Earth mantle conductivity beneath the Ukrainian territory

Studia Geophysica et Geodaetica - Magnetovariation methods, which are applicable to study the mantle conductivity, require long lasting registration of natural magnetic field variations. Such data...     

The amplitude ratioPcP/P and the core-mantle boundary

Summary Using the Haskell matrix formulation, theoretical reflection coefficient curves have been calculated for a multi-layered core-mantle boundary for comparison with observational data. Two cases are considered, first when the shear velocity in the core is equal to zero and second when the core has a finite rigidity. If the velocity contrast is large between the imbedded layer and the mantle, the reflection coefficient curves for the multi-layered medium are irregular in shape as compared to those for two half-spaces, representing the core and the mantle, respectively. The reflection coefficient curves show an oscillatory character if the imbedded layer is thick and has a high velocity contrast.The observational data consist of short-period vertical-component seismograph records ofP andPcP from nuclear explosions in the Aleutian chain, Nevada, Novaya Zemlya, Kazakh and Sahara. Attenuation and geometrical spreading are taken into consideration. Four different models for the quality factorQ are applied to the observational data. The data are found to be much affected by theQ-model used for the corrections.Based on proposedQ-values, a model for the core-mantle boundary is found, characterized by two low-velocity layers at the bottom of the mantle. The thicknesses are 16.10 km (outer layer) and 19.96 km (inner layer), the compressional wave velocities 12.17 km/sec and 10.94 km/sec and the shear wave velocities are 6.29 km/sec and 5.33 km/sec, respectively. A better fit to this model is found when in addition the shear velocity in the outer core is 2.20 km/sec and the density ratio at the core-mantle boundary is 1.07. In other words, the observations favour a layer of finite rigidity in the outer core rather than a fluid one.     

On the theory of core-mantle coupling

This article commences by surveying the basic dynamics of Earth's core and their impact on various mechanisms of core-mantle coupling. The physics governing core convection and magnetic field production in the Earth is briefly reviewed. Convection is taken to be a small perturbation from a hydrostatic, “adiabatic reference state” of uniform composition and specific entropy, in which thermodynamic variables depend only on the gravitational potential. The four principal processes coupling the rotation of the mantle to the rotations of the inner and outer cores are analyzed: viscosity, topography, gravity and magnetic field. The gravitational potential of density anomalies in the mantle and inner core creates density differences in the fluid core that greatly exceed those associated with convection. The implications of the resulting “adiabatic torques” on topographic and gravitational coupling are considered. A new approach to the gravitational interaction between the inner core and the mantle, and the associated gravitational oscillations, is presented. Magnetic coupling through torsional waves is studied. A fresh analysis of torsional waves identifies new terms previously overlooked. The magnetic boundary layer on the core-mantle boundary is studied and shown to attenuate the waves significantly. It also hosts relatively high speed flows that influence the angular momentum budget. The magnetic coupling of the solid core to fluid in the tangent cylinder is investigated. Four technical appendices derive, and present solutions of, the torsional wave equation, analyze the associated magnetic boundary layers at the top and bottom of the fluid core, and consider gravitational and magnetic coupling from a more general standpoint. A fifth presents a simple model of the adiabatic reference state.     

The effect of a rough core-mantle boundary on PKKP

Scattering by a slightly-rough core-mantle boundary (CMB) with small-scale radial variations of up to a few hundred metres, has been an attractive (though non-unique) interpretation of at least part of the precursors to PKIKP. Here it is shown that a slightly-rough CMB has an observable effect on PKKP as well, if the signal-to-noise ratio is sufficiently high. The effect may be observed as precursive arrivals and is due to back-scattering

at CMB. This work was prompted by observations by Chang and Cleary at LASA of “PKKP” and precursors from the Novaya Zemlya explosions. NORSAR data from several source regions are presented here; small-scale radial variations of 100–200 metres are inferred from these data, although in some regions the CMB appears to be much smoother. On the other hand, the LASA data are anomalous and suggest much larger topography in the sampled region of the CMB. Both large- and small-scale topography must be dynamically produced, if current estimates of the viscosity of the lower mantle (～10²² Poise) are correct.     

Axial poloidal electromagnetic core-mantle coupling torque: A re-examination for different conductivity and satellite supported geomagnetic field models

We investigate the temporal behaviour of the axial component of the electromagnetic core-mantle coupling torque that is associated with the poloidal part of the geomagnetic field observable at the Earth surface. For its computation, we use different models of the geomagnetic field, expanded into spherical harmonics (Wardinski and Holme, 2006; Sabaka et al., 2004), and the mantle conductivity. The geomagnetic field, which we have to know at the core-mantle boundary for the associated computations, will be inferred from the field at the Earth surface by the non-harmonic field continuation through a conducting mantle shell. The aims of this investigation are (i) to check how sensitive is the computation of the torque with respect to the different geomagnetic field models, (ii) to check its dependence on the spherical harmonic degree n, and (iii) to determine the difference between the mechanical torque derived from the observed length-of-day variations (atmospheric influence subtracted) and the poloidal electromagnetic torque in dependence on the assumed conductivity. To use the non-harmonic field continuation for the torque calculation and to obtain an insight into the influence of the different geomagnetic field models on the EM torques are the major aspects of this paper. grm@gfz-potsdam.de     

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.     

On the topographic coupling at the core-mantle interface

The mean tangential stresses at a corrugated interface between a solid, electrically insulating mantle and a liquid core of magnetic diffusivity λ are calculated for uniform rotation of both mantle and core at an angular velocity Ω in the presence of a corotating magnetic field B. The core and mantle are assumed to extend indefinitely in the horizontal plane. The interface has the form z = η(x, y), where z is the upward vertical distance and x, y are the zonal and latitudinal distances respectively. The function η(x, y) has a planetary horizontal length scale (i.e. of the order of the radius of the Earth) and small amplitude and vertical gradient. The liquid core flows with uniform mean zonal velocity U₀ relative to the mantle. Ω and B possess vertical and horizontal components.The vertical (poloidal) component B_p is uniform and has a value of 5 G while the horizontal (toroidal) field B_T = B_pαz, where α is a constant. When |α| ? 1, the mean horizontal stresses are found to have the same order of magnitude (10^?2 N m^?2) as those inferred from variations in the decade fluctuations in the length of the day, although the exact numerical values depend on the orientation of Ω as well as on the wavenumbers in the zonal and latitudinal directions.The influence of the steepness (as measured by α) of the toroidal field on the stresses is investigated to examine whether the constraint that the mean horizontal stresses at the core-mantle interface be of the order of 10^?2 N m^?2 might provide a selection mechanism for the behaviour of the toroidal field in the upper reaches of the outer core of the Earth. The results indicate that the restriction imposed on α is related to the value assigned to the toroidal field deep into the core. For example, if |α| ? 1 then the tangential stresses are of the right order of magnitude only if the toroidal field is comparable with the poloidal field deep in the core.     

Amplitudes of long-period PcP and the core-mantle boundary

The amplitudes of the core reflection PcP are sensitive to the wave velocities and densities in the neighborhood of the core-mantle boundary (CMB). We study the amplitude ratio of the long-period phases PcP and P from two South American deep-focus earthquakes with favorable fault-plane solution, depth and magnitude, as recorded by WWNSS and CSN stations in North America.Comparison is made with long-period PcP/P amplitude ratios, derived from theoretical seismograms for a variety of CMB models. Models from previous studies, which were mainly derived from short-period PcP observations and which are characterized by discrete layers above the CMB, are almost all inconsistent with the long-period data. The data also discriminate against low nonzero S velocities below the CMB. Simple first-order-discontinuity models of the CMB, for instance according to the Jeffreys-Bullen earth model or according to recent models based mainly on free oscillations, explain the data reasonably well.Model improvements are attempted by varying the P-velocity gradient above the CMB. The best amplitude fit is obtained for a rather strong decrease in P velocity with depth in this zone which, however, gives no acceptable traveltime fit for PcP. The scatter in body-wave amplitudes is considerable even for long-period waves and may prevent the correct assessment of that part of the amplitude variation of a phase with distance that is due to the variation of velocities and densities with depth alone.     

Hydromagnetic spin-up under conditions of the earth's core-mantle boundary

Summary The disturbances of the velocity and magnetic fields close to the Earth's core-mantle boundary, caused by sudden irregular changes in the Earth's rotation, are investigated. The problem leads to the investigation of the structure of the Ekman-Hartman hydromagnetic boundary layer, the magnetic diffusive region and the currentless region. Precise Laplacean inversions of the images of all disturbances in the Earth's core-mantle system are obtained for the limiting case of a zero magnetic Prandtl number, =0. The disturbance of the velocity in the direction of the axis of rotation (Ekman suction) in the currentless region has the nature of inertial oscillations with a frequency of 2. Additional disturbances (with respect to the case of =0) of the velocity in the azimuthal and radial directions, particularly for the EHL and MDR region, are determined for the case when 0< « 1. The disturbance in the velocity again has the character of inertial oscillations with the frequency 2, being exponentially damped in EHL asexp (–2²t) and in MDR asexp (–²t).     

On the formation of a stably stratified layer near the core-mantle boundary

Within the framework of a model of liquid immiscibility in the outer core, we calculate a stably stratified layer about 11 km thick near the core-mantle boundary and discuss its reflection and scattering properties for seismic waves.     

True polar wander in the Earth system

True polar wander(TPW), or planetary reorientation, is the rotation of solid Earth(crust and mantle) about the liquid outer core in order to stabilize Earth’s rotation due to mass redistribution. Although TPW is well-documented on Earth presently with satellites and for multiple planets and moons in the Solar System, the prevalence of TPW in Earth history remains contentious. Despite a history of controversy, both the physical plausibility of TPWon Earth and an empirical basis for it are now und...     

地球系统科学综述

首先从人类面临全球性的重大问题、地球系统的全球化和地球系统科学的关系与传统地球科学三个方面介绍了地球系统科学提出的背景,阐述了地球系统科学国内外研究现状．然后,详细介绍了地球系统科学的概念与研究方法,主要包括研究思路、基本概念、地球系统过程、全球——区域信息获取、海量信息处理和分析及地球系统模型等．第三,构建了地球系统科学理论基础．主要包括：地球系统的连续动态系统、离散动态系统、地球系统的随机性、地球系统的自组织和地球系统的简单巨系统与复杂巨系统,重点介绍了地球系统科学子系统与各圈层相互作用的动力学模型与效应．第四,概述了地球系统的数字表达一数字地球和地球系统科学是可持续发展战略科学基础．最后,简述了中国开展地球系统科学研究的方向和面临的主要科学问题。     

The origin of the Earth

It is not possible to consider the formation of the Earth in isolation without reference to the formation of the rest of the solar system. A brief account is given of the current scientific consensus on that topic, explaining the origin of an inner solar system rocky planet depleted in most of the gaseous and icy components of the original solar nebula. Volatile element depletion occurred at a very early stage in the nebula, and was probably responsible for the formation of Jupiter before that of the inner planets. The Earth formed subsequently from accumulation of a hierarchy of planetesimals. Evidence of these remains in the ancient cratered surfaces and the obliquities (tilts) of most planets. Earth melting occurred during this process, as well as from the giant Moon-forming impact. The strange density and chemistry of the Moon are consistent with an origin from the mantle of the impactor. Core-mantle separation on the Earth was coeval with accretion. Some speculations are given on the origin of the hydrosphere.     

Influence of the topography of the surface of the Earth on vertical sounding of the temperature profile

Atmospheric temperature and humidity fields as well as information on other meteorological parameters are nowadays retrieved from radiance measurements recorded by operational meteorological satellites. Up to now, the inversion procedures used only take into account crude information on the topography of the Earth’s surface. However, the applied radiative transfer codes have to consider the Earth’s surface as the lower boundary of the atmospheric model and, therefore, need a more precise mean elevation and a classification of the roughness of the Earth’s surface. The influence of the topography of the Earth surface on retrieved temperature profiles is studied by using a physico-statistical inversion method. An objective analysis is made of the more precise mean elevation and derivation of roughness parameters using a new high-resolution digital elevation model (DEM) with a resolution of 500 m×500 m. By means of a geomorphological process and a newly developed topography rejection test, areas with a high surface roughness are localized and singled out. The influence of topography on the retrieved temperature profiles is illustrated by case studies. Changes are found predominantly in areas with a high variation of topography. Using the new high-resolution DEM and the topography rejection test, the geographical position of the calculated temperature profiles tends to be shifted towards areas with a small vertical variation of topography. The mean elevation determined by the new elevation model better characterizes the area observed. Hence, the temperature profiles can be calculated down to lower atmospheric levels. Furthermore, a guess profile better describing the atmospheric situation is selected by the more precise elevation. In addition, the temperature profiles obtained near the coast are improved considerably by the more precise determination of the surface property ‘sea’ and ‘land,’ respectively. Integration of an independent physical information such as topography leads, on average, to a slight improvement of the results of the physico-statistical inversion procedure. In some cases, however, significant improvements have been achieved regarding the desired accuracy of temperature profiles of the order of 1 K. In future, the spatial resolution of new high-resolution sounding instrumentation on the next generation of operational meteorological satellites will be increased. To exploit the resolving power of this new instrumentation, the different variation of the topography of the Earth surface, especially in regions with a high variation of topography, can be taken into account more precisely by using a high-resolution DEM.     

Z-model of the nearly symmetric hydromagnetic dynamo with electromagnetic core-mantle coupling

Summary The present paper deals with theZ-model of the nearly symmetric hydromagnetic dynamo as a generation mechanism of the Earth's magnetic field. TheZ-model of Braginsky [2] was solved for viscous core-mantle coupling [3]. It is shown that a similarZ-model can also be constructed for electromagnetic core-mantle coupling, or for both effects combined. A new part of the azimuthal velocity appears in the equations, but the character of the boundary layer is not changed too much. No numerical solution is presented.

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The electrical conductivity of the Moon

Investigations of the lunar electrical conductivity were described in excellent reviews by Sonett (1974) and Dyalet al. (1976). In this paper we will try to consider some new aspects of this problem in comparison with the Earth's data.