Abscissa-Transforming Second-Order Polynomial Functions to Approximate the Unknown Historic Production of Non-renewable Resources

For many non-renewable resources, reliable production data are only available from a certain point in time but not from the beginning of production periods. In order to constrain the unknown historic production of such resources for those ancient times for which no reliable annual production data are available we present a novel mathematical technique, based on Verhulst’s logistic function. The method is validated by the United States’ crude oil production for which the complete production cycle, starting in 1859, is well documented. Assuming that the oil production in the USA between 1859 and 1929 is unknown, our method yields values for this period of 16.0 gigabarrels (Gb) based on a second-order polynomial fit and 13.5 Gb based on a third-order polynomial fit of post-1929 production data, respectively. Especially the latter amount compares well with the actual value of 12.1 Gb, thus illustrating the strength of the method. For global gold (Au) production, our method yields an ancient production up to the year 1850, when official and reliable production statistics began, of approximately 10,000 metric tons (t) based on a second-order polynomial fit. For mercury (Hg) a production of 64,000 t was determined for the time up to the year 1900, when annual production figures started to become available, again using a second-order polynomial fit. While the results obtained by the application of second-order polynomial functions could be confirmed by higher-order polynomial functions in the cases of both USA oil as well as global Au production, this was not possible in the case of global Hg production because of a highly irregular production curve.     

Rumuruti chondrites: Noble gases,exposure ages,pairing, and parent body history

Abstract— In this paper, we present concentration and isotopic composition of the light noble gases He, Ne, and Ar as well as of ⁸⁴Kr, ¹³²Xe, and ¹²⁹Xe in bulk samples of 33 Rumuruti (R) chondrites. Together with previously published data of six R chondrites, exposure ages are calculated and compared with those of ordinary chondrites. A number of pairings, especially between those from Northwest Africa (NWA), are suggested, so that only 23 individual falls are represented by the 39 R chondrites discussed here. Eleven of these meteorites, or almost 50%, contain solar gases and are thus regolithic breccias. This percentage is higher than that of ordinary chondrites, howardites, or aubrites. This may imply that the parent body of R chondrites has a relatively thick regolith. Concentrations of heavy noble gases, especially of Kr, are affected by the terrestrial atmospheric component, which resides in weathering products. Compared to ordinary chondrites, ¹²⁹Xe/¹³²Xe ratios of R chondrites are high.     

Metamorphism of the Permo-Triassic Cape Fold Belt and its basement, South Africa

Summary  The Permo-Triassic Cape Fold Belt around the southern tip of Africa consists of a thick sequence of Palaezoic siliciclastic sedimentary and pre-Cape basement rocks believed to be of Pan-African age. Both the basement rocks and the supracrustal rocks of the Cape Supergroup display only low metamorphic grades. Application of chlorite, chlorite-chloritoid Fe-Mg exchange, and calcite-graphite carbon isotope geothermometry to rocks from the unconformable contact between pre-Cape basement and the Cape Supergroup made it possible to distinguish pre-Cape and syn-Cape metamorphic overprints. During Pan-African metamorphism temperatures of up to middle greenschist facies conditions (around 400 °C) were reached, whereas lowermost greenschist facies conditions (around 300 °C) were not exceeded during the 220–290 Ma Cape orogeny. In the past, most if not all of the pre-Cape basement rocks, which form the Pan-African Saldania Belt, were considered to be of Neoproterozoic age. A hiatus of about 100 °C observed between two adjacent limestone horizons that previously had been grouped together into a single formation at the bottom of the allegedly Neoproterozoic Kango Group indicates that almost all of this group is syn- to post-orogenic with respect to the Pan-African orogeny. A revision of the stratigraphy of the Kango Group is therefore suggested. Only its lowermost member is truly Pan-African and probably related to about 620–740 Ma post-Sturtian cap carbonates in other Pan-African belts of southern Africa. The remainder of the Kango Group reflects the successive development of two stages of orogen-related intra-continental basins: The older stage led to a typical syn-orogenic foreland basin related to tectonic loading in the Gariep and Damara orogenic belts further north(west) between 570 and 540 Ma; the younger is believed to have formed either a further foreland basin or an intra-orogen pull-apart basin caused by later tectonic loading in the Ross orogenic belt and its continuation into the southern Saldania Belt between 510 and 480 Ma. Received May 7, 2000;/revised version accepted January 15, 2001     

Isotopic constraints on fluid/rock ratios in carbonate rocks: Barite-sulfide mineralization in the Schwaz Dolomite, Tyrol (Eastern Alps, Austria)

The significance of isotopic data on constraining the physical conditions of fluid-rock interaction and mineralization processes in carbonate rocks is discussed, based on the example of barite-tetrahedrite mineralization in Lower Devonian platform carbonates of the Western Greywacke Zone (Tyrol, Austria). Available strontium, oxygen, carbon and sulfur isotopic data are complemented with oxygen isotopic data for barite. Barites are homogeneous in δ¹⁸O_V-SMOW and δ³⁴S_CDT with values of + 15.4 and + 23.5‰, respectively. Their ⁸⁷Sr/⁸⁶Sr ratios vary between 0.7128 and 0.7113 for the first generation and between 0.7117 and 0.7123 for younger remobilization. The dolomitic host rock shows a significant variation in Sr, O and C isotopic composition between non-mineralized and mineralized zones: ⁸⁷Sr/⁸⁶Sr ratios vary between 0.7076 and 0.7133, δ¹⁸O_V-SMOW-values between +28.11 and +20.65‰, and δ¹³C_PDB-values between −1.15 and + 3.06‰. Fluid/rock volume ratios on the order of 1.3–3.2 are calculated for open-system behaviour by modelling Sr, O and C isotopic shifting capacities. The isotope data combined with other geological evidence support the following genetic model: Subsequent to synsedimentary sulfide mineralization during an Early Devonian rifting stage, collision tectonics in Carboniferous time led to the expulsion of Ba- and Sr-rich orogenic brines, which evolved from metamorphic fluids consisting essentially of H₂O and some CH₄, into an external sedimentary fold-and-thrust belt. The brines remobilized the synsedimentary sulfides, mixed with meteoric waters in the platform carbonates, reacted with evaporitic horizons and finally caused the recrystallization of dolomite and the precipitation of Sr-rich barite in structurally weak zones at 70–130°C. During the later Alpine orogeny supergene oxidation products were formed, and sulfates, sulfides and carbonates were further remobilized into late faults and fractures.     

Hafnium isotope homogenization during metamorphic zircon growth in amphibolite-facies rocks: Examples from the Shackleton Range (Antarctica)

Hafnium isotope analyses of a large number of metamorphic zircon grains of two garnet-kyanite-staurolite schist samples from the Shackleton Range yielded ¹⁷⁶Hf/¹⁷⁷Hf of 0.28160 ± 0.00003 and 0.28142 ± 0.00003, respectively. The variations of these analyses are less than ±1.2 epsilon units and indicate that all metamorphic zircon grains in the two rocks formed in environments with nearly homogenous Hf isotopic composition. The metamorphic origin of the zircon grains is constrained by textures as well as by their low Th/U (<0.2), ¹⁷⁶Lu/¹⁷⁷Hf (<0.0003), and ¹⁷⁶Yb/¹⁷⁷Hf ratios (<0.009), indicating that they grew in the presence of garnet. Furthermore, the grains yield Pb-Pb ages of c. 1.7 Ga, which is the time of amphibolite-facies metamorphism. In combination with petrological results, it is suggested that the observed ¹⁷⁶Hf/¹⁷⁷Hf homogeneity was caused by a fluid- and deformation-assisted dissolution of detrital zircon grains, followed by new zircon re-precipitation that was accompanied by Hf transport on at least a hand-specimen scale. This interpretation is supported by results obtained from an additional paragneiss sample that contains zoned zircon grains with xenocrystic cores formed at 2.6-1.8 Ga and metamorphic rims with a U-Pb age of 1.7 Ga. The ¹⁷⁶Hf/¹⁷⁷Hf variation of the zircon rims is mostly at ±0.0003, which is much less than that of the magmatic cores (±0.0019). The metamorphic fluid for the dissolution-homogenization-re-precipitation process most likely resulted from prograde reactions among the minerals chlorite-muscovite-biotite-garnet-staurolite-apatite, in agreement with thin section observations and P-T pseudosection calculations.     

A two-stage evolution model for the Amantaytau orogenic-type gold deposit in Uzbekistan

A lithogeochemical, mineral chemical, isotopic, and fluid inclusion study of barren, low-, and high-grade Au-mineralized samples from the shear zone-hosted Amantaytau gold deposit, Uzbekistan, shows that the local host rocks, Late Ordovician–Earlz Silurian carbonacous shales, are likely to have been an important source of Au, As, Ni, and S in the formation of the deposit. Syn-depositional pyrite in these shales contains on average 0.23 ppm Au, 1,083 ppm As, and 861 ppm Ni. The distribution of rare earth elements (REE) indicates a homogeneous source of light REE, whereas the heavy REE distribution reflects most likely primary variations in the sediments. The mineralized zone is marked by a positive Eu anomaly, which supports reducing conditions during the mineralization. A hydrothermal overprint by an aqueous–carbonic fluid is reflected in a high-grade Au-mineralized sample by δ¹³C values of ?13.0?‰ (V-PDB). The δ ³⁴S values in pyrite (?0.13 to +7.30?‰ CDT) from barren and mineralized samples are consistent with marine sulfate being the principal source of the ore sulfur. Assuming a formation temperature of between 300 and 400 °C for the main stage of mineralization, as indicated by the alteration mineral assemblage, the calculated δ ¹⁸O_fluid is between 9.5 and 13.4?‰ V-SMOW, which points at a metamorphic origin of the ore fluid.     

Strömungsuntersuchungen im Fehmarnsund (Ostsee)

Zusammenfassung Im ersten Abschnitt werden mehrere Strommessungen, die vom verankerten Forschungskutter Südfall im Fehmarnsund gewonnen wurden, in ihrer Beziehung zu Wind und Wasserstandsdifferenzen qualitativ diskutiert. Ein Beispiel für Strom bei ruhiger Wetterlage zeigt deutlich vorwiegend Gezeiten. Ein anderes Beispiel für die Verhältnisse bei stürmischen Winden läßt extreme Wasserstandsschwankungen erkennen, die die Gezeitenwelle zum Verschwinden bringen.Im zweiten Abschnitt wird mit Hilfe hydraulischer Formeln für turbulente Strömungen (S. 93) das Oberflächengefälle in Richtung des Fehmarnsundes ermittelt. Ferner wird eine Beziehung zwischen dem Absolutbetrag des Gefälles und der mittleren Stromgeschwindigkeit eines bestimmten Stromprofils abgeleitet, die durch die Messungen befriedigend bestätigt wird.Zum Schluß wird, ebenfalls unter Benutzung von Ansätzen aus der Hydraulik (S. 97), die Verteilung der Oberflächenströmung im Fehmarnsund berechnet, die durch weitere Strommessungen auf verschiedenen Positionen bestätigt wird. Das benutzte Verfahren ist geeignet, die Auswirkungen vorauszuberechnen, die wasserbauliche Änderungen im Fehmarnsund zur Folge haben werden. Die Grenzen dieser Methode werden anhand von mehreren Beispielen aufgezeigt.

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On current investigations in the Fehmarn Sound

Summary The first paragraph deals with several current measurements obtained on board the anchored research cutter Südfall in the Fehmarn Sound and discusses their relation to wind and variations in sea level in a qualitative way. An example of current measurements in calm weather clearly shows the effect of the tides whilst in case of stormy weather, extreme variations in sea level cause the tidal wave to vanish.In the second paragraph, the surface gradient oriented in the axis of the Fehmarn Sound is ascertained with the aid of hydraulic formulae for turbulent currents (see page 93). Besides, a relation between the absolute value of the gradient and the mean current velocity of a certain current profile is derived; this relation is satisfactorily confirmed by the current measurements.At last, hydraulic formulae (see page 97) serve again for calculating the distribution of surface currents in the Fehmarn Sound. Their results are confirmed by a number of current measurements from various stations. The applied method is a suitable aid in predicting the effects of planned hydraulic constructions on the conditions in the Fehmarn Sound. Several examples show the utmost limit of application of this method.

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Sur des recherches de courant dans le Sund de Fehmarn

Résumé Le premier chapitre traite plusieurs mesures du courant effectuées dans le Sund de Fehmarn par le bateau mouillé de recherche Südfall et expose qualitativement leurs rapports avec le vent et avec les différences du niveau de la mer. On donne deux exemples dont l'un se réfère à des mesures du courant prises par un temps calme et l'autre à des mesures ducourant effectuées par un temps orageux. Le premier exemple nous montre nettement la prépondérance de la marée, le deuxième exemple fait voir que les extrêmes variations du niveau de la mer font disparaître l'onde de marée.Dans le deuxième chapitre on calcule, à l'aide des formules hydrauliques pour des courants turbulents (voir page 93), le gradient superficiel incliné dans la direction du Sund de Fehmarn. En outre, on dérive un rapport entre la valeur absolue du gradient et la vitesse moyenne du courant d'une certaine coupe transversale; des mesures du courant vérifient satisfaisamment l'existence d'un tel rapport.A la fin, on calcule, également à l'aide de formules hydrauliques (voir page 97), la distribution des courants superficiels dans le Sund de Fehmarn; ce calcul correspond aux mesures spéciales du courant effectuées à diverses stations. Le procédé y employé est un moyen convenable permettant de prévoir des effets qui pourraient être produits dans le Sund de Fehmarn par des constructions hydrauliques projetées. Plusieurs exemples montrent les limites de cette méthode.

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Herrn Prof. Dr. G. Wüst, meinem verehrten Lehrer, zum 65. Geburtstage gewidmet.