【作者】 喻铮铮；

【导师】 张捍卫；

【作者基本信息】 河南理工大学 ， 测绘科学与技术， 2021， 博士

【摘要】 地球自转是深空导航、卫星精密定轨、时间尺度以及不同时空参考系连接的基本问题。地球自转运动指的是地球参考轴(极)相对于地球本体的运动,表现为极移和自转速率变化;以及相对于惯性空间的运动,表现为岁差章动。地球自转变化的力学机制主要包括:外界天体的引力、地球内部的物质迁移、地球表面的各种质量负荷变化等。缔合Legendre多项式和矢量球面函数分别是研究地球引力位和地壳形变的基本数学工具。本文首先对其进行了理论研究,接着简要介绍了地球引力位和潮汐的若干基本概念,然后在进一步完善地球自转动力学和运动学理论的基础上,详细研究了地球自转运动的潮汐与非潮汐变化。论文的主要工作如下:缔合Legendre多项式递推公式的改进。对目前常用的递推算法进行研究,指出了Belikov(1991)递推算法系数存在的问题,并进行了改正;首次提出一种超跨阶次的缔合Legendre多项式递推算法,通过实际计算和比较,证实了其具有更广的适用范围及更好的精度和效率。完善了关于复数球矢量函数的描述,给出了位移场、应变张量场的复矢量球函数表达,以及潮汐形变位移和地球形状轴的定义。空间测地技术中的潮汐效应研究。在引潮力位展开研究过程中,指出了前人研究结果中存在的一些问题,给出了6阶引潮力位Laplace展开式,并据此导出了6阶岁差章动力矩表达式;重新计算了Love数频率特性对地球引力位系数和测站位移的影响,指出在高精度空间大地测量中需要考虑极移、地球自转速率变化对重力观测值和垂线偏差的影响。液核地球自转动力学理论研究。推导了任意天球参考轴的极移和岁差章动与地球自转轴的极移和岁差章动之间的理论转换关系,并对其正确性和便捷性进行了数学证明。详细推导了顾及三轴性的液核地球自转动力学方程,对其激发函数进行了深入研究与修正,给出了便于计算和应用的激发函数表达式。地球自转潮汐变化研究。地球自转变化的显著特征是太阳、月球引潮力所引起的潮汐变化。本文在以上理论研究的基础上,详细讨论了尺度因子的取值,结合最新的精密引潮力位展开,给出了顾及大气效应和地幔滞弹性的地球自转潮汐变化序列,并与IERS(2010)及前人相关研究进行了对比。地球自转非潮汐变化研究。研究了地球自转变化中的非潮汐影响,计算结果显示在地球自转速率的长期变化中,有约23.8%的绝对量来自于非潮汐效应的影响。对陆地水储量之于地球自转变化的激发影响进行了计算,结果显示陆地水储量对周年极移的顺向激发振幅约为16.85mas,对周年日长变化的激发约为44μs。表明将大气激发与陆地水储量激发相结合能很好地解释与天文观测激发之间的差异,同时也发现还有未知激发源存在,其量级约为10mas。随后对其它非潮汐因素及其对地球自转变化的影响机制进行了探讨,表明太阳活动和冰期后地壳回弹也是重要的非潮汐因素,同时也还有其它非潮汐影响需进一步探寻。图17幅,表13个,参考文献186篇。更多还原

【Abstract】 The study of Earth’s rotation variation is the basis of space navigation,precise satellite orbit determination,time scale and space reference frame connection.The Earth rotation refers to the motion of its reference axis(pole)with respect to the Earth’s body which characterized by polar motion and rotation velocity variation,and the motion with respect to the inertial space which characterized by precession-nutation.The mechanical mechanism of the Earth rotation mainly include: the gravitation of the external celestial bodies(mainly the Sun and the Moon);the material migration on the Earth’s surface and inside;the various load variations on the Earth’s surface.Associated Legendre polynomials and vector spherical functions are the basic mathematical tools for the study of Earth gravitational potential and crustal deformation.In this study,these mathematical tools are studied theoretically,and the basic concepts of the Earth’s gravitational potential and tide are briefly introduced.Then,on the basis of further improving the dynamic and kinematic theory of the Earth rotation,the tidal and non-tidal variations of the Earth’s rotation are studied in detail.The main works are as follows:Improvement of recursive formula of associated Legendre polynomials.In this part,the general recursive algorithms are studied firstly,a defect in Belikov(1991)is pointed out and the correction is given.A super cross order recursive algorithm is proposed in this study,and the related calculation is carried out.Then,the description of the complex spherical vector function is improved.At the end of this part,the expressions of the displacement field,strain tensor field are deduced,and the definitions of the tidal deformation displacement and Earth’s figure axis are given.Study of the tidal effects in spatial geodesy.In the research of tidal potential generating development,some defects in previous studies are pointed out,the six order Laplace tidal potential generating development and the torque expressions of precession-nutation are given.Then,the influence of the Love number frequency characteristics on the Earth’s gravity field and station displacement are recalculated.It is pointed out that the influence of polar motion and Earth’s rotation rate on gravity observation and vertical deviation should be considered in modern high-precision space geodesy.Further study on the dynamic theory of Earth rotation with liquid core.Firstly,a geometric theorem of the Earth rotation kinematics is established.The theoretical transformation relationship between the polar motion and precession-nutation of an arbitrary celestial reference axis and the polar motion and precession-nutation of the Earth’s rotation axis is given,and its correctness and convenience are proved.The dynamic equations of the triaxial Earth rotation with liquid core is re-deduced,and its excitation functions are studied in depth,the final expression of the excitation functions are given which are convenient for calculation and application.Study of the tidal variation of Earth rotation.The most salient feature of the Earth’s rotation is the tidal variation caused by the tidal generating force of the Sun and the Moon.Based on the above theoretical researches,the value of the scale factor is discussed in detail,combined with the latest tidal generating potential development,a new tidal variation sequence of the Earth’s rotation considering the atmospheric effect and mantle anelasticity is given.Compared with IERS(2010)and other related studies,the results show that the variations of the main periodic terms are relatively consistent.Study of the non-tidal variation of Earth’s rotation.The non-tidal influence on the variation of the Earth’s rotation is studied.The calculation result shows that there are about 23.8% of the long-term variations of the Earth’s rotation rate caused by the non-tidal effect.Then,the influence of global continental water storage on the Earth rotation is calculated,the results show that the induced excitation for prograde component of annual polar motion from land water storage is about 16.85 mas,and for annual component of LOD is about 44μs.The combination of atmospheric excitation and water storage excitation could well explain the difference between theory and observation,and there are still orther unknown excitation sources exist,the magnitude is about 10 mas.Finally,other non-tidal factors and their influence mechanism on the Earth’s rotation are discussed.The study shows that the Solar activity and crustal rebound after the last ice age are the orther important non-tidal factors,and there are also other non-tidal factors need to be further discussed.更多还原