Best-fitting tri-axial earth ellipsoid parameters derived from satellite observations

Résumé De l'ensemble des coefficients harmoniques du développement du géopotentiel [3, 6, 7], calculé à partir des variations des éléments orbitaux des satellites, on a calculé les paramètres de l'ellipso?de terrestre triaxial, représentant la surface du géo?de. La solution fut effectuée par méthode analytique sous la condition du minimum de l'intégrale du carré de l'écart du rayon vecteur du géo?de et de l'ellipso?de, de même que par calcul numérique à partir des valeurs discrètes 10°×10°.

---

---

Address: Politickych vězňů 12, Praha 1-Nové Město.     

水准椭球密度问题研究

本文总结了作者等最近十年来对地球重力学"水准椭球密度问题"进行研究的初步结果,首次提出了"密度水准椭球"概念,给出了从"匀质椭球"、"参数椭球"、"纬向密度椭球"、"似水准椭球"到"密度水准椭球"的研究路线,并对该问题的研究前景进行了讨论.     

Directions of axes of the Earth's ellipsoid of inertia derived from satellite orbit dynamics

Studia Geophysica et Geodaetica - Обсуж¶rt;aеmся 3 возможносmь...     

Physical properties of the Earth's core

Calculations of the compression and temperature gradient of the core are facilitated by the use of the thermodynamic Grüneisen ratio, =3Ks/C _P . A pressure-dependent factor in is found to have the same numerical value for the core as for laboratory iron, justifying the use of a constant value for (1.6) in core calculations. The density of the outer core is satisfied by the assumption that it contains about 15% of light elements, particularly sulphur, whereas the inner core is probably ironnickel with very little lighter component. The presence of sulphur in the outer core reduces its liquidus at least 600° below pure iron, so that the adiabatic gradient does not intersect the liquidus, as Higgins and Kennedy have shown would occur in a pure iron core. The inner core is probably close to its melting point, 4700 K, and the adiabatic temperature gradient of the outer is calculated with this as a fixed point, giving 3380 K at the core-mantle boundary. The estimated electrical resistivity of the outer core, 3×10^–6 m, corresponds to a thermal conductivity of 28 W·m^–1·deg^–1, which, with the adiabatic core gradient gives a minimum of 3.9×10¹² W of heat conduction to the mantle. The only plausible source of this much heat is the radioactive decay of potassium in the core. As pointed out by Goles, Lewis, and Hall and Murthy, the presence of potassium becomes geochemically probable once sulphur is admitted as a core constituent. Thus it appears that the recognition of sulphur in the core resolves the two major difficulties which we have faced in attempting to understand the core.List of Symbols a equilibrium atomic spacing at zero pressure, also a constant - A surface area of core - b a constant - c a constant - C _V ,C _P specific heat at constant volume, constant pressure - D dimension of core (or core eddy) - E(r) atomic interaction energy - E energy due to atomic displacement from equilibrium - lattice energy of material - f ₁,f ₂ structure-dependent constants - F(P) pressure dependent factor in Grüneisen's ratio - g gravitational acceleration; also a constant (Equation (13)) - H latent heat of solidification - I integral (Equation (23)) - k Boltzmann's constant - K incompressibility (bulk modulus) - K _T ,K _S isothermal, adiabatic incompressibilities - N number of atoms in a volume of material - P pressure - dQ/dt core to mantle heat flux - r atomic spacing - r _e equilibrium value ofr under pressure - R _m magnetic Reynolds number - T temperature - T _c critical temperature - T _R reduced temperature (Equation (39)) - U specific internal energy of a material - v velocity of internal core motion - V volume - 3 volume expansion coefficient - compressibility - thermodynamic Grüneisen ratio (Equation(2)) - magnetic diffusivity - thermal conductivity - _e electronic contribution to - ₀ permeability of free space - density - _e electrical resistivity - R reduced conductivity,eM/e     

New views of the Earth's interior

The Earth beneath our feet is a complex place. James Wookey reports on a meeting that took a broad multidisciplinary approach to understanding its composition, structure and dynamics.     

Increase of the Earth's mean magnetization

Summary All the investigations carried out up to date regarding the magnetic state of the Earth have led unanimously to the conclusion that during the last one hundred years the average mean magnetization of our planet has been diminishing at the rate of 1/1.500 annually. In the above-mentioned study a comparison is made between the present magnetic state of the Earth and that of earlier periods, and it is shown that the absolute value of the mean magnetization of the globe has experienced a notable increase since about the year 1930. Finally, an analysis is made of the geographic distribution shown by the signs and gradients of the secular variation offered by geomagnetic intensity.     

地球内核处于熔融状态

地球的磁场是由液态铁核形成的地磁发电机所产生的,这种液态铁核在上覆层地幔岩石的冷却下导致对流.地核由最里面向外冷却,生成固态的内核和释放轻元素.这些驱动着组分上的对流[1-3].地幔从地核以一定的速率吸收了热量,且吸热速率在空间上存在着很大的横向变化和差异[4].本文利用地磁发电机模拟显示这种横向差异会传递至内核边界,从而足以导致热量流入内核.如果地球内部确实是这样,将导致局部的熔融作用.熔融释放密度较重的液体形成变化的组分层,这一点可由内核上边界向上150 km处的地震波速度异常来解释[5-7].     

Lame surfaces as a generalisation of the triaxial ellipsoid

In modern geodesy the triaxial ellipsoid as a generalisation of the ellipsoid of revolution has a significant position in studying the figure of the Earth. Lame surfaces represent a generalisation of the triaxial ellipsoid. The following paragraphs are devoted to curvatures of the Lame surfaces.     

Effects of the Sun on the Earth's environment

Solar disturbances are observed to have significant effects in near-Earth space. Over the past half-century of observation, a relatively clear picture has developed of how and why the typical solar wind — as well as the most extreme solar events — drive geospace responses. It is clear that magnetospheric substorms, geomagnetic storms (both recurrent and aperiodic events), and even certain atmospheric chemical changes have their origins in the solar–terrestrial coupling arena. High-speed solar wind streams and fast coronal mass ejections (CMEs) can often have strong interplanetary shock waves and southward magnetic fields which can initiate strong storm responses. We demonstrate in this review that available modern space-observing platforms and ground facilities allow us to trace drivers from the Sun to the Earth's atmosphere. This allows us to assess quantitatively the energy transport that occurs throughout the Sun–Earth system during both typical and extreme conditions. Hence, we are continuously improving our understanding of “space weather” and its effects on human society.     

Shortwave forcing of the Earth's climate: Modern and historical variations in the Sun's irradiance and the Earth's reflectance

Changes in the Earth's radiation budget are driven by changes in the balance between the thermal emission from the top of the atmosphere and the net sunlight absorbed. The shortwave radiation entering the climate system depends on the Sun's irradiance and the Earth's reflectance. Often, studies replace the net sunlight by proxy measures of solar irradiance, which is an oversimplification used in efforts to probe the Sun's role in past climate change. With new helioseismic data and new measures of the Earth's reflectance, we can usefully separate and constrain the relative roles of the net sunlight's two components, while probing the degree of their linkage. First, this is possible because helioseismic data provide the most precise measure ever of the solar cycle, which ultimately yields more profound physical limits on past irradiance variations. Since irradiance variations are apparently minimal, changes in the Earth's climate that seem to be associated with changes in the level of solar activity—the Maunder Minimum and the Little Ice age for example—would then seem to be due to terrestrial responses to more subtle changes in the Sun's spectrum of radiative output. This leads naturally to a linkage with terrestrial reflectance, the second component of the net sunlight, as the carrier of the terrestrial amplification of the Sun's varying output. Much progress has also been made in determining this difficult to measure, and not-so-well-known quantity. We review our understanding of these two closely linked, fundamental drivers of climate.     

Energy regimes in the Earth's magnetosphere

Summary The dynamics of the main processes of energy accumulation and dissipation in the Earth's magnetosphere at various geomagnetic disturbance levels is examined. The results of the relevant calculations are tabulated. The relationships between the energy parameters of the solar wind and the Earth's magnetosphere are analyzed. Some conclusions concerning the field-aligned currents in polar caps, the Joule dissipation of energy and the energy injection into the ring current, the energy releases in the upper ionosphere, etc., are drawn.

---

ama ¶rt;uaua n anu u ¶rt;uunauu uu aum u nu au aum mu. mam uu n¶rt;ma maua. auum au ¶rt; muuu aamumuau ma u aum u. u¶rt;m m au n¶rt; ma n an, uu ¶rt; ¶rt;uunauu, uu uuu m, uu, ¶rt; u, u m. ¶rt;.

     

Local turbulence in the Earth's core

Abstract

It is shown that in the Earth's core, where the geodynamo is at work (and is supplied with energy by the prevailing unstable density stratification), a buoyancy instability of a local character exists which is highly supercritical. This instability results in fully developed turbulence dominated by small scale vortices. The influence of the Earth's rotation and of the magnetic field produced by the geodynamo makes this small scale turbulence highly anisotropic. A qualitative picture of this local anisotropic turbulence is devised and the main parameters characterizing it are estimated. Expressions for the turbulent diffusivity are developed and discussed.     

Molecular refraction in the Earth's mantle

The Drude law (molecular refraction) for the temperature radiation in a monoatomic model of the Earth's mantle is derived. The considerations are based on the Lorentz electron theory of solids. The characteristic frequency (or eigenfrequency) of independent electron oscillators (in energy units, ) is identified with the band gapE _G of a solid. The only assumption is that solid material related to the Earth's mantle has the mean atomic weight A21 g/mole, and its energy gap (E _G) is about 9 eV. In this case the value of molecular refraction (in cm³/g) is (n ²–1)/=0.5160.52, where andn are the density and the refractive index at wavelength _D=0.5893 m (sodium light), respectively. The average molecular refraction of important silicate and oxide minerals with A21, obtained byAnderson andSchreiber (1965) from laboratory data, is , where denotes the mean arithmetic value calculated from three principal refractive indices of crystal. For the rock-forming minerals with 19A<24 g/mole the new relation was found byAnderson (1975).     

Thermal regime of the Earth's outer core

Summary First an introduction into the dynamo problem and the core paradox is given. A novel theory of the volume dependence of Grüneisen's parameter is used for calculating the adiabatic temperatures on the assumption that the melting temperature of the material is reached at the boundary between the inner and outer cores of the Earth (IOB). On this condition, thermal convectionthroughout the outer core is impossible according to the melting-point curves ofKennedy andHiggins (1973) andLiu (1975), whereas it is permitted by that ofLeppaluoto (1972),Boschi (1975), andStacey (1977). Various possibilities of solving the core paradox are described.Mitt. d. ZIPE Nr. 682.     

Rock magnetism and the Earth's palaeopoles

Summary On the assumption of a constant earth radius the spherical-trigonometric determination of former pole positions depends on the position of the North Pole of today. On the basis of an expanding earth, the determination of the palaeopoles should not be attempted on the present globe. There should rather be used a pole position on a model globe with a reckoning pole which is situated along the present northern direction of the measuring origin and spaced therefrom by its present pole distance. In that way Palaeozoic pole positions formerly determined in the Mid-Pacific shift to northeastern Siberia.

---

Zusammenfassung Bei der sphärisch-trigonometrischen Berechnung früherer Pollagen unter Voraussetzung eines konstanten Erddurchmessers spielt die Lage des heutigen Nordpols eine wichtige Rolle. Bei Voraussetzung einer expandierenden Erde darf jedoch die Bestimmung der Paläopole nicht am heutigen Globus erfolgen. Vielmehr ist an einem Modellglobus ein Berechnungspol zu verwenden, der auf der heutigen Nordrichtung des Meßorts in seiner heutigen Poldistanz von ihm entfernt liegt. Auf diese Weise ergeben sich für das Paläozoikum Pollagen in Nordostsibirien an Stelle von Pollagen mitten im Pazifik.