PK (1982) 1980 IAU theory of nutation: The final report of the IAU working group on nutations. Celestial Mechanics 27: 79–106.
[27] Gross RS (2001) A combined length-of-day series spanning 1832–1997: LUNAR97. Physics ofEarth and Planetary Interiors 123: 65–76.
[28] Munk WH and MacDonald GJF (1960) The Rotation of the Earth: A Geophysical Discussion. New York: Cambridge University Press.
[29] Bock Y and Leppard N (eds.) (1990) Global Positioning System: An Overview. Proceedings of the IAG Symposium no. 102, 459p. New York: Springer.
[30] Blewitt G (1993) Advances in Global Positioning System technology for geodynamics investigations: 1978–1992. In: Smith DE and Turcotte DL (eds.) Contributions of Space Geodesy to Geodynamics: Technology, American Geophysical Union
[31] Beutler G, Hein GW, Melbourne WG, and Seeber G (eds.) (1996) GPS Trends in Precise Terrestrial, Airborne, and Spaceborne Applications. Proceedings of the IAG Symposium no. 115, 351p. New York: Springer.
[32] Hofmann-Wellenhof B, Lichtenegger H, and Collins J (1997) Global Positioning System: Theory and Practice. New York: Springer.
[33] Leick A (2003) GPS Satellite Surveying. New York: Wiley.
[34] Tavernier G, Fagard H, Feissel-Vernier M, et al. (2005) The International DORIS Service (IDS). Advances in Space Research 36(3): 333–341.
[35] Willis P, Jayles C, and Bar-Sever Y (2006) DORIS: From orbit determination for altimeter missions to geodesy. Comptes Rendus Geoscience 338: 968–979 (doi:10.1016/j.crte.2005.11. 013).
[36] Stedman GE (1997) Ring-laser tests of fundamental physics and geophysics. Reports on Progress in Physics 60: 615–688.
[37] Schreiber KU, Velikoseltsev A, Rothacher M, Klu¨gel T, Stedman GE, and Wiltshire DL (2004) Direct measurment of diurnal polar motion by ring laser gyroscopes. Journal of Geophysical Research 109: B06405 (doi:10.1029/2003JB002803).
[1]陈景润,《初等数论I》[M],科学出版社,1987.
[2] Wadg W-J, Decadal free polar motiod of triaxial Earth, Geophys.J.Idt. 2004,158:1—15.
[3]王文均,地极移动的非线性动力学机制,天文学报,1998,39(3):287.
[4]叶建军,非线性受迫振动系统的次谐共振解,西南交通大学学报,2003年,014.
[5]漆安慎,杜婵英,《力学II》[M]高等教育出版社,2005年,283—327.
[2] Johnson, T.J., W. Kosek, M. Kalarus, et al., 2005, Recent advancements in the determination of Earth orientation combination solutions and prediction, AGU 2005 Fall Meeting, San Francisco, California.
[3]金文敬,唐正宏,黄剩利,王叔和.国际地球自转服务IERS简评[J].天文学进展, 2003, 21(1):26-32.
[4]张捍卫,许厚泽,柳林涛.动力大地测量学中的地球自转理论[M].北京:中国科学技术出版社, 2006.
[5]郭俊义.地球物理学基础[M].北京:测绘出版社, 2001.
[6]魏子卿.地球主惯性矩[J].测绘学报, 2005, 34: 7–13.
[7] Vondrák, J., C. Ron, R. Weber, Combined VLBI/GPS series of precession-nutation and comparison with IAU2000 model[J], Astronomy and Astrophysics, 2003, 397: 771–776.
[8] Dehant V, F. Arias, Ch. Bizouard, et al., Considerations concerning the non-rigid Earth nutation theory[J], Celestial Mechanics and Dynamical Astronomy, 1999, 72: 245–310.
[9] Wang, W-J(王文均), Decadal free polar motion of triaxial Earth[J], Geophysical Journal International, 2004, 158:1-15.
[10]许厚泽.地球各圈层相互作用的大地测量研究和检测[J].大地测量与地球动力学, 2002, 22(4):1-5.
[11] Mathews, P. M., T. A. Herring, and B. A. Buffett, Modeling of nutation-precession: New nutation series for nonrigid Earth, and insights into the Earth's interior[J], Journal of Geophysical Research, 2002, 107(B4):10.1029 /2001JB000390.
[12]高布锡.天文地球动力学原理[M].北京:科学出版社, 1997.21-125
[13] Merriam JB (1980) Zonal tides and changes in the length of day. [J] Geophysical Journal of the Royal Astronomical Society 62: 551–561.
[14] Wahr JM (1981) The forced nutations of an elliptical, rotating, elastic and oceanless earth. [J]Geophysical Journal of the Royal Astronomical Society 64: 705–727.
[15] Dahlen FA (1976) The passive influence of the oceans upon the rotation of the Earth. [J]Geophysical Journal of the Royal Astronomical Society 46: 363–406.
[16] Wahr JM (1983) The effects of the atmosphere and oceans on the Earth’s wobble and on the seasonal variations in the length of day—II. Results. [J] eophysical Journal of the Royal Astronomical Society 74: 451–487.
[17] Dickman SR (2003) Evaluation of‘‘effective angular momentum function’’formulations with respect to core–mantle coupling. [J] Journal of Geophysical Research 108(B3): 2150 (doi:10.1029/2001JB001603).
[18] Wilson CR and Vicente RO (1990) Maximum likelihood estimates of polar motion parameters. In: McCarthy DD and Carter WE (eds.) Variations in Earth Rotation, American Geophysical Union Geophysical Monograph Series, vol. 59, pp. 151–155.
[19] Smith ML and Dahlen FA (1981) The period and Q of the Chandler wobble. Geophysical Journal of the Royal Astronomical Society 64: 223–281.
[20] Sovers OJ, Fanselow JL, and Jacobs CS (1998) Astrometry and geodesy with radio interferometry: Experiments, models, results. Reviews of Modern Physics 70(4): 1393–1454.
[21] Goldstein H (1950) Classical Mechanics. Reading, MA: Addison-Wesley. Greff-Lefftz M (2004) Upwelling mantle plumes, superswells, and true polar wander. Geophysical Journal International 159: 1125–1137.
[22] Gross RS (1992) Correspondence between theory and observations of polar motion. Geophysical Journal International 109: 162–170.
[23] Brzezinski A (1992) Polar motion excitation by variations of the effective angular momentum function: Considerations concerning deconvolution problem. Manuscripta Geodaetica 17: 3–20.
[24] Brzezinski A and Capitaine N (1993) The use of the precise observations of the celestial ephemeris pole in the analysis of geophysical excitation of Earth rotation. Journal of Geophysical Research 98(B4): 6667–6675.
[25] Capitaine N (2000) Definition of the celestial ephemeris pole and the celestial ephemeris origin. In: Johnston KJ, McCarthy DD, Luzum BJ, and Kaplan GH (eds.) Towards Models and Constants for Sub-Microarcsecond Astrometry, Proc. IAU Colloquium 180, US Naval Obs, pp. 153–163. Washington, DC: US Naval Observatory.
[26] Seidelmann PK (1982) 1980 IAU theory of nutation: The final report of the IAU working group on nutations. Celestial Mechanics 27: 79–106.
[27] Gross RS (2001) A combined length-of-day series spanning 1832–1997: LUNAR97. Physics ofEarth and Planetary Interiors 123: 65–76.
[28] Munk WH and MacDonald GJF (1960) The Rotation of the Earth: A Geophysical Discussion. New York: Cambridge University Press.
[29] Bock Y and Leppard N (eds.) (1990) Global Positioning System: An Overview. Proceedings of the IAG Symposium no. 102, 459p. New York: Springer.
[30] Blewitt G (1993) Advances in Global Positioning System technology for geodynamics investigations: 1978–1992. In: Smith DE and Turcotte DL (eds.) Contributions of Space Geodesy to Geodynamics: Technology, American Geophysical Union
[31] Beutler G, Hein GW, Melbourne WG, and Seeber G (eds.) (1996) GPS Trends in Precise Terrestrial, Airborne, and Spaceborne Applications. Proceedings of the IAG Symposium no. 115, 351p. New York: Springer.
[32] Hofmann-Wellenhof B, Lichtenegger H, and Collins J (1997) Global Positioning System: Theory and Practice. New York: Springer.
[33] Leick A (2003) GPS Satellite Surveying. New York: Wiley.
[34] Tavernier G, Fagard H, Feissel-Vernier M, et al. (2005) The International DORIS Service (IDS). Advances in Space Research 36(3): 333–341.
[35] Willis P, Jayles C, and Bar-Sever Y (2006) DORIS: From orbit determination for altimeter missions to geodesy. Comptes Rendus Geoscience 338: 968–979 (doi:10.1016/j.crte.2005.11. 013).
[36] Stedman GE (1997) Ring-laser tests of fundamental physics and geophysics. Reports on Progress in Physics 60: 615–688.
[37] Schreiber KU, Velikoseltsev A, Rothacher M, Klu¨gel T, Stedman GE, and Wiltshire DL (2004) Direct measurment of diurnal polar motion by ring laser gyroscopes. Journal of Geophysical Research 109: B06405 (doi:10.1029/2003JB002803).
[1]陈景润,《初等数论I》[M],科学出版社,1987.
[2] Wadg W-J, Decadal free polar motiod of triaxial Earth, Geophys.J.Idt. 2004,158:1—15.
[3]王文均,地极移动的非线性动力学机制,天文学报,1998,39(3):287.
[4]叶建军,非线性受迫振动系统的次谐共振解,西南交通大学学报,2003年,014.
[5]漆安慎,杜婵英,《力学II》[M]高等教育出版社,2005年,283—327.