On the effects of a bumpy core-mantle interface

Motivated by the high degree of correlation between the variable parts of the magnetic and gravitational potentials of the Earth discovered by Hide and Malin (using a harmonic analysis approach and utilizing the geomagnetic data) when one field is suitably displaced relative to the other, Moffatt and Dillon (1976) studied a simple planar model in an attempt to find a quantitative explanation for the suggestion that this high degree of correlation may be due to the influences produced by bumps on the core-mantle interface. Moffatt and Dillon assumed that the core-mantle interface was z = η(x) where |?η/?χ| ? 1 and such that in the core [z < η(x)] a uniform flow (U₀, 0, 0) prevails in the presence of a uniform ‘toroidal’ field (B₀, 0, 0); (here z is the vertical coordinate and x is the eastward distance). The whole system rotates uniformly about the vertical with angular velocity Ω. The present work extends the model discussed by Moffatt and Dillon to include a horizontal component of angular velocity Ω_H and a uniform small poloidal field B_p. In addition, the uniform toroidal field is here replaced by one which vanishes everywhere in the mantle and increases linearly, from zero on the interface, with z. It is shown that the presence of Ω_H and B_p, together with the present choice of toroidal magnetic field, has a profound effect both on the correlation between the variable parts of the magnetic and gravitational fields of the Earth, and on how far the disturbances caused by the topography of the interface [which is necessarily three-dimensional i.e. z = η(x, y) here] can penetrate into the liquid core. In particular it is found that the highest value of the correlation function is +0.79 which corresponds to a situation in which the magnetic potential is displaced both latitudinally and longitudinally relative to the gravitational potential.     

An improvement for calculating the correlation between the geomagnetic and the Earth's gravitational fields

There is a correlation between the geomagnetic and the Earth's gravitational fields to a certain degree. We should consider the zeral harmonic terms to calculate the correlation function. Correlation between the geomagnetic non-dipole field of epoch 1980, which was moved eastwards 165; and the departure part of the Earth's gravitational field from the hydrostatic equilibrium, yields a value of 0.6278. It is significant at the 0.01 level. Calculating the correlations of different epochs, we find that the westward drifting velocity of the geomagnetic non-dipole field is 0.3° year⁻¹. It is not necessary to calculate the correlations between any individual harmonic term from either field.     

The interaction of elastic waves with a solid-liquid interface,with applications to the core-mantle boundary

The paper discusses basic ideas and principles underlying methods, which have proved useful in the interpretation of diffraction and scattering phenomena by a smooth or slightly rough solid-liquid interface. Generally, the wave interaction may be formulated as an excitation problem; it involves (1) finding an equivalent dislocation or source distribution on the interface, and (2) evaluating the excited wave field. These steps are taken through perturbation theory and/or adopting the appropriate generalization of ray theory. In this context an explicit form of Green's function is also given. The methods have been applied to the core-mantle boundary, with a view toward the interpretation of recent data: (a) diffracted P and S waves around the core (in particular, their attenuation); (b) scattered short-period core phases (in particular, precursors to PKP and PKKP). Other types of wave interaction, and implications for models of the core-mantle boundary structure, are briefly mentioned.Paper presented at the EGS/ESC workshop on Generation and propagation of seismic waves in Neustadt, Federal Republic of Germany, August 1978.     

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.     

The perturbation of alternating geomagnetic fields by discontinuities with high conductivity contrasts

The perturbation of alternating geomagnetic fields by conductivity discontinuities is considered. A numerical method is used to solve the two-dimensional induction problem. Models in which the conductivity contrast between conductive regions is great, such as between oceanic and continental regions, are considered. The perturbation field distributions for models with higher conductivity contrasts are compared with lower conductivity contrast models using a method recently developed by Jones (1972). Total field solutions are obtained for several models by using a very large grid as well as a folding-in technique. Results from the two methods for the various models are compared. It is found that the folding-in technique offers an alternative method for handling higher conductivity contrasts.     

The perturbation of geomagnetic fields by two-dimensional and three-dimensional conductivity inhomogeneities

Summary A numerical method is used to calculate the geomagnetic fields associated with a three-dimensional conductivity anomaly. Fields associated with a two-dimensional model are also studied numerically for a range of frequencies and apparent resistivity curves for the two models are compared with that calculated for a layered earth. The apparent resistivity curves for both the three-dimensional model and the two-dimensional model differ considerably from the layered case, and it is evident that if a layered model is used for interpretation the results may be very misleading.     

Effects of a rigid core on the reflection and transmission coefficients from a multi-layered core-mantle boundary

Summary The aim of this paper is to present the formulations which can be used in calculating reflection and transmission coefficients when the rigidity in the core is taken into consideration. The theoretical curves presented can be used as a guide for studies of the physical parameters of the core-mantle boundary. It is hoped that these curves may lead to a clarification of the great differences between observed data and theoretical calculations, when the geometrical spreading and attenuation are taken into account.The Thomson-Haskell matrix formulations are used to calculate the reflection and transmission coefficients for a multi-layered medium imbedded between two half-spaces representing the solid mantle and a rigid core. A rigid core is defined here as having a rigidity in the range 10¹⁰<<10¹¹ cgs units. For five proposed models of the core-mantle boundary the rigidity in the core is varied and the results are compared with those for a liquid core.     

The correlation between the variation in ionospheric conductivity and that of the geomagnetic Sq field

Effects of the solar activity on the geomagnetic Sq field were studied by examining the correlation of the Sq amplitude in the Y-component with the sunspot number or height integrated Pedersen and Hall conductivities of the ionosphere at Kakioka, Chambon La Foret and Port Moresby for a period of 21 years. It was found that solar activity dependence of the Sq amplitude is almost explained by the effect of the local ionospheric conductivity if the month is fixed. That is, the solar activity dependence in each month is mainly caused by the local conductivity. However, the amplitude is clearly small in winter for the same conductivity value. This is probably due to the seasonal difference of the neutral winds driving ionospheric dynamo currents or to the magnetic effect of the field-aligned currents connecting both hemispheres driven by the asymmetric dynamo action in the ionosphere.     

The correlation between geomagnetic disturbances and topology of quasi-open structures in the solar magnetic field

Results of photospheric magnetic field extrapolation in a potential approximation and of the technique for separating the open part of magnetic flux have revealed that changes in the relationship between the open part of the south polarity magnetic flux obtained in the chromosphere and corona from July to November 2006 correlate with variations in the Akasofu parameter calculated from data on the solar wind parameters and interplanetary magnetic field at Lagrange point L1, and with the K _p index.     

Analysis of a lower jurassic geomagnetic reversal based on a model that relates transitional fields to variations of flux on the core surface

Summary For the last 12 Myr the transitional virtual geomagnetic poles (VGPs) of different reversals lie close to two preferred and practically antipodal longitudinal paths. In spite of some controversies about these transitional paths, it has been pointed out that they are linked to geomagnetic phenomena. Jurassic transitional VGP paths are quite similar to those of the last 12 Myr. Paleomagnetic data recorded in Stormberg Lavas (195 ± 5 Ma) belonging to two sampling localities of South Africa have been rotated according to an absolute palaeoreconstruction of Africa for the lower Jurassic. In order to avoid the hypothesis about dipolarity implicit in the VGPs calculations, the transitional directions recorded in the lavas were compared with others that were simulated on the basis of a model that relates transitional fields to variations of flux on the Earth's core surface. They were quite similar. For both, recorded and simulated data, the VGPs showed similar paths. Similar conditions could thus have driven both late Cenozoic and Jurassic reversals.     

闽赣交界地区流动地磁变化特征与地震关系的分析

利用1990年以来闽赣交界地区流动地磁观测资料,分析研究1990年以来发生的地震与地磁异常变化的关系。结果表明,闽赣交界地区流动地磁变化与该地区的地震存在一定的对应关系,在震前一年内出现异常,表现出地磁场变化的群体性和同向性的特征,震级越大,震磁异常关系越显著。     

Magnetic field generation by the motion of a highly conducting fluid

Abstract

Using an asymptotic expansion of Green's function for the problem of magnetic field generation by 3D steady flow of highly conducting fluid a general antidynamo theorem is proved in the case of no exponential stretching of liquid particles. Explicit formulae connecting the spectrum of the magnetic modes with the geometry of the Lagrangian trajectories are obtained. The existence of the fast dynamo action for special flows with exponential stretching is proved under the condition of smoothness of the fields of stretching and non-stretching directions.     

The period of the free core nutation: towards a dynamical basis for an ‘extra-flattening’ of the core-mantle boundary

Indirect observations and theoretical predictions for the period of the free core nutation (FCN) differ by anywhere from 15 to 30 days, and various effects have been invoked in attempts to explain this difference. The favored explanation remains as much as 5% departure in the flattening of the core-mantle boundary (CMB) from that of its hydrostatic reference figure. This 5% ‘extra-flattening’ of the CMB is not seen at the Earth's surface, where the difference is only about 0.5%. In contrast to the a posteriori model adjustments used to determine this up to 5% value, and the kinematic results available from viscous flow modeling using the seismically determined lateral heterogeneity in density data, we consider this problem from the perspective of a forward-modeling dynamical study. More specifically, we investigate the related problem of flow-induced surface and CMB topography, arising from convection in the mantle. As such, we have completed a comparative and systematic study of relative surface and CMB topography resulting from numerical models of mantle convection. When effects resulting from boundary curvature are isolated, it appears that the magnitude of CMB topography produced is insufficient in producing a significant extra-flattening of the CMB. However, results concerning effects solely resulting from a depth-dependent mantle viscosity profile, indicate that this factor may indeed lead to enhanced topography at the CMB of the magnitude required to produce the extra-flattening there.     

含黏性流体孔隙介质分界面上反透射系数特征研究

地下岩石由岩石骨架和孔隙流体组成,通常流体含黏性.地震波在地下介质中传播时受岩石骨架和黏性流体的影响会呈现出复杂的变化.本文将流、固体位移和应力连续作为边界条件,推导出含黏性流体孔隙介质分界面上反透射系数方程;通过建立上层为饱油、下层为饱盐水的砂岩孔隙介质模型,开展反透射系数特征研究,分别分析不同频率、不同黏滞系数条件下,含黏性流体孔隙介质分界面上反透射系数随入射角的变化.研究表明,孔隙介质分界面上和等效介质分界面上的反透射系数分别随入射角的变化趋势基本一致,说明方程推导和数值计算的正确性;快纵波反透射系数受频率、流体黏性的影响较小,而快横波反透射系数在一定入射角范围内受频率、流体黏性的影响比较大;由于黏性孔隙流体的作用,慢纵波和慢横波的反透射系数受入射角、频率及流体黏性的影响都很大.

     

On the question of the relation between the fields of pressure and motion in low latitudes

Резюме В настоящей работе приводится теоретическое рассмотрение соотношения между полем давления и полем движения вблизи экватора. Было показано, что ветер в этих областях может дуть вдоль изогипс лишь в стационарных циклональных образованиях.

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Address: Praha II, Ke Karlovu 3.     

Non-local memory effects of the electromotive force by fluid motion with helicity and two-dimensional periodicity

In mean-field dynamo theory, the electromotive force term 〈u′ × B′〉 due to small-scale fields connects the small-scale magnetic field with the large-scale field. This term is usually approximated as the α-effect, assumed to be instantaneous in time and local in space. However, the approximation is valid only when the magnetic Reynolds number Rm is much less than unity, and is inappropriate when Rm ? 1, which is the condition satisfied in the Earth's core or solar convection zone. We introduce a function φ _qr as a non-local and non-instantaneous generalization of the usual α-effect and examine its behaviour as a function of Rm in the range 1/64 ≤ Rm ≤ 10 for a kinematic dynamo model. We use the flow of G.O. Roberts 1972 Roberts, GO. 1972. Dynamo action of fluid motions with two-dimensional periodicity. Phil. Trans. Roy. Soc. London Ser. A, 271: 411–454. [Crossref], [Web of Science ®] , [Google Scholar] (Phil, Trans. Roy. Soc. London Ser. A, 1972, 271, 411–454), which is steady and has non-zero helicities and two-dimensional periodicity. As a result, we identify three regions in Rm space according to the behaviour of the function φ _qr : (i) Rm ? 1/4, where the function φ _qr is local and instantaneous and can be approximated by the traditional α and β effects, (ii) 1/4 ? Rm ? 4, where the deviation from the traditional α and β effects increases and non-localness and non-instantaneousness increase, and (iii) Rm ? 4, where boundary layers develop fully and non-localness and non-instantaneousness are prominent. We show that the non-local memory effect for Rm ? 4 strongly affects the dynamo action and explains an observed augmentation of the growth rate in the dispersion relation. The results imply that the non-local memory effect of the electromotive force should be important in the geodynamo or the solar dynamo.     

SH波入射时半圆形凸起与凹陷地形的地震动

研究了弹性半空间中半圆形凸起与凹陷相连地形对SH波的散射问题。将整个求解区域分割为2部分,在其中分别构造满足边界条件的位移解,通过移动坐标使之满足“公共边界”以及半圆形凹陷表面上的边界条件,从而建立起求解该问题的无穷代数方程组。最后,给出了地表位移幅值的数值结果以及凸起地形顶点和凹陷地形最低点处位移幅值的反应谱并进行了讨论。     

The relation between geomagnetic pulsations and an increase in the fluxes of geosynchronous relativistic electrons during geomagnetic storms

The dynamics of the Pc5 and Pi1 pulsation characteristics and relativistic electron fluxes at geostationary orbit were comparatively analyzed for three nine-day intervals, including quiet periods and periods of geomagnetic storms. It was shown that relativistic electron fluxes increase considerably when the power of global Pc5 pulsations and the index of midlatitude irregular Pi1 pulsations increase simultaneously. The correlation between the characteristics of Pi1 and Pc5 geomagnetic pulsations and the level of the relativistic electron flux at geostationary orbit during the magnetic storm recovery phase were studied. It was shown that the correlation coefficient of the relativistic electron maximal fluxes during the magnetic storm recovery phase with the parameter of midlatitude Pi1 pulsations is slightly higher than such a correlation coefficient with the solar wind velocity.