Solution to the rotation of the elastic earth by method of rigid dynamics

Hamiltonian mechanics is applied to the problem of the rotation of the elastic Earth. We first show the process for the formulation of the Hamiltonian for rotation of a deformable body and the derivation of the equations of motion from it. Then, based on a simple model of deformation, the solution is given for the period of Euler motion, UT1 and the nutation of the elastic Earth. In particular it is shown that the elasticity of the Earth acts on the nutation so as to decrease the Oppolzer terms of the nutation of the rigid Earth by about 30 per cent. The solution is in good agreement with results which have been obtained by other, different approaches.     

A rigorous Hamiltonian approach to the rotation of elastic bodies

When the problem of the rotation of a non-rigid body is studied, the usual procedure consists of adding perturbations to the Hamiltonian of the rigid solid. In some cases, as occurs with the centrifugal deformation, the new perturbations contains potentials which depend on the velocity, but usually one alter neither the definition of the canonical variables nor the method for obtaining the Hamiltonian. Although this procedure gives good estimates and its formulation is simpler, it is incorrect from a theoretical point of view.In this paper we rigorously develop a Hamiltonian formulation of the problem, considering potentials that depend on the velocity. Thus the differences between the two procedures are clearly shown, giving special emphasis to the case of the elastic Earth, for which we show that the differences obtained cannot be ignored within the accuracy limits at present required.     

The Earth's decelerated rotation and regularities in orientation of its surface lineaments and faults

The Earth's crust faults and lineaments group in clusters with predominant N-S and E-W (System I) and NW-SE and NE-SW (System II) directions. The earthquake epicenters of the Benioff seismofocal zones follow the same regularities. In other words, seismofocal zones (epicenters of earthquakes) constitute a part of the regular network of the Earth's crust and lithosphere faults and lineaments. Mathematical modeling of stress distribution in the lithosphere due to a change of the Earth's ellipsoid compression showed that the principal stresses σ₁ and σ₂ are oriented in N-S and E-W directions, while corresponding shear stresses τ are oriented in NE-SW and NW-SE directions. It is shown that the secular deceleration of the Earth's rotation can be a reasonable mechanism for the change of Earth's ellipsoid compression and, consequently, for the origin of the regular system of faults and lineaments described above.     

The theory of the nutation for the rigid earth model at the second order

We perform a complete reconstruction of the series of the nutation for a rigid Earth model with the use of the very accurate theories ELP2000 and VSOP82 for the motion of the Moon and the planets respectively, in such a way that all the individual contributions up to 0.005 mas should be taken. This implies the introduction of the planetary effects, of the influence of second-order parts of the potential of the Earth (J3, triaxiality), and some improvements due to an extension of the theory at the second order. All this increase notably the number of coefficients to be taken in account, and modifies also in a significant way the value of some of them.     

液核地球自转速率变化的带谐潮效应Ⅰ--理论公式

根据液核地球动力学原理,重新推导了在日月子引潮力作用下的地球自转速率变化的理论公式,由此明确地引入了液核影响因子,它与地球和液核的极转动惯量的变化有关。不同于Yoder.C.F(1981)的理论,本文给出了基于引潮力位Doodson展开的地球自转速率变化、日长变化和世界时变化的理论公式,指出尺度因子的转动惯量应取为地幔的有效极转动惯量,Love数应取地幔的有效Love数的理由。     

全球海洋对极移周年运动的激发

目前海洋对极移季节变化的激发尚未得到合理的定量结果.许多研究已经表明大气运动是极移季节变化最大的激发源,海洋运动是剩余部分最主要的激发源之一.利用新一代SODA海洋同化资料(SODA_1.4.2和SODA_1.4.3)以及ECCO海洋同化资料,深入研究了1992—2004年全球海洋对极移周年变化的激发以及激发随纬度的分布.结果表明,SODA海洋激发的季节变化与从测地激发函数中扣除大气、陆地水作用剩余部分的季节变化在所研究的大部分时段非常接近,二者的周年振幅和位相结果基本相当.此外,与早期SODA_Beta 7的结果比较,新一代的SODA海洋激发有了明显改善.SODA和ECCO海洋对极移周年激发的纬度分布,在格林威治方向上比较一致;在东经90°方向上有明显的差别.     

液核地球自转速率变化的带谐潮效应Ⅱ--数值计算与比较

地球自转速率的潮汐变化可由无量纲参数k/cm)(k和cm分别为壳幔的有效Love数和有效极转动惯量)来表征。对于一个具有弹性地幔、平衡海潮和核幔不耦合的地球k/cm=0.944,且与潮波频率无关。海潮的非平衡扰动使k/cm为复数,且与频率有关。大气对自转速率有效勒夫数的贡献约为Δkat=0.0075。同时地幔滞弹性对勒夫数也产生扰动。利用本文得到的理论公式和最新的潮汐数据计算了地球自转速率的潮汐变化,及其有关地球物理机制的影响。     

The rotation of 53 Be stars

Through spectral observations we obtained the rotational velocity Vsini for 53 Be stars, and estimated the values of V and i on the basis of Hutching's method. We analysed the effect of rotation on the width of emission lines and used the emission peak separation to determine the relative size of the shell and the photosphere and the dilution factor. We discuss in depth fast rotating models where stellar winds are present and their relation to the Be phenomenon.     

The influence of the electromagnetic core-mantle coupling torques on earth's rotation

The electromagnetic core-mantle coupling is one of the most likely hypotheses to explain the connections between both, the decade fluctuations of the Earth rotation and such of the magnetic field of the Earth. Within this paper, the axial and equatorial electromagnetic torques are computed at time intervals of two years from 1903.5 to 1975.5. They are compared with mechanical torques necessary for the excitation of the decade variations of the rotation of the Earth. The comparison is made with regard to the magnitude of the torques, to their time behaviour and to the periods within the time variations of both types of the torques. The computed electromagnetic torques are comparable with that necessary to excite the variations of the rotation of the Earth. But they are two or three orders less than that necessary to excite the decade variations of the polar motion. Some comparable periods were found within the spectra of the electromagnetic and the mechanical torques. This speaks in favour of the core-mantle coupling. But there are differences between both spectra too hinting at other processes which we cannot describe by a simple model of the core-mantle coupling.     

Length of the day and evolution of the Earth's core in the geological past

In this paper, we study quantitatively the effect of the Earth's core formation on the secular rate of change of the length of day (LOD). We find that for the present epoch, a growth rate of the core comprised between 1 and 10 mm/cy seems to be a plausible guess, leading to a relative de crease of LOD comprised roughly between 10 and 100 μs/cy. Such values do not affect significantly the observed secular in crease of LOD caused by tidal braking, which amounts to about 1.79 ms/cy. However, in the remote geological past, before the Phanerozoic, the effects of core growth may have been much more important, because the total change of LOD associated with core formation has been estimated by Birch in 1965 to be 2.4 hours for an initially undifferentiated cold Earth, and 3.1 hours for an initially undifferentiated hot Earth. We consider a number of scenarios, some of them corresponding to very early and/or very fast core formation, others corresponding to slow and/or late core formation. We show that palaeo‐LOD measurements seem to favour slow core formation during the Proterozoic, contrarily to the now largely prevailing hypothesis based on geochemical arguments that the iron core formed very early in the Earth's history and during a geologically short time interval (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variations of the solid Earth's center of mass due to oceanic tides

Periodic variations in the location of the center of mass of the solid Earth due to ocean tides are derived from the ocean tide model of Seiler (1991). The sum of nine partial tides leads to changes in the coordinates X, Y, Z within a range of 1cm.     

The Earth's rotation: Definition of the pole and of the angle of sidereal rotation

The use of new techniques for measuring the Earth's orientation in space and the intrinsic qualities of their attached terrestrial and celestial reference frames have now raised the accuracy of the computed polar coordinates and the angle of sidereal rotation to a level usually better than 0.001. The conceptual and conventional definitions of the Earth's pole of rotation and of the Universal Time UT1 must accordingly be given with the same order of precision. This paper gives a review of the past and present definitions of the celestial pole and UT1 as well as an evaluation of their deficiencies. Some necessary improvements in these definitions are proposed.     

20世纪中国8级大地震与日长关系的初析

本文分析了20世纪中国8级地震与日长变化的关系,并介绍了日长与地球自转速率间的换算,为使其均一化提供了方法。     

The solution for seasonal variations in the Earth's rate of rotation

New physical principles for an explanation of seasonal variations in the Earth's rate of rotation are proposed. It is thought that the variations are caused by a variation of the total energy of the Earth's atmosphere in the course of the planet's revolution about the Sun in elliptic orbit. Jacobi's virial equation for the Earth's atmosphere is derived from the Eulerian equations. The virial theorem is obtained. The existence of the relationship between Jacobi's function and potential energy of the atmosphere is confirmed. In the framework of this relationship, Jacobi's equation is reduced to the equation of unperturbed virial oscillations. The solution of the above-mentioned equation expresses the periodic virial oscillations of Jacobi's function (moment of inertia) of the Earth's atmosphere with time. The solution of the perturbed virial oscillation problem of the atmosphere-solid Earth system is obtained. The perturbation term in Jacobi's virial equation regards, in explicit form, the energy changes occurring in the atmosphere in the course of the planet's revolution about the Sun in elliptic orbit. The annual and semi-annual periodic variations in the Earth's rate of rotation can be considered as an astrometrical result following from the obtained solution. A satisfactory accord of the theoretical results with experimental data is shown.     

Imprint of Galactic dynamics on Earth's climate

A connection between climate and the Solar system's motion perpendicular to the Galactic plane during the last 200 Myr years is studied. An imprint of galactic dynamics is found in a long‐term record of the Earth's climate that is consistent with variations in the Solar system oscillation around the Galactic midplane. From small modulations in the oscillation frequency of Earth's climate the following features of the Galaxy along the Solar circle can be determined: 1) the mass distribution, 2) the timing of two spiral arm crossings (31 Myr and 142 Myr) 3) Spiral arm/interarm density ratio (ρ _arm/ρ _interarm ≈ 1.5–1.8), and finally, using current knowledge of spiral arm positions, a pattern speed of Ω_P = 13.6 ± 1.4 km s^–1 kpc^–1 is determined. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Deceleration of the Earth's rotation from old solar tables

The solar tables of ibn Yunis and of King Alfonso, those of Kepler, of G. D. and J.-J. Cassini, and of Lalande are compared with Newcomb's theory of the Sun to determine the deceleration of the Earth's rotation. Comparisons of mean motion and of longitude lead to separate determinations. A value for the deceleration, , assumed to be independent of time is obtained for the period — 146 through 1892. This result is based on the assumption that Newcomb's theory converts the Earth's orbital motion into a perfect clock, and the result is independent of lunar and tidal theory. The deceleration seems greater than that obtained from the literature for the tidal deceleration caused by the Moon.     

IERS1996规范中地球引力势模型和测量模型的改进

简要而系统地介绍ＩＥＲＳ１９９６规范采用的地球引力势模型和各种测量模型,着重叙述了其与ＩＥＲＳ１９９２标准相比所作的改进。规范用ＪＧＭ－３地球引力势模型取代ＧＥＭ－Ｔ３模型,在计算地球潮汐形变产生的附加势时展开到３阶,并考虑了地幔的滞弹效应。在测站位移的计算中,规范引入了３倍洛夫数,计及地幔的滞弹性,引入了计算冰后期回弹的ＩＣＥ－４Ｇ模型,列出了改正ＶＬＢＩ观测中天线形变改正的公式。关于地球自转和     

大气角动量函数在日长变化非线性预报中的重要作用

日长变化具有复杂的时变特性,传统的线性时间序列分析方法往往难以取得良好的预报效果.采用非线性人工神经网络技术对日长变化进行预报,网络模型的拓扑结构由最小均方误差法来确定.考虑到日长变化与大气环流运动间的密切关系,在神经网络预报模型中引入轴向大气角动量序列.结果表明,联合日长和大气角动量序列,比起单独采用日长资料,预报精度得到显著的提高.