SNREI地球对表面负荷和引潮力的形变响应

基于PREM模型，利用非自转、球型分层、各向同性、理想弹性（SNREI）地球的形变理论，讨论了地球在不同驱动力作用下的形变特征．采用地球位移场方程的4阶Runge Kutta数值积分方法，解算了在表面负荷和日月引潮力作用下地球表面和内部形变和扰动位，并给出了地球表面的负荷Love数和体潮Love数．结果表明在固体内核中的形变很小，液核中低阶(n＜10)负荷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，负荷阶数越高这种衰减的速度越快．SNREI地球的地表负荷Love数和体潮Love数与信号频率的依赖关系很弱．在计算体潮Love数的过程中，采用了SNREI地球的运动方程，同时考虑了由于地球自转和椭率引起的核幔边界附加压力，这一近似处理方法获得的结果能很好地符合地球表面重力潮汐实际观测结果．     

地球表面质量负荷的静态响应

本文给出了单位点质量负荷作用在球状成层地球模型上的解。对较新的G-D1066A地球模型求出了n直到10000阶的负荷勒夫数,并利用这组负荷勒夫数计算了格林函数的值。简述了如何利用格林函数计算地球对表面任何负荷的响应。讨论了负荷潮研究在地球物理和海洋学方面的一些应用。     

地幔滞弹性对Chandler摆动的影响

基于简正模扰动理论和勒夫数扰动方法,采用Zschau 的地幔流变模型,在假设Chandler摆动的能量全部耗散于地幔滞弹性摩擦的条件下,导出Chandler 摆动Q(Q_w)的理论值.还考虑了滞弹地球的平衡极潮对摆动的影响,所得结果与绝大部分天文实测值非常一致.分析表明.平衡部分的影响大,地幔滞弹性很可能是Chandler 摆动最主要的能量耗散源,Q_w 的理论值约为71.还推算了吸收带模型参数α,研究了该模型的适用性,并讨论了Q_w 与地幔Q(Q_m)的关系.     

固体潮应变理论值的计算

本文从勒夫数h、l的概念出发,讨论弹性地球在起潮力作用下的潮汐形变,制定了一套适于电子计算机计算的固体潮应变理论值的计算公式和步骤。     

海潮负荷对地球内部潮汐应力和应变的影响

详细介绍了海潮负荷影响的计算理论,基于PREM地球模型计算了地球内部的负荷勒夫数及负荷格林函数;并以上海台和武汉台为例,计算了海潮负荷对不同深度处的应力和应变潮汐的影响. 结果表明:深度是影响海潮负荷应力的一个重要因素,在靠近计算点的区域,应力负荷的影响随深度增大而减小;而对于远离计算点的区域,应力负荷的影响却随深度增大而增大;另外,深度会影响某些应力和应变潮汐分量时间变化的相位. 在沿海地区,海潮负荷对应力和应变的影响超过了应力和应变固体潮的影响,因此该影响在应力和应变测量中必须要加以考虑.      

Earth''''s deformation due to the dynamical perturbations of the fluid outer core

Introduction The fluid outer core separates the solid inner core from the solid elastic mantle, and as a result, makes the free and forced movement of this mechanical system more complicated and profuse. As the elastic mantle, the free oscillations may occur within the Earths fluid outer core (FOC) due to excitation of a strong and deep earthquake (Crossley, 1975b; Friedlander, Siegmann, 1982; Shen, 1983; Friedlander, 1985). However, compared with the oscillations of the elastic mantle, i…     

液核动力学扰动引起的地球形变

讨论了地球固体部分对液核动力学效应引发的核幔边界和内核边界上压力和引力扰动的形变响应．采用弹性-引力形变理论描述地幔和内核的形变，给出了内部负荷Love数的一般表达式．以初始参考地球模型为例，分别计算了在地球表面、核幔边界和内核边界上的内部负荷Love数．探讨了液核边界上压力和引力扰动导致的地球形变场的空间和频率分布特征．本文的结果可以为中短周期液核动力学理论模拟提供必要的边界条件．      

Body tides on a 3-D elastic earth: Toward a tidal tomography

The deformational and gravitational response of the Earth to the tide generating potential has generally involved 1-D (i.e., depth varying) Earth models. Progressive improvement in observational constraints on body tides, generated from both ground and space-based surveys, suggests that an examination of the potential impact of lateral variations in Earth structure is warranted. We present a suite of predictions of the body tide response within the semi-diurnal, diurnal and long-period tidal bands computed using a finite-volume numerical code. The calculations adopt 3-D density and elastic structure taken from seismic inferences and, in a subset of the calculations, dynamic topography on the surface and internal interfaces. We find that perturbations in the radial displacement and surface gravity within the semi-diurnal band reach ~ 1 mm and 0.15 µgal, respectively. The perturbations in the diurnal band are comparable to these values, and within the long-period band they are a factor of 3–5 smaller. We also demonstrate that lateral variations in the elastic moduli, which have been ignored in recent work, contribute greater than 50% of the total perturbation. The level of perturbation associated with 3-D structure exceeds the current observational uncertainty obtainable using space-geodetic methods, and this suggests the possibility of performing tidal tomographic inversions of such data.     

Earth’s deformation due to the dynamical perturbations of the fluid outer core

The elasto-gravitational deformation response of the Earth’s solid parts to the perturbations of the pressure and gravity on the core-mantle boundary (CMB) and the solid inner core boundary (ICB), due to the dynamical behaviors of the fluid outer core (FOC), is discussed. The internal load Love numbers, which are formulized in a general form in this study, are employed to describe the Earth’s deformation. The preliminary reference Earth model (PREM) is used as an example to calculate the internal load Love numbers on the Earth’s surface, CMB and ICB, respectively. The characteristics of the Earth’s deformation variation with the depth and the perturbation periods on the boundaries of the FOC are also investigated. The numerical results indicate that the internal load Love numbers decrease quickly with the increasing degree of the spherical harmonics of the displacement and depend strongly on the perturbation frequencies, especially on the high frequencies. The results, obtained in this work, can be used to construct the boundary conditions for the core dynamics of the long-period oscillations of the Earth’s fluid outer core. Foundation item: State Natural Science Foundation of China (40174022 and 49925411) and the Projects from Chinese Academy of Sciences (KZCX2-106 and KZ952-J1-411).     

Dependence of the Love numbers upon the inner structure of the Earth and comparison of theoretical models with results of measurements

Summary The question this paper is examining is the following: to what extent are the Love numbers dependent on certain characteristics of the inner structure of the Earth? It has been proven — on the basis of calculations carried out by the author-that these quantities are only in a small degree dependent on the density values measured on the surface of the Earth and on the selection of the density function in the mantle of the Earth. On the other hand the value of Love numbersh, k andl is considerably influenced by the assumptions made about the core of the Earth, namely by the position of the boundary between the core and the mantle and by the magnitude of the rigidity coefficient presumed in the core in the vicinity of the core-mantle boundary.The results of the calculations are compared with those mean values of Love numbers obtained from the data of stations operating at different places of the Earth. By reason of this it can be assumed that the core of the Earth has, in the vicinity of the core-mantle boundary, a coefficient of effective rigidity of the order of 10¹⁰ dyn/cm², if the core-mantle boundary is placed at the relative Earth radius of 0.545 from the centre of the Earth.     

Time changes of the potential Love tidal parameters k2 and k3

The planet Earth is continuously changing in time, so there are phenomena that require continuous observation, including tidal parameters. The main goal of this study is to analyze time changes of the Love potential tidal parameters. This paper concerns an analysis of the estimated Love numbers k for the second and the third degree tides (numbers k₂ and k₃), associated with the tide variations of the satellite motion. The measured data used for determining the parameters k₂, k₃ were conducted within the period of January 1, 2014 until July 1, 2016 by LAGEOS-1 and LAGEOS-2 satellites. The results were compared with our previous determination of these parameters from LAGEOS data during the period from January 1, 2005 until July 1, 2007 to examine whether any systematic differences and time evolution occur. The adjusted values for k₂ equalling 0.29842 ± 0.00008 and k₃ equalling 0.0901 ± 0.0034 are discussed and compared with the nominal values given in International Earth Rotation and Reference Systems Service standards. The differences between the k₂ and k₃ values obtained for the time interval 2005.0–2007.5 and the results for 2014.0–2016.5 interval are –0.00288 for k₂ and 0.0042 for k₃. The obtained differences in the k₂ and k₃ values may indicate their evolution in time.     

上地幔各向异性介质对固体潮及负荷潮的影响

讨论了上地幔各向异性介质中的潮汐运动方程,根据Deiewonski提供的地球模型参数,利用经典的Runge－Kutta数值积分方法,计算了固体潮勒夫数和负荷勒夫数．结果表明,考虑上地幔介质各向异性与否对固体潮勒夫数的影响较小（约为0．06％）,而对负荷勒夫数的影响较大（2．5％）,进一步说明了中低阶负荷勒大数对上地慢介质特性的敏感性．     

液核地球的周日固体潮响应

本文研究了液核地球对日月引潮力位球谐函数项的变形响应,即周日固体潮。作为数值结果,计算了1066A地球模型的周日潮汐勒夫数。所建立的周日固体潮理论模型改进了Molodensky液核动力学理论模型。为了比较两者之间的差异,还根据Molodensky理论模型计算了1066A地球模型的周日潮汐勒夫数。     

Lunar Laser Ranging: Glorious Past And A Bright Future

Lunar Laser Ranging (LLR), a part of the NASA Apollo program, has beenon-going for more than 30 years. It provides the grist for a multi-disciplinarydata analysis mill. Results exist for solid Earth sciences, geodesy and geodynamics,solar system ephemerides, terrestrial and celestial reference frames, lunar physics,general relativity and gravitational theory. Combined with other data, it treatsprecession of the Earth's spin axis, lunar induced nutation, polar motion/Earthrotation, Earth orbit obliquity to the ecliptic, intersection of the celestial equatorwith the ecliptic, luni-solar solid body tides, lunar tidal deceleration, lunar physicaland free librations, structure of the moon and energy dissipation in the lunar interior.LLR provides input to lunar surface cartography and surveying, Earth station and lunar retroreflector location and motion, mass of the Earth-moon system, lunar and terrestrial gravity harmonics and Love numbers, relativistic geodesic precession, and the equivalence principle of general relativity. With the passive nature of the reflectors and steady improvement in observing equipment and data analysis, LLR continues to provide state-of-the-art results. Gains are steady as the data-base expands. After more than 30 years, LLR remains the only active Apollo experiment. It is important to recognize examples of efficient and cost effective progress of research. LLR is just such an example.     

Temporal variations of rotational origin in the absolute value of gravity

Summary When correcting precise gravity measurements for polar motion, the Earth's rotational deformation must be considered, as this will increase the correction based on a rigid Earth by about 15%. Conversely the gravity observations can be used to estimate the Love numbers h₂ and k₂ at the Chandler frequency.     

A global experimental model for gravity tides of the Earth

The long-term, continuous and high-quality tidal gravity data, recorded with the superconducting gravimeters (SGs) at 19 stations in the Global Geodynamics Project (GGP), were simultaneously used to investigate the global pattern of the tidal gravity variations. The atmospheric effects were removed from the gravity observations by using the simultaneous pressure records at the stations. A total of six global co-tidal models were employed to remove the loading effects of oceanic tides. The resonance parameters of the Earth's free core nutation (FCN), as well as the spheroidal constant components in the gravimetric factors of waves O₁ and M₂, were accurately retrieved. As a result, a global experimental model for gravity tides (GEMGT) was developed, considering the nearly diurnal resonance and the latitude-dependence of the gravimetric amplitude factors. The final results indicate that the mean discrepancy of the four main tidal waves (i.e. O₁, K₁, M₂ and S₂) between the GEMGT and SG observations is less than 0.2% on average. The GEMGT is in good agreement with the theoretical models based on the inelastic non-hydrostatic equilibrium Earth models [Dehant, V., Defraigne, P., Wahr, J., 1999. Tides for a convective Earth. J. Geophys. Res. 104, 1035–1058; Mathews, P.M., 2001. Love numbers and gravimetric factor for diurnal tides. J. Geodetic Soc. Jpn. 46 (4), 231–236] with a mean discrepancy less than 0.15%. However, the GEMGT is in closer accordance with the theoretical model given by Mathews [Mathews, P.M., 2001. Love numbers and gravimetric factor for diurnal tides. J. Geodetic Soc. Jpn. 46 (4), 231–236] for the diurnal tides while it is in closer agreement with one obtained by Dehant et al. [Dehant, V., Defraigne, P., Wahr, J., 1999. Tides for a convective Earth. J. Geophys. Res. 104, 1035–1058] for the semi-diurnal tides.     

Earth tides

The main geometrical characteristics and mechanical properties of bodily tides are described, using the convenient elastic parameters of Love. The problem of the Earth's deformation is a problem of spherical elasticity of the sixth order. The importance of Earth tides in astronomy and geophysics is emphasized by their relation to the precession-nutation and tesseral tidal problems, the secular retardation of the Earth's speed of rotation due to the dissipation of energy in sectorial tides, the periodic variations of the speed of rotation due to zonal tides, the satellite orbit perturbations due to the Earth's potential variation, and the radial deformations in laser distance measurements. The possibility that dynamical effects would be produced in the Earth's liquid core was pointed out by Poincaré and developed by Jeffreys, Vicente, and Molodensky. An experimental confirmation is presented here. The role of the Earth tide phenomenon in gravimetry and oceanography is also described, as are the perturbing effects due to regional tectonic features. Instrumental developments are critical in the acquisition of precise data; the calibration problem is fundamental for a correct comparison with Earth models.     

Long-period Love wave overtone data in North America and the Pacific Ocean: new evidence for upper mantle anisotropy

Two Tonga-trench earthquakes recorded in North America on WWSSN long-period instruments have been processed by making use of spatial analysis techniques to retrieve the phase velocities of Love wave modes. Dispersion data up to the third overtone at periods longer than 30 s have been obtained for two broad areas: the Pacific Ocean and North America. It is found that the observed Love wave phase velocities are not in agreement with the values predicted from the previously published models inferred from Rayleigh wave data. Phase velocity discrepancies as large as 3–4% in the Pacific Ocean and 2% in North America are observed up to the second overtone. Preliminary direct computations, which have been performed in the framework of transversely isotropic models with the axis of symmetry oriented vertically, suggest that the cause for this departure from isotropy probably extends to depths > 200 km.     

基于一种新智能优化算法与谱相关方法对重力固体潮的分析

根据月球与太阳相对于地球位置的关系,建立一个三维正交分解模型来揭示重力固体潮中包含的谐波成分。在此基础上,提出一种基于单形邻域与多角色进化策略智能优化算法的独立分量分析方法,用以提高算法效率和全局寻优能力;并结合谱相关方法,对重力固体潮观测数据进行处理和分析,观察其频域和时域的变化。最后引入理论信号和理论计算值作为参考背景,以凸显其异常变化特征。研究表明,利用该方法可以有效地反映出重力固体潮潮汐的日波、半日波、长周期波等特征。同时,发现重力固体潮潮汐的异常变化中隐含有地震前兆信息,通过对云南地区观测数据的分析,在排除测量误差和环境影响外,发现在地震前2~5个月内,重力固体潮的长周期波均呈现出规律性的异常变化。这反映出地震的前兆异常信息,可能对地震时间和地点的预测提供依据。     

Earth Rotation Parameters 1899.7–:1992.0 After Reanalysis Within The Hipparcos Frame

Earth rotation parameters (ERP) in the interval 1899.7–1992.0 are obtained from re-analysis of the observed latitude/universal time variations by optical astrometry. Hipparcos Catalogue is used to define the celestial reference frame, within which the ERP are described, with special care devoted to 'problematic' double and/or multiple stars. The terrestrial reference frame is defined by the adopted latitudes/longitudes of participating instruments and their secular motions as given by the NUVEL-1 NNR model of plate motions, and it is chosen to be very close to the International Terrestrial Reference Frame (ITRF). More than four million observations made with 48 different instruments at 31 observatories, located all over the world, are utilized to determine polar motion, celestial pole offsets and (after 1956) universal time UT1, all at 5-day intervals. Along with these parameters, the combinations of Love and Shida numbers, governing the tidal variations of the local verticals at individual observatories, are also determined. The analysis of the results covering almost a century, namely the long-periodic polar motion and length-of-day changes, is presented.