Inferences on the lunar temperature from gravity,stress state and flow laws

Inferences on the lunar temperature regime are made from the inversion of gravity for density anomalies and the stress-state of the Moon's interior, and by comparing these results with flow laws and estimates of likely strain-rates.The nature of the spectrum of the lunar gravitational potential indicates that the density anomalies giving rise to the potential are mainly of near-surface origon. The average stress-differences in the lunar mantle required to support these density anomalies are of the order of a few tens of bars and have persisted for more than 3 · 10⁹ years. If current flow laws for dry olivine can be extrapolated to the conditions of the lunar mantle, and the selenotherms based on electrical conductivity models are valid, the strain rates are too high to explain the preservation of the lateral near-surface density anomalies. We suggest that the present temperatures in the Moon are relatively low, of the order of 800°C or less, at a depth of about 300 km. This compares with 1100°C based on electrical conductivity models and is near the lower limit predicted by Keihm and Langseth (1977) from lunar heat-flow observations.     

A transferable interatomic potential for crystalline phases in the system MgO—SiO2

A central interatomic potential model is presented for compounds in the binary system MgO-SiO₂. The potential, of a simple form which consists of a Coulombic term, a Born repulsive term, and a Van der Walls term for oxygen-oxygen interactions, is designed to predict the properties of magnesium silicates containing Si in octahedral and tetrahedral coordination. This is achieved by fitting simultaneously to forsterite and MgSiO₃ ilmenite crystal structure data, and fixing the partial ionic charges using elastic data for forsterite. The potential is found to transfer successfully to γ-Mg₂SiO₄ and MgSiO₃ perovskite. The potential results in local structural errors around the bridging oxygen ions in clinoenstatite and β-Mg₂SiO₄. The predicted structure for MgSiO₃ garnet is similar to the experimentally measured structure of the MnSiO₃ analogue. Calculated elastic constants average to K=2.41 Mbar and μ=1.44 Mbar for the bulk and shear moduli of MgSiO₃ perovskite, and K=1.87 Mbar and μ=1.10 Mbar for the bulk and shear moduli of MgSiO₃ garnet.     

Der Neubau der Meteorologie

Summary The radiation as origin of the weather.

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Résumé Le temps, comme dépendant de la radiation solaire.

     

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Zur Analyse der Beobachtungen der Sonnenstrahlung

Summary The method of the equilibrium of radiation is demonstrated on two observed series of observations.

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Resumen El método del equilibrio de irradiación utilízase en 2 series de observaciones.

     

Die Registrierung der Energie-Verteilung im Sonnen-Spektrum

Zusammenfassung Die Möglichkeiten einer mechanischen Registrierung der Verteilung der Energie im Spektrum der Sonne werden gezeigt.

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Summary The possibility of a mechanical record of the distribution of energy in the spectre of the sun is demonstrated.

     

A Bounding Surface Plasticity Model for Intact Rock Exhibiting Size-Dependent Behaviour

A new constitutive model for intact rock is presented recognising that rock strength, stiffness and stress–strain behaviour are affected by the size of the rock being subjected to loading. The model is formulated using bounding surface plasticity theory. It is validated against a new and extensive set of unconfined compression and triaxial compression test results for Gosford sandstone. The samples tested had diameters ranging from 19 to 145 mm and length-to-diameter ratios of 2. The model captures the continuous nonlinear stress–strain behaviour from initial loading, through peak strength to large shear strains, including transition from brittle to ductile behaviour. The size dependency was accounted for through a unified size effect law applied to the unconfined compressive strength—a key model input parameter. The unconfined compressive strength increases with sample size before peaking and then decreasing with further increasing sample size. Inside the constitutive model two hardening laws act simultaneously, each driven by plastic shear strains. The elasticity is stress level dependent. Simple linear loading and bounding surfaces are adopted, defined using the Mohr–Coulomb criterion, along with a non-associated flow rule. The model simulates well the stress–strain behaviour of Gosford sandstone at confining pressures ranging from 0 to 30 MPa for the variety of sample sizes considered.     

A zircon study from the Rhodope metamorphic complex, N-Greece: Time record of a multistage evolution

Zircons from an eclogite and a diamond-bearing metapelite near the Kimi village (north-eastern Rhodope Metamorphic Complex, Greece) have been investigated by Micro Raman Spectroscopy, SEM, SHRIMP and LA-ICPMS to define their inclusion mineralogy, ages and trace element contents. In addition, the host rocks metamorphic evolution was reconstructed and linked to the zircon growth domains.

The eclogite contains relicts of a high pressure stage (ca. 700 °C and > 17.5 kbar) characterised by matrix omphacite with Jd_40–35. This assemblage was overprinted by a lower pressure, higher temperature metamorphic event (ca. 820 °C and 15.5–17.5 kbar), as indicated by the presence of clinopyroxene (Jd_35–20) and plagioclase. Biotite and pargasitic amphibole represent a later stage, probably related to an influx of fluids. Zircons separated from the eclogite contain magmatic relicts indicating Permian crystallization of a quartz-bearing gabbroic protolith. Inclusions diagnostic of the high temperature, post-eclogitic overprint are found in metamorphic zircon domain Z2 which ages spread over a long period (160 – 95 Ma). Based on zircon textures, zoning and chemistry, we suggest that the high-temperature peak occurred at or before ca. 160 Ma and the zircons were disturbed by a later event possibly at around 115 Ma. Small metamorphic zircon overgrowths with a different composition yield an age of 79 ± 3 Ma, which is related to a distinct amphibolite-facies metamorphic event.

The metapelitic host rock consists of a mesosome with garnet, mica and kyanite, and a quartz- and plagioclase-bearing leucosome, which formed at granulite-facies conditions. Based on previously reported micro-diamond inclusions in garnet, the mesosome is assumed to have experienced UHP conditions. Nevertheless, (U)HP mineral inclusions were not found in the zircons separated from the diamond-bearing metapelite. Inclusions of melt, kyanite and high-Ti biotite in a first metamorphic zircon domain suggest that zircon formation occurred during pervasive granulite-facies metamorphism. An age of 171 ± 1 Ma measured on this zircon domain constrains the high-temperature metamorphic event. A second, inclusion-free metamorphic domain yielded an age of 160 ± 1 Ma that is related to decompression and melt crystallization.

The similar age data obtained from the samples indicate that both rock types recorded a high-T metamorphic overprint at granulite-facies conditions at ca. 170 – 160 Ma. This age implies that any high pressure or even ultra-high pressure metamorphism in the Kimi Complex occurred before that time. Our findings define new constraints for the geodynamic evolution for the Alpine orogenic cycle within the northernmost Greek part of the Rhodope Metamorphic Complex. It is proposed that the rocks of the Kimi Complex belong to a suture zone squeezed between two continental blocks and result from a Paleo-ocean basin, which should be located further north of the Jurassic Vardar Ocean.