Natural Metrics in the Spaces of Elliptic Orbits

Different natural metrizations by Hölder type on the five dimensional space of Keplerian elliptic orbits are introduced. Certain applications of topological and metrical properties of the space of Keplerian elliptic orbits to several problems of Celestial Mechanics are discussed.     

Multispectral polarimetry as a tool to investigate texture and chemistry of lunar regolith particles

We report results of telescope polarimetric imaging of the Moon with a CCD LineScan Camera at large phase angles, near 88°. This allows measurements of the polarization degree with an absolute accuracy better than 0.3% and detection of features with polarization contrast as small as 0.1%. The measurements are carried out in two spectral bands centered near 0.65 and 0.42 μm. We suggest characterizing the lunar regolith with the parameter a(Pmax)A, where Pmax,A, and a are the degree of maximum polarization, albedo, and the parameter describing the linear regression of the correlation Pmax-A. The parameter bears significant information on the particle characteristic size and packing density of the lunar regolith. We also suggest characterizing the lunar regolith with color-ratio images obtained with a polarization filter at large phase angles. We here consider the color-ratios C||(0.65/0.42 μm) and C_⊥(0.65/0.42 μm). Using light scattering model calculations we show that the color-ratio images obtained with a polarization filter at large phase angles suggest a new tool to study the lunar surface. In particular, it turns out that the color-ratios C||(0.65/0.42 μm) and C_⊥(0.65/0.42 μm) are sensitive to somewhat different thicknesses of the surfaces of regolith particles. We consider the applicability of the Hubble Space Telescope, the Very Large Telescope (ESO), and a spacecraft on a lunar polar orbit for polarimetric observations of the lunar surface.     

The age of unusual xenogenic zircons from Yakutian kimberlites

Several spindle-shaped grains of zircon, which have a small size (<0.25 mm) and a distinct purplish pink coloration were found in the crushed samples of kimberlites from the Aykhal, Komsomolskaya-Magnitnaya, Botuobinskaya (Siberian platform), and Nyurbinskaya (Yakutia) pipes and olivine lamproites of the Khani massif (West Aldan). U-Pb SHRIMP II zircon dating performed at the VSEGEI Center for Isotopic Research yielded the ages of 1870–1890 Ma for the pipes of the Western province (Aykhal and Komsomolskaya) and 2200–2750 Ma for the pipes of the eastern province (Nyurbinskaya and Botuobinskaya), which allowed us to consider these zircons to be xenogenic to kimberlites. Although these zircons resemble in their age and color those from the granulite xenoliths in the Udachnaya pipe [2], no other granulite minerals are found there. Thus, major geological events in the mantle and lower crust, which led to the formation of zircon-bearing rocks, happened at 1800–1900 Ma in the northern part of the kimberlite province, whereas in the Eastern part of the province (Nakyn field) these events were much older (2220–2700 Ma). It is known that the period of 1800–1900 Ma in the Earth’s history was accompanied by intense tectonic movements and widespread alkaline-carbonatite magmatism. This magmatism was related to plume activity responsible for overheating the large portions of the mantle to the temperatures at which some diamonds in mantle rocks would burn (northern part of the kimberlite province). In the Nakyn area, the mantle underwent few or no geological processes at that time, and perhaps for this reason this area hosts more diamondiferous kimberlites. The age of olivine lamproites from the Khani massif is 2672–2732 Ma. Thus, these are some of the world’s oldest known K-alkaline rocks.     

Potassium alkaline lamproite-carbonatite complexes: petrology,genesis, and ore reserves

This paper studies the petrology of K-alkaline lamproite-carbonatite complexes, which are widespread in Siberia. They are exemplified by the Murun and Bilibino massifs in West and Central Aldan. In these massifs, the entire range of differentiates was first found, from K-ultrabasic-alkalic rocks through basic and intermediate ones to alkali granites and unique residual calc-silicate rocks (benstonite Ba-Sr carbonatites and charoite rocks). Also, intrusive equivalents of lamproites occur in these massifs, and the Murun massif was probably formed from highly differentiated lamproite magmas. In many K-alkaline complexes, silicate and silicate-carbonate magma layering takes place. Stages of magmatism are described for both massifs. Binary and ternary petrochemical diagrams exhibit the same compositional trend from early to late rocks.In this paper, lamproites are considered from the chemical point of view; their diagnostic properties are described in terms of chemical and mineral composition. From geological, petrological, and geochemical data, formational analysis of alkaline complexes was performed, four formational types of world lamproites were first identified, and diamond content criteria were developed for them.The carbonatite problem was studied from the petrological point of view, and four formational types of carbonatites were identified using geological, geochemical, and genetic criteria. It has been suggested that for dividing carbonatite complexes into four formational types the following criteria be used: the alkalinity type (Na or K) of alkalic rocks in the complex and the time when the carbonatite liquid separates from silicate melts in different stages of primary magma differentiation. These linked parameters influence the ore content type of carbonatite complexes.A formation model for K-alkaline carbonatite complexes is given, and the Tomtor alkaline carbonatite massif with tuffaceous rare-metal ores is described to prove that they have ore reserves. The geochemistry of C, O, Sr, and Nd isotopes shows that K-alkaline complexes, depending on their geotectonic setting, can originate from three types of mantle sources: depleted mantle, enriched mantle 1 (EM1), and enriched mantle 2 (EM2). It is concluded that ore-bearing ultrabasic-alkaline complexes of lamproites and carbonatites can melt out of different types of mantle, whose composition only slightly influences their ore content. Apparently, the main factors are the low degree of selective mantle melting (less than 1%) and plumes supplying fluid and alkaline components, which stimulate this melting. Later on, the processes important for the accumulation of ore and trace elements are long-term magma differentiation and its layering during crystallization.     

New data on the age and nature of the Khan–Bogd alkaline granites,Mongolia

New age dating (291 Ma) was obtained for one of the largest alkaline granite massifs in the world, the Khan–Bogd Massif (Mongolia). For the first time, apart from zircon, other zirconium silicates, elpidite and armstrongite, have been analyzed. Our determinations showed the highly depleted nature of the mantle sources of granites with ε_Nd = 12. All the studied Zr-silicates demonstrate positive Eu anomalies in the REE patterns, which indicate a low oxidation potential during alkaline granite formation.     

Monomineral universal clinopyroxene and garnet barometers for peridotitic,eclogitic and basaltic systems

New versions of the universal Jd-Di exchange clinopyroxene barometer for peridotites,pyroxenites and eclogites,and also garnet barometer for eclogites and peridotites were developed.They were checked using large experimental data sets for eciogitic(~530) and peridotitic systems(650).The precision of the universal Cpx barometer for peridotites based on Jd-Di exchange is close to Cr-Tschermalite method produced by Nimis and Taylor(2000).Cpx barometer was transformed by the substitution of major multiplier for K_D by the equations dependent from Al-Na-Fe.Obtained equation in combination with the thermometer of Nimis and Taylor(2000) allow to reconstruct position of the magma feeder systems of the alkali basaltic magma within the mantle diapirs in modern platforms like in Vitim plateau and other Southern Siberia localities and several localities worldwide showing good agreement of pressure ranges for black and green suites.These equations allow construct PTX diagrams for the kimberlite localities in Siberia and worldwide calculating simultaneously the PT parameters for different groups of mantle rocks.They give very good results for the concentrates from kimberlite lamproites and placers with mantle minerals.They are useful for PT estimates for diamond inclusions.The positions of eclogite groups in mantle sections are similar to those determined with new Gar—Cpx barometer produced by C.Beyer et al.(2015).The Fe rich eclogites commonly trace the boundary between the lower upper parts of subcontinental lithospheric mantle(SCLM) at 3-4 CPa marking pyroxenite eclogites layer.Ca-rich eclogites and especially grospydires in SCLM beneath Precambrian kimberlites occurs near pyroxenite layer but in younger mantle sections they became common in the lower parts.The diamondiferous Mg Cr-less group eclogites referring to the ancient island arc complexes are also common in the middle part of mantle sections and near 5-6 GPa.Commonly eclogites in lower apart of mantle sections are remelted and trace the high temperature convective branch.The Mg-and Fe-rich pyroxenites also show the extending in pressure trends which suggest the anatexic melting under the influence of volatiles or under the interaction with plums.     

Geology, Geochronology, and Geodynamics of the Khan Bogd alkali granite pluton in southern Mongolia

The Khan Bogd alkali granite pluton, one of the world’s largest, is situated in the southern Gobi Desert, being localized in the core of the Late Paleozoic Syncline, where island-arc calc-alkaline differentiated volcanics (of variable alkalinity) give way to the rift-related bimodal basalt-comendite-alkali granite association. The tectonic setting of the Khan Bogd pluton is controlled by intersection of the near-latitudinal Gobi-Tien Shan Rift Zone with an oblique transverse fault, which, as the rift zone, controls bimodal magmatism. The pluton consists of the eastern and the western ring bodies and comes into sharp intrusive contact with rocks of the island-arc complex and tectonic contact with rocks of the bimodal complex. The inner ring structure is particularly typical of the western body and accentuated by ring dikes and roof pendants of the country island-arc complex. According to preliminary gravity measurements, the pluton is a flattened intrusive body (laccolith) with its base subsiding in stepwise manner northwestward. Reliable geochronologic data have been obtained for both plutonic and country rocks: the U-Pb zircon age of alkali granite belonging to the main intrusive phase is 290 ± 1 Ma, the ⁴⁰Ar/³⁹Ar ages of amphibole and polylithionite are 283 ± 4 and 285 ± 7 Ma, and the Rb-Sr isochron yields 287 ± 3 Ma; i.e., all these estimates are close to 290 Ma. Furthermore, the U-Pb zircon age of red normal biotite granite (290 ± 1 Ma) and the Rb-Sr age of the bimodal complex in the southern framework of the pluton are the same. The older igneous rocks of the island-arc complex in the framework and roof pendants of the pluton are dated at 330 Ma. The geodynamic model of the Khan Bogd pluton formation suggests collision of the Hercynian continent with a hot spot in the paleoocean; two variants of this model are proposed. According to the first variant, the mantle plume, after collision with the margin of the North Asian paleocontinent, reworked the subducted lithosphere and formed a structure similar to an asthenospheric window, which served as a source of rift-related magmatism and the Khan Bogd pluton proper. In compliance with the second variant, the emergence of hot mantle plume resulted in flattening of the subducted plate; cessation of the island-arc magmatism; and probably in origin of a local convective system in the asthenosphere of the mantle wedge, which gave rise to the formation of a magma source. The huge body of the Khan Bogd alkali granite pluton and related volcanic rocks, as well as its ring structure, resulted from the caldera mechanism of the emplacement and evolution of magmatic melts.     

Seasonal, interannual and long-term variability of precipitation and snow depth in the region of the Barents and Kara seas

Observation data of temperature, precipitation and snow depth have been compiled and generalized climatologically for a network of 38 stations in and around the Barents and Kara seas, for the period 1951–1992. The monthly precipitation totals were corrected for measuring errors, and the correction method is described in detail. The corrected precipitation values show that the annual precipitation in the region ranges from more than 500 mm along the coast of the Kola Peninsula to less than 200 mm in parts of the north-eastern Kara Sea. The solid fraction of the annual precipitation ranges from 70% in northern parts to 35% in southern parts. For the period 1951–1992 the analysis indicates decreasing trends in annual values of temperature, precipitation and snow depths in the north-eastern parts of the region.     

Lidar and Sun photometer observations of atmospheric boundary-layer characteristics over an urban area in a mountain valley

We present measurements of the vertical aerosol structure and the aerosol optical depth in the lower troposphere performed above the city of Sofia (an urban area situated in a mountain valley), western Bulgaria by means of a ground-based aerosol lidar operating continuously for a number of years. The lidar measurements were accompanied by measurements of the aerosol optical depth (AOD) in the visible and near infrared regions of the spectrum performed in October 2004 using Microtops II radiometers. The maximum values of the AOD were found to occur 1–2 h before the complete development of the atmospheric boundary layer, i.e. during the residual layer destruction, which confirms our hypothesis concerning the slope circulation effect on the processes taking place in the atmospheric boundary layer. The AOD values obtained by the lidar are lower than those taken by the sun photometer. Further, the AOD exhibits two different types of behaviour. In the case of a ‘clear atmosphere’ (i.e. in the absence of volcanic eruptions and/or dust transport from the Sahara) most of the aerosol accumulated within the atmospheric boundary layer over the urban area considered. The combined use of the two instruments allows the comparison between the optical characteristics of the atmospheric aerosol (e.g. aerosol extinction coefficient, etc.) obtained by the lidar and through an independent method (sun photometer).