Deciphering an Archean mantle plume: Abitibi greenstone belt,Canada

The 2724–2722 Ma Stoughton-Roquemaure Group (SRG) of the Abitibi greenstone belt (the Archean Superior Province, Canada) is a ≤ 2 km thick komatiite–basalt succession intermittently exposed for about 50 km along strike. The ultramafic and mafic rocks occur mainly as pillowed, brecciated, and massive flows with well preserved spinifex textures in the komatiites. Volcanological, comparative stratigraphic and geochemical studies of the group along a volcanic marker horizon at the base of the succession allow the assessment of magma emplacement processes and mantle source rocks. Major feeder channels, secondary distributary tubes surrounded by pillowed flows with minor breccias and hyaloclastites display facies architecture of small volume flow fields (1–2 km³). Within the SRG, Al-depleted (ADK; Barberton-type) and Al-undepleted (AUK; Munro-type) komatiitic lavas are intercalated with tholeiitic basalt flows at a m- to 10s of m scale. Basalts and komatiites are inferred to be mantle plume-related; both rock types form two groups with characteristics of ADK and AUK including Al₂O₃/TiO₂ ~ 9–12 for ADK versus 17–22 for AUK, as well as (Gd/Yb)_n with > 1.3 versus ~ 1, respectively. The interdigitation of compositionally different flow units, limited extent of SRG volcanic rocks and facies architecture with the prevalence of small volume flows argue for a relatively small, heterogeneous mantle plume during the incipient stage of the evolution of the Archean Abitibi belt. Assuming that the scale of heterogeneities is comparable to the field expression of compositional changes and stratigraphy, it can be suggested that geochemical plume ‘layering’ is on 10s to 100s of m-scale. The evolution of this Archean mantle plume from inception to demise compares favorably with the Yellowstone hotspot which is assumed to have developed over 17 m.y. and had a diameter of about 300 km.     

Geoid Determination through Ellipsoidal Stokes Boundary-Value Problem

Martinec and Grafarend (1997) have shown how the construction of Green's function in the Stokes boundary-value problem with gravity data distributed on an ellipsoid of revolution is approached in the O(e ₀ ² )-approximation. They have also expressed the ellipsoidal Stokes function describing the effect of ellipticity of the boundary as a finite sum of elementary functions. We present an effective method of avoiding the singularity of spherical and the ellipsoidal Stokes functions, and also an analytical expression for the ellipsoidal Stokes integral around the computational point suitable for numerical solution. We give the numerical results of solving the ellipsoidal Stokes boundary-value problem and their difference with respect to the spherical Stoke boundary-value problem.     

Uranium in metamorphic rocks

The distribution of U has been studied in two metamorphic rock-series with a gradient of regional metamorphism. One series ranges from the lowest greenschist to amphibolite facies and the other one shows increasing metamorphic grade from amphibolite to granulite facies. Several medium and high pressure granulitic inclusions from alkali basalts were also analyzed. The abundances of U in the rocks do not appear to be affected by metamorphism below the granulite facies grade. Granulites are depleted in U in comparison with equivalent rocks of amphibolite facies grade. There are also differences in their U distribution, as the bulk of U in amphibolite facies rocks is located along the fractures and cleavage planes of ferro-magnesian minerals and in U-rich accessories, while in granulites, most of the U resides in accessory minerals. It seems that the depletion of U in granulites is due to a loss of U which is not located in accessory minerals or in the crystal structure of rock-forming minerals and may also be related to a migration of hydrous fluids, perhaps during dehydration.     

A determination of the parameters of the level surface of lunar gravity

The spectral coefficients of the selenoid have been obtained by inverting the potential series for lunar gravity. The reference value of the lunar level surface has been determined on the base of the mean radius of lunar topography. This enables to evaluate the parameters of the tri-axial reference ellipsoid best fitted to the lunar level surface.     

A refined method of recovering potential coefficients from surface gravity data

Summary A new method for computing the potential coefficients of the Earth's external gravity field is presented. The gravimetric boundary-value problem with a free boundary is reduced to the problem with a fixed known telluroid. The main idea of the derivation consists in a continuation of the quantities from the physical surface to the telluroid by means of Taylor's series expansion in such a way that the terms whose magnitudes are comparable with the accuracy of today's gravity measurements are retained. Thus not only linear, but also non-linear terms are taken into account. Explicitly, the terms up to the order of the third power of the Earth's flattening are retained. The non-linear boundary-value problem on the telluroid is solved by an iteration procedure with successive approximations. In each iteration step the solution of the non-linear problem is estimated by the solutions of two linear problems utilizing the fact that the non-linear boundary condition may be split into two parts; the linear spherical approximation of the gravity anomaly whose magnitude is significantly greater than the others and the non-linear ellipsoidal corrections. Finally, in order to solve the problem in terms of spherical harmonics, the transform method composed of the fast Fourier transform and Gauss Legendre quadrature is theoretically outlined. Immediate data processing of gravity data measured on the physical Earth's surface without any continuation of gravity measurements to a reference level surface belongs to the main advantage of the presented method. This implies that no preliminary data handling is needed and that the error data propagation is, consequently, maximally suppressed.     

cD galaxies of apparent supergiant sizes due to the curvature of space

By combining two two-dimensional subspaces, closed into themselves due to curvature, it is possible to create a model of three-dimensional space of the same properties. If the Universe is a space of this type, its effect is that of a monstrous lens. Close objects are observed to diminish according to the normal law of perspective; however, the remote galaxies are seen to be very highly magnified.The apparent angular size² of a galaxy is more than the size¹ in flat space according to relation:² =¹ cosec , where is the angular distance from the observer to the galaxy. The diameter² d of a galaxy in curved space must be in the same relation to a diameter¹ d with no curvature of space:² d=¹ d cosec . The apparent angular size² and diameter² d are distorted shapes in consequence of an optical illusion caused by the spatial curvature.It is necessary to distribute the multitude of galaxies into two parts in accordance with their location on the close or reverse hemihypersphere of the Universe. The minimum of apparent angular size² of a galaxy of diameter¹ d is at the equatorial zone.The most likely candidates for location in the reverse hemi-hypersphere are cD's of apparent supergiant sizes due, probably, to the curvature of space. The existence of supergiant sizes of galaxies is the second indirect proof, besides superluminal velocities, that the Universe is closed into itself through curvature. The third indirect evidence, i.e., inductive confirmation of the same fact, is the superposition of galaxies which need not inevitably be a new alternative to the present theories of collisions, cannibalism, merger, etc.The fourth indirect proof of the positive curvature of the Universe is the occurrence of background radiation, because that must vanish in hyperbolic space irrespective of its origin. The gravitational lens effect acquires another theoretical form, as usual, in the case of remote galaxies, because it is impossible to distinguish between gravitator and lensing image.     

Pufferungskurven der Gewässer in der Typologie

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