Magnetic variation generated by a tangential magnetic dipole located in the Earth's core

Summary The harmonically variable magnetic field, generated by a tangential magnetic dipole (TMD), located eccentrically at the surface of the Earth's core, is investigated for various periods of time variations and for a three-layer conductivity model of the Earth. Numerical computations have shown that the field is inductively damped for variation periods of less than 500 years as compared to the field of a static TMD. It is proved that the field appropriate to the TMD, has a more complicated distribution of the Earth's surface than the field of a radial magnetic dipole. Comparison with maps of the non-dipole part of the geomagnetic field shows that the TMD is not as suitable for interpreting the observed non-dipole field and its variations as the eccentric radial magnetic dipole.     

Magnetic torque and convection in the earth's core

Summary The problem of expressing analytically the magnetic torque, acting on the electrically conducting part of the Earth's mantle, is treated as a function of the system of convection on the surface of the core. The changes of velocities in the system of convection are estimated for decadic changes of the Earth's rotation and for the perturbation of the Earth's rotation in 1897. As regards the decadic changes of the Earth's rotation a change of velocity in the system of convection at the surface of the core of the order of 10^–4 m/s corresponds, and as regards the perturbation of the Earth's rotation in 1897 (10^–3 s/year) a change of velocity of 10^–3 m/s reduced to the whole surface of the core corresponds, and 10^–2 m/s corresponds for the region of the focus of the world geomagnetic anomaly (dimension of this region is 10⁶ m).     

A dipole approximating to the highest possible degree the earth's magnetic field

Summary The coordinates and the components of the dipole approximating to the highest possible degree the earth's magnetic field are determined minimizing a sum of squares of differences between the dipole field and the earth's magnetic field. Numerical results by the aid of a digital computer have been obtained for epoch 1932, 1937, 1942, 1945, 1950, 1955 and 1960 on the basis of magnetic data from 61 observatories.     

Magnetohydrodynamic disturbances in the earth's core,II

Summary In paper I, (Mohandis [2]²)), the author contributes to the discussion of the origin of the secular variation of the earth's magnetic field. A mathematical solution of magnetohydrodynamic disturbances and fluid motion due to the sudden introduction of an oscillating dipole in the earth's core has been obtained. Only the symmetrical case of the problem, where the axis of the dipole is placed perpendicular to the mantle and parallel to a poloidal field, has been discussed.In this paper, the source of disturbance is still considered to be the oscillating dipole, but the exciting field is taken as a toroidal field always parallel to the mantle. Two unsymmetric different cases of the problem are considered but the disturbed field is sonsidered only in the mantle. It is worth to note here that simpler results can be obtained by applying more conditions than those used in the present work. The new method will be illustrated in a forthcoming paper of this series, Magnetolydrodynamic disturbances in the earth's core, IV where another case of the problem will be discussed.     

地球主磁场电磁转矩导致的地球差异旋转

为探索驱动地球系统差异旋转的力源,选择整个地球作为研究对象,应用经典电磁学理论,分析地球固体介质中的电荷在地球主磁场中的运动特点,发现存在一个与地球自转方向相反的切向洛伦兹力.通过电荷与介质间的相互作用,切向洛伦兹力传递至介质迫使介质西漂.为探索地球差异旋转的规律,建立了地球薄圆筒圈层模型.应用经典物理学理论和方法推导出了地球主磁场电磁转矩及其产生的角加速度公式.研究得到四点主要结论:1)作用于半径不同的地球薄圆筒圈层的地球主磁场电磁转矩及其产生的角加速度绝对值不同:地轴及赤道附近圈层的小,其自转相对较快;半径等于3～(1/2)倍地球半径的薄圆筒圈层及其相邻圈层的大,其自转相对较慢.2)同一薄圆筒圈层中的差异旋转缘于介质的介电常数、阻力系数及质量密度的差异.3)地球差异旋转缘于地球的自转、正负电荷的非对等分布及介质的介电常数、阻力系数、质量密度的差异.4)地球差异旋转导致地壳运动,孕育地震,地球主磁场是地球差异旋转和地震孕育的敏感因子.     

Magnetohydrodynamic disturbances in the earth's core,IV

Summary In Paper III (Mohandis [1]²) we considered the sudden introduction of amagnetic dipole in the earth's core to act as a source of disturbance to the exitation field taken as a poloidal one. A symmetrical case was considered where the dipole axis is placed parallel to the original field and perpendicular to the earth's mantle. In the present work, we consider an unsymmetric case where the axis of themagnetic dipole is placed perpendicular to both the mantle and the exitation field which is taken as a toroidal one. A mathematical study is made for the resulting fluid motion in the core as well as for the generated hydromagnetic perturbations in both the mantle and the earth's fluid core. A more powerful method has been adopted than those used in previous cases.     

Magnetohydrodynamic disturbances in the earth's core,III

Summary It is in the hope of establishing a theorem contributing to the origin of the Secular Variation of the geomagnetic field that this third paper under the same heading, is written, —In this paper it is supposed that amagnetic dipole is suddenly introduced in the earth's core to act as a source of disturbance to the exciting field taken as a poloidal one. The dipole axis is placed parallel to the original field and perpendicular to the mantle. Mathematical solutions have been obtained for the resulting fluid motion in the core as well as for the generated magnetohydrodynamic perturbations in the earth's core and in the mantle. It can be seen from the mathematical results obtained that although the disturbances in the core are so complicated, yet they are much less complicated in the mantle and specially at the plane boundary separating core and mantle.     

Forced magnetohydrodynamic oscillations of the earth's core

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Flow in the earth's core and the hydromagnetic dynamo

Zusammenfassung Den Hauptgegenstand des Artikels bildet die Auswahl von Geschwindigkeiten für ein kinematisches Modell eines hydromagnetischen Dynamos. Die Ergebnisse der theoretischen Analyse betreffend die M?glichkeit der Entwicklung des magnetischen Feldes werden durch die Angaben über die Oberfl?chenstr?mung an der Grenze zwischen dem Erdkern und dem Mantel erg?rzt, die man aus der beobachteten sekul?ren ?nderung des magnetischen Feldes der Erde erwcrben hat. Das dreidimensionale Geschwindigkeitsfeld wurde in der Weise gew?hlt, damit die notwendige Bedingung der Entwicklung, d.i. das Nichtverschwinden des Braginskischen Entwicklungskoeffizienten, erfüllt werde und damit der Charakter von Str?mung auf der Kernoberfl?che den aus der sekul?ren ?nderung gewonnenen Angaben entspreche. Eine m?glichen Form des dreidimensionalen Geschwindigkeitsfeldes wird im Modell des hydromagnetischen Dynamos angewendet, das durch ein System von Integralgleichungen dargestellt wird. Die vorausgesetzte numerische L?sung ist nicht durchgeführt.

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Address: Boční II, Praha 4-Spořilov.     

基于偶极弯曲波频散的横波慢度径向分布反演

本文针对地层横波慢度径向分层模型,分析了地层横波慢度的径向非均匀性对弯曲波频散的影响.基于径向非均匀与均匀模型之间弯曲波频散的差异,结合微扰法和Backus-Gilbert(BG)理论建立了反演横波慢度径向分布的方程,求取了地层横波慢度的径向分布.在无噪声和参数误差时,反演结果较好地反映了实际地层横波慢度的径向分布,当井孔流体或井外地层纵波慢度的选取误差在10%内变化时,反演结果基本保持不变;存在信噪比(SNR)为20 dB(信号的功率为噪声的100倍)或10 dB(信号的功率为噪声的10倍)噪声时,反演结果没有发生明显的改变,其相对误差基本控制在10%以内,可见噪声对反演结果的影响不大.以上反演结果说明,本文采用的结合微扰法和BG理论的反演方法来估测地层横波慢度的径向分布时,具有很好的鲁棒性,可以被用于现场了解井壁周围的地层性质.     

Long-term variations in the earth's motion and crustal movements

Astronomical observations of time and latitude providing precise information on the motion of the earth as a whole (rotation and polar motion) point to the existence of secular and periodical variations due to tidal forces and geophysical and meteorological causes.Together with these variations, there is also evidence that the earth's crust is wandering as a result of the action of different forces, and the mean latitudes and longitudes of the observatories vary because of continental and/or local displacements.In this paper an analysis of a long series of latitude and time astronomical observations is carried out in order to investigate their long-term variations, and an important result is found: there is significant evidence for the existence of a relationship between the rotational accelerations of the earth and the variation in the positions of the mean rotation pole over periods of about thirty years. This result is discussed from the viewpoint of a deformable earth and/or crustal movements.     

A geophysical aspect of a disturbed fluid motion in the earth's core

Summary A magnetic dipole is supposed to be suddenly introduced in the earth's core (taken as an inviscid, incompressible fluid of finite electrical conductivity) to act as a source of disturbance. It is shown that although in the symmetric case of the problem the disturbed fluid is stagnant in any direction at the interface separating core from the solid insulating mantle; yet it should slip in any tangential direction at the interface, in each of the three unsymmetric cases considered here.     

Inviscid,frozen-flux velocity components at the top of earth's core from magnetic observations at earth's surface: Part 1. A new methodology

Abstract

Two alternative methods are described for obtaining inviscid velocity components at the surface of earth's liquid core, assumed perfectly conducting, given perfect and complete measurements of the geomagnetic main field and secular variation at earth's surface. The mantle is treated as a spherically-symmetric insulator for purposes of extrapolation to the core. Both methods utilize the vertical component of the induction equation and require one-dimensional interpolation along special curves on the core surface as the initial step. For the next step, the first method then utilizes the two horizontal components of the induction equation, whereas the second method relies on the horizontal components of Ohm's law. Both methods work within the confines of the ambiguity elucidated by Backus (1968) but nonetheless can still yield results of value, because the two horizontal velocity components are determined separately and at distinct locations. A brief comparison of the two methods suggests that the one, based in part on Ohm's law, should be superior from a practical viewpoint.     

磁偶极子构造法球形磁性矿体磁异常正演

球形磁性地质体是地质勘探中广泛遇到的基本地质体之一,选择合适的磁异常分析方法对其磁场进行准确正演计算具有重要的意义.为了准确快速地求解球形磁性地质体磁场特征,本文提出了一种基于磁偶极子构造原理求解球形磁性地质体磁场的数值计算方法,对球形磁性地质体按半径由小增大进行多层单元分割,再对每层单元进行块单元分割,将每个块单元视为"磁偶极子",利用基本磁偶极子公式计算了所有块单元在探测平面(线)的磁场大小,同时分析了球体磁场的剖面特征,并将数值解与解析解结果进行了对比和误差分析,最后建立双球组合模型结合Comsol多物理场仿真工具对其仿真对比,验证了磁偶极子构造法求解球体磁场的准确性.研究结果表明:数值解法结果与解析解结果磁异常波动趋势完全一致;不同测点处绝对误差有所差别,但磁异常值均在1 nT以下.本文提出的数值解法无需复杂的数学推导,计算结果稳定可靠.     

印度洋9.0级大地震激发的地球球型振荡和环型振荡

综合分析了中国数字地震台网（CDSN）改造后的5个长周期地震仪台站观测的3天的VHZ、VHE和VHN波形资料,利用功率谱密度估计方法,在没有对资料进行去固体潮处理的情况下,准确获得了2004年12月26日印度洋地震激发的0S3~0S78的基频球型振荡和部分谐频球型振荡和0T3~0T67的基频环型振荡,并与地球初步参考模型（PREM）的理论自由振荡周期进行了对比,发现实测振荡周期与PREM预测的振荡周期符合的很好.频率与PREM模型略微不一致的球型或环型振荡可以解释为地球介质的横向不均匀性和各向异性所致.因此地球自由振荡信息可用于揭示地球的三维不均匀结构信息或各向异性信息,并可能对区分地幔对流模式有所帮助.     

Density perturbations in the earth's core due to hydromagnetic oscillations

Summary The equation for density perturbation induced by plane hydromagnetic waves (responsible for geomagnetic secular variation) has been derived based on -plane formulation. It is deduced that for the usual physical properties of the earth's core such a density perturbation would be small and would not be, in the main, responsible for the recently discovered correlation between gravitation and geomagnetic potentials.     

Geomagnetic secular variation and motion of the earth's core

Summary A general theory of a time-dependent magnetic dipole in the earth is discussed. On the basis of the weastward drift of the «equatorial» dipole in the two eccentric dipoles model due toH. G. Macht, the impossibility of the origin of geomagnetic secular variation being in a deep interior of the earth's core is established from the standpoints of the shielding effect and the motions in the core. But the westward drift of the core's top layer relative to the mantle seems to be quite reasonable, even if we take into account the shielding effect of the mantle.     

A moving magnetic dipole in a conductive medium

A thorough investigation of the role that the source velocity has in the spatial and temporal variation of the secondary electromagnetic energy scattered by the Earth is necessary because marine controlled-source electromagnetic geophysical surveys employ moving sources. A first step towards this goal is the analysis, for this type of survey, of the difference of the measured value of the secondary electromagnetic energy between two systems: one with a moving source and the other with a fixed source. The model that suffices to stress this kinematic aspect is a vertical magnetic dipole moving at a constant speed along a horizontal line in a homogeneous medium separated from two homogeneous half-spaces by horizontal boundaries both above and below the dipole. The results show that both the velocity and the relative displacement between the source and the medium may cause a measurable variation relative to the static condition. Therefore, it may be necessary to take them into account in geophysical interpretation and to adapt the concepts of time and frequency domain for electromagnetic systems with moving sources.     

The electrical state of the earth's interior and the origin of the earth's main magnetic field

Summary From the standpoint of the electrical state of the earth's interior as inferred from both geophysical and physical researches, the possibility ofElsasser-Bullard's theory is discussed. The electromagnetic shielding within the earth's mantle is also taken into account. It is of interest that the theory seems to well harmonize with the electrical state considered.     

P in the shadow zone of the earth's core—Part I

Summary Regional variations have been indicated in the slope of theP travel-time curve in the shadow zone of the earth's core. Further study is needed since the uncertainties of the slope are large, especially for the observations from North American stations. There is no significant difference between themean slope of theP travel-time curve in the 95°102.9 range and those obtained byJeffreys, andJeffreys andBullen. However, there is a significant difference between themean slope in the 103° to 135° range as obtained in this study, and those obtained byJeffreys andBullen, and in a later revision byJeffreys. Themean travel-time curve ofP in the shadow zone of the earth's core should be lowered. A trial travel-time table is given with amean slope of 4.41 sec/deg. This table is in close agreement with the times obtained byGutenberg andRichter, and with the trial travel-times ofLehmann. Under the assumption of diffraction the longitudinal wave velocity has been determined to be 13.7 km/sec at the core-mantle boundary.This paper was presented at the Annual Meeting of the Seismological Society of America Reno, Nevada, 1966.