Fundamental geodetic parameters of the earth's figure and the structure of the earth's gravity field derived from satellite data

Summary Using the geocentric constant GM=398 601.3 × 10 ⁹ m ³s ^–2 , the known value of the angular velocity of the Earth's rotation , Stokes' constants J _n ^(k) and S _n ^(k) upto n=21 (zonal), n=16 (tesseral and sectorial) [2], the geocentric co-ordinates and heights above sea-level of SAO satellite stations [2], the following will be derived: the potential on the geoid W_o, the scale factor for lengths R_o=GM/W_o, the radius-vector of the surface W=W_o, the parameters of the best-fitting Earth tri-axial ellipsoid, and the components of the deflections of the vertical with respect to the geocentric rotational IAG ellipsoid (Lucerne 1967), as well as to the best-fitting geocentric tri-axial ellipsoid. Some of the differences in the structure of the gravity field over the Northern and Southern Hemispheres will be given, and the mean values of gravity over the equatorial zone, determined from the dynamics of satellite orbits, on the one hand, and from terrestrial gravity data, on the other, will be compared.Presented at the Fifteenth IUGG General Assembly, Moscow, July 30 — August 14, 1971.     

Satellite orbit computations using gravity anomalies

Summary A typical geodetic satellite orbit has been computed by numerical integration for a period of thirty hours. The gravitational potential of a standard orbit was represented by the SAO 1969 Standard Earth potential coefficients taken to degree 18. Other orbits were generated using the generalized Stokes' equations and the coating method applied to gravity anomalies and surface densities, in 5°, 10°, 15° and 30° equal-area blocks, derived from the given potential coefficients. The differences between these orbits yield the position differences to be expected when representing the potential field by using gravity data instead of potential coefficients. Using 10°, 15°, and 30° blocks and the generalized Stokes' equations, the position error at the end of thirty hours was 89 meters, 224 meters, and 2060 meters respectively. This error is primarily due to the integration error in computing the gravitational field by summation over a finite number of areas.     

Les formes différentielles extérieures dans la géodésie I: Courbure de Gauss

1) , 2) 3) .     

Comparison of satellite and terrestrial gravity data

Summary The integral mean values of gravity on the surface W=W ₀ , obtained from satellite observations with the use of harmonic coefficients[3, 7] and from terrestrial gravity measurements[12], are compared. The squares and products of the harmonic coefficients were neglected, with the exception of [J ₂ ⁽⁰⁾ ] ² , which was taken into account. The Potsdam correction and the geocentric constant are being discussed. The paper ties up with[13–15] and the symbols used are the same. The given problem was treated, e.g., in[2, 4, 6, 8–10]; in the present paper the values of gravity are compared directly.     

Coexisting clinopyroxene,garnet and amphibole from an “eclogite”, Kakanui,New Zealand

Analyses of major and rare earth elements are presented for co-existing garnet, clinopyroxene, and amphibole from a Kakanui eclogite.New and previously published analyses of garnets suggest a gradual increase of Fe and decrease of Mg from xenocrysts through garnet pyroxene eclogitic rocks to amphibole-rich eclogitic rocks. Clinopyroxenes show a parallel increase in Fe/Mg ratio and an increase in Jadeite component and decrease in Tschermak's component. These data indicate crystallization of garnet and clinopyroxene from an alkali-rich undersaturated magma and are consistent with the concept of eclogite fractionation, but rare earth data allow severe constraints to be placed on this process. The eclogites are considered to be deep-seated crystallization products of nephelinite, but eclogite fractionation is small and cannot account for the association of alkali basalt, basanite and nephelinite.     

The differences in structure of the gravity field and the figure of the earth in the northern and southern hemispheres

Summary It was shown in [5] that the flattening of parallel sections of the geoid (ϕ=const.) differs in the northern and southern hemispheres. This leads up to the idea of studying further the size and shape of the Earth and the structure of the gravity field separately for the northern and for the southern hemispheres. In this paper attention is devoted especially to the mean values of the radius-vectors, to the best fitting ellipsoid parameters and to the mean values of gravity for the whole hemispheres, on the one hand, and for their ϕ=const. sections, on the other. The symbols used are the same as in [5,6]. Address: Politickych vězňů 12, Praha 1-Nové Město.     

On the determination of propagation paths of mid-latitude whistlers for purposes of estimating the magnetospheric electron density

Zusammenfassung Mit dem Ziel das Profil der magnetosph?rischen Elektronendichte auf Grund einj?hriger Beobachtungsreihe der Station Panská Ves zu bestimmen, wurden M?glichkeiten von Ermittlung des tats?chlichen Ausbreitungsweges von Whistlern untersucht, die in den mittleren Breiten w?hrend des Minimums der Sonnenaktivit?t beobachtet wurden. Da die beobachteten Whistler keine “nose frequency” aufweisen, gründete sich die Bestimmung des Ausbreitungsweges auf Messungen der Dispersion auf 10 und 4 kHz, ?hnlich wie bei der Extrapolationsmethode der “nose frequency” [4]. Die gewonnenen Resultate zeigen, dass es m?glich ist, die Ausbreitungswege einer grossen Anzahl von Ein-Sprung-Whistler mit genügender Genauigkeit zu bestimmen. Alle auf diese Weise ermittelten Ausbreitungswege fallen in den BreitenbereichФ ₀=38°−56°, was der bekannten Tatsache entspricht, dass man verwendbare Whistler-Komponenten bis zu einer Entfernung von 1000 km vom Endpunkt ihres Ausbreitungsweges beobachten kann. Die analysierten Whistler entsprechen den unter Voraussetzung einer konstanten Elektronendichte in der H?he der Basis der Magnetosph?re (700 km) berechneten theoretischen Modellen. Unter diesen Bedingungen zeigte es sich als m?glich, alle analysierten Whistler zur Bestimmung des Profils der magnetosph?rischen Elektronendichte zu gebrauchen. Trotz aller Vereinfachungen, die bei der Konstruierung von Modellen angewendet wurden, ist es also m?glich, vernünftige Werte der Elektronendichte für den Breitenbereich L=1,5–3 unter Anwendung von Whistler-Beobachtungen aus einer einzigen Station in mittleren Breiten zu gewinnen.

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Address: Bočni II, Praha 4-Spořilov.     

Large-scale motions of the tropics in observations and theory

Recent observations of the tropical and subtropical atmosphere are interpreted in terms of scaling arguments and wave propagation theory advanced byCharney (1963, 1969).Charney’s idealizations describe the tropical atmosphere in terms of large regions of quasi-nondivergent flow containing small subdomains of heavy convection and divergence, and place emphasis upon the quasi-rotational regions. FGGE (First GARP Global Experiment) observations suggest that strongly divergent local tropical circulations are forced by latent heating and produce important direct modifications of the total wind field. We describe the extent to which the resulting field consists of divergent and rotational components in different analyses of the FGGE data, and present independent supporting documentation of the results in terms of heating estimates and rainfall observations. Local tropical heating rates on the order of 10°C/day are apparently due to latent heat release associated with precipitation rates as large as 6 cm/day during extended periods. The large contribution of the divergent wind is generally underestimated in models that do not retain such energetic local forcings, and this deficiency may be related to general underestimation of tropical-extratropical connections of many linear models. Such connections are commonly cited in relation to El Niño events, the Southern Hemisphere stationary-wave pattern, and in FGGE studies, but are not well simulated in most linear theories. It is not yet clear whether this is an inherent limitation of linear models, or whether the linear models have not yet explored all the potentially relevant ambient states. We explore the latter possibility by construction of a basic state that allows reasonable latitudinal evolution of the wave field. This basic state has zero absolute vorticity gradient throughout the tropics, and deviations linearized about this state are dynamically analogous to a “local” Hadley cell. To the extent that it is appropriate to regard the results in terms of wave propagation, our analysis suggests a prominent role for gravity-inertia waves in the tropics and for the extratropical connections. The relevance of gravity modes to observations and the theoretical explanation of the flat vorticity field remain to be established.     

Ocean, continents and orogens

In this paper, the processes related to subduction and mountain building are discussed, and some new models and notions are proposed.At all known epochs, the Earth's surface comprised essentially migrating plates and large belts (of the order of 10,000 × 2000 km) where the lithosphere is mobilised, so that subductions and crustal resorption occur in complex structural patterns. Through time, these orogens start as island arcs and evolve into folded ranges.The formation and location of island-arc belts is shown to be related to the obliquity between rifts and continental margins i.e. to lateral relative movements of plates: torsion couples are developed bringing arcs to bulge through the inducted arc mechanism. This accounts for tensions prevailing in the back-arc basin while compressive stresses accumulate as vertical deformations in the arc-trench or uplift—subsidence couple. When the rupture limit is reached, a tangential tectonic phase occurs.It is suggested that the energy output (heat flow) varies with the pressure exerted by the top (elastic) lithosphere upon the underlying mantle. A compensation tends to be established between the inner flow and tectonic stress, as the latter brings about pressure variations through uplift-subsidence couples. These may therefore be related to the generation of paired metamorphic belts.The evolution from island arcs to completed folded ranges is briefly described, with special attention being paid to ophiolitic and crystalline basement nappes, as well as to strike-slip faults, which are the final expression of lateral relative movements.