Endmember graphics

Thek points inp-space corresponding to a specified set ofk (k<p) linearly independent endmember estimates associated with ap-variate (n×p) compositional datasetX, define the vertices of a (k?1) dimensional simplexH. Then estimated mixtures which together account for the systematic variation in the datasetX, are each convex combinations of thek fixed endmember estimates. Accordingly, then-points inp-space which represent these mixtures must be interior points of the simplexH. The purpose of this paper is to describe a simple graphical procedure for examining the positions of the estimated mixtures relative tok=3 or 4 putative endmembers, and for assessing their compliance or otherwise with the convexity constraints. Since the mixture coefficients must be estimated first in order to obtain the mixture estimates, the paper begins with a review of the least-squares partitioning procedure.     

Die Strukturgeschichte der Zentralsahara

The author has investigated paleogeographic and structural problems in the middle part of the Sahara desert since 1959. Detailed studies of thickness changes, of disconformities and unconformities and of structural events resulted in the definition of the different tectonical eras and their individual paleogeographic elements. The middle part of North Africa is characterized by three major periods of structural development:

1. Folding and consolidation in Precambrian time.
2. Formation of NW to NNW striking horsts during Cambrian time, which became the core of uplifts (separated by troughs) in Silurian and Devonian time. This structural relief of the early Paleozoic era possibly is the result of regional stretch in NE-SW direction.
3. Formation of uplifts and troughs striking NE during late Paleozoic and Mesozoic time. Blockfaulting occurred along the edge of some uplifts during Jurassic time or at the Jurassic-Cretaceous transition. These movements were the result of regional compression from SE toward NW. The formation of this large scale undulation of the earth's crust coincides with the separation of the Sahara platform from the so-called Tethys (geosynclinal area in NW Africa, the Mediterranean and parts of Asia). This separation most probably began in Northwest Africa during late Carboniferous or early Permian time, it reached Northeastern Libya in Jurassic time. The Sirte grabens were formed as the result of east-west shearing movements, during Upper Cretaceous. Finally, in late Tertiary to Pleistocene time, volcanic activity formed large basalt plateaus. Volcanism occurs mainly along well defined old structural elements.

The results of this analysis were used to interpret structural aspects of larger parts of Africa. The structural relief of the early Paleozoic Era seems to extend far southeast into areas of the old African shield indicating that there is no principal structural difference between the shield and the Sahara platform. The orientation of the late Paleozoic to Mesozoic large scale undulation indicates that the reason for the SE-NW compression is the rotation tendency of Africa which began in late Carboniferous time and culminated during the Tertiary, when Africa was separated from Asia along the Red Sea graben. At approximately the same time, the Atlas area of Northwest Africa was folded.     

Das geochemische Verhalten des Strontiums bei der Genese und Diagenese von Ca-Karbonat- und Ca-Sulfat-Mineralen

Experimental partioning of Sr between solutions, aragonite, calcite, gypsum and anhydrite show that the isomorphous replacement of Ca²⁺ by Sr²⁺ can be described as a linear function. The constants of the distributions are used to calculate primary Sr-contents of the various Ca-carbonates and Ca-sulfates precipitated from seawater and to estimate the point of precipitation of celestite. Comparism of these data with actual Sr-contents in sediments and sedimentary rocks show that in most cases gypsum has to be considered as the primary precipitate. Anhydrite in general is formed by diagenetic alteration of gypsum. The average Sr-content of gypsum rocks make it very probable that the Sr-concentration of seawater has stayed virtually unchanged since the end of Mesozoic. Sr-contents of carbonate rocks show that most of the limestones have been altered diagenetically. The distribution of Sr within the various sedimentary units of the earth's crust make it very probable that this alteration occurred in a system open to pore solutions.     

Die Rolle der Strukturänderung und Mischkristallentwicklung bei der Deutung der Differentiation und Kristallisation vulkanischer Gesteine

Zusammenfassung Es wird ein Überblick über die Änderung des Gefüges und der Mischkristalle einer Generation vulkanischer Gesteine gegeben. Die Gesteinsproben lassen sich nach ihren Einsprenglingen in eine genetische Reihenfolge der Schmelzentwicklung gliedern und zeigen dabei eine kontinuierliche Veränderung der Mischkristallphasen der Grundmasse. An Meßreihen für Olivin, Plagioklas und Sanidin und an der Verschiebung der Röntgenreflexe ist dieser Phasenwandel nachgewiesen. Zwölf Abbildungen zeigen den Übergang des Mineralbestandes und des Gefüges in der Grundmasse von Probe zu Probe.

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A survey of the changes of the structure and of the mixed crystals in a generation of volcanic rocks is given. According to their accessory minerals (Einsprengunge) the rock samples can be arranged in a genetic sequence of the melting-process; in this they show a continuous change in the phases of mixed crystals of the ground-mass. This change of phase is demonstrated by measuring sequences for Olivine, Plagioclase and Sanidine and by shift of the X-ray reflexes. Twelve figures show the transition of the mineral stock and of the structure in the ground-mass from sample to sample.

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Résumé Une vue d'ensemble sur les changes de structure et des cristaux composés d'une génération de roches volcaniques est présentée. Les spécimens de roches peuvent être organisés — selon leurs phénocrystaux — dans une série génétique du procès de fusion; ils montrent une change continuelle des phases de cristaux composés de la matrice. La change des phases ist prouvée par mesurages en séries et par le déplacement des reflexes radiographiques. Douze figures montrent la transition du dépót de minéraux et de la structure dans la matrice d'un spécimen à l'autre.

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Eo-alpine metamorphism in the uppermost unit of the Cretan nappe system — Petrology and geochronology

The uppermost unit of the Cretan nappe system consists of ophiolites on the top, and an ophiolitic mélange at the base.Among the various constituents of the mélange, there are slices of low-P/high-T metamorphics. They form a variegated series consisting of tholeiitic ortho-amphibolites, para-amphibolites, andalusite and sillimanite-cordierite-garnet bearing mica schists, calcsilicate rocks, and marbles. The metamorphic sequence is locally intruded by early tectonic magmatites of gabbroic, dioritic and granitic composition. Critical mineral assemblages lead to a maximum temperature of about 700° C reached during metamorphism, at a total pressure of 4–5 kilobars. K — Ar dating on 6 hornblendes, 7 biotites and 1 muscovite yielded cooling ages of 75–66 m.y. and confirmed earlier results according to which the metamorphism and related magmatism took place in Late Cretaceous times.In order to evaluate the age relationships between the hightemperature metamorphics within the ophiolitic mélange and the ophiolites, hornblendes from ultramafic and mafic rocks of the ophiolite complex were dated by the K — Ar method. Hornblende from one schistose hornblendite forming a constituent of the ophiolites proper yielded 156 m.y. and thus provides a middle Jurassic minimum age for the formation of this piece of oceanic lithosphere. Four hornblendes of calc-alkaline gabbrodiorite dikes within the ophiolite complex gave distinctly lower K — Ar dates of about 140 m.y.. The dikes probably intruded after the detachment of the ophiolites in an island-arc or continental-margin environment.As a consequence, the high-temperature metamorphics and related intrusives in the ophiolitic mélange of Crete are genetically unrelated to the overlying ophiolites. The paleogeographic position of the crystalline terrane, slices of which are now incorporated into the ophiolitic mélange is still open to discussion.     

Geochronology of high-pressure rocks on Sifnos (Cyclades,Greece)

Polymetamorphic rocks of Sifnos (Greece) have been investigated by Rb-Sr, K-Ar, and fission track methods. Critical mineral assemblages from the northern and southernmost parts of Sifnos include jadeite+quartz+3T phengite, and omphacite+garnet +3T phengite, whereas the central part is characterized by the assemblage albite+chlorite+epidote+2M ₁ phengite.K-Ar and Rb-Sr dates on phengites (predominantly 3T) of the best preserved high P/itTmetamorphic rocks from northern Sifnos gave concordant ages around 42 m.y., indicating a Late Lutetian age for the high P/T metamorphism. Phengites (2M ₁+3T) of less preserved high P/T assemblages yielded K-Ar dates between 48 and 41 m.y. but generally lower Rb-Sr dates. The higher K-Ar dates are interpreted as being elevated by excess argon.K-Ar and Rb-Sr ages on 2M ₁ phengites from central Sifnos vary between 24 and 21 m.y. These ages date a second, greenschist-facies metamorphism which overprinted the earlier high-pressure metamorphic rocks.     

Paläoklimatische Information im Isotopengehalt14C-datierter Saharawässer: Kontinentaleffekt in D und18O

Zusammenfassung In den¹⁴C-Altern der Saharawässer spiegelt sich die wechselnde Abfolge von Feucht- und Trockenphasen während des späten Pleistozäns und Holozäns wider. Außerdem zeigt sich ein West-Ost-Gefälle in ihrem D- und¹⁸O-Gehalt, das als Kontinentaleffekt im Grundwasser gedeutet wird. Dieser Kontinentaleffekt setzt voraus, daß das nordafrikanische Klimageschehen vergangener Feuchtphasen von der Westdrift bestimmt wurde, die regenbringende atlantische Luftmassen weit ins Saharainnere getrieben hat. Ein einfaches mathematisches Modell, das den Kontinentaleffekt durch eine Rayleigh-Kondensation beschreibt, ergibt die beste Anpassung an die Meßwerte, wenn für die Sahara (ähnlich wie heute in Europa) ein West-Ost-Gefälle in den Paläo-Winterniederschlagsmengen von –30% pro 1000 km angenommen wird. Unter der Annahme ehemaliger Winterniederschläge (Sept.-März) von 600 mm (entspricht Lissabon heute) für das Gebiet an der nordafrikanischen Atlantikküste ergibt diese Modellrechnung z. B. 250 mm für die Paläo-Winterniederschläge im Gebiet des Murzuk-Beckens.

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The¹⁴C-age distribution of Saharian groundwaters shows the alternating sequence of humid and arid periods in the late Pleistocene and Holocene. The observed west-east decrease of the D- and¹⁸O-content of the Sahara waters is interpreted to be the Continental Effect in rain and groundwater. The paleoclimatic situation during ground-water formation therefore was controlled by the western drift carrying wet Atlantic air masses across the Sahara. The best fit of a simple Rayleigh condensation model of the continental effect to the experimental data is obtained with a west-east decrease of the Saharian paleo-winter precipitation of –30% per 1000 km (similar to the one in Europe today). With an annual winter precipitation rate (Sept.-March) of 600 mm (corresponding to the one of Lisboa today) for the Northafrican coastal area at the Atlantic Ocean a previous winter precipitation rate of 250 mm is obtained for the Murzuq Basin.

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Résumé Une succession de périodes humides et arides à la fin du Pléistocène et à l'Holocène se réflète dans la distribution des âges¹⁴C d'eaux souterraines du Sahara. Les teneurs en D et¹⁸O diminuent d'Ouest en Est, ce qui est interprété comme un effet continental dans l'eau souterraine. Celui-ci signifie que la climatologie des phases pluviales passées, dans l'Afrique du Nord, était déterminée par des vents d'Ouest qui apportaient des masses d'air atlantique humide à l'intérieur du Sahara. Un modèle mathématique simple décrivant l'effet continental par une condensation du type Rayleigh, reproduit avec la meilleure conformité les valeurs expérimentales, pour autant qu'on admette que les pluies hivernales au Sahara diminuaient anciennement d'Ouest en Est de 30% par 1000 km (comme à présent en Europe). En supposant qu'autrefois la quantité de pluie hivernale, de septembre à mars à la côte atlantique de l'Afrique du Nord était de 600 mm (comme aujourd'hui à Lisbonne), on obtient à l'aide de ce modèle une précipitation hivernale ancienne de 250 mm dans le bassin du Mourzouk.

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, ¹⁴C, . , ¹⁸O, , . , , , , . , Rayleigh, — , — — 30 % 1000 . , - , . . , 600 , — —, 250 .

     

Chloritoid-bearing metapelites associated with glaucophane rocks in western Crete,Greece

Problems related to the formation of chloritoid in metapelites, associated with lawsonite-glaucophane bearing metabasalts, in the quartzitephyllite series of western Crete (Greece) are discussed. It is supposed that chloritoid was formed, during prograde metamorphism, according to a gliding-equilibrium reaction of the type (Fe,Mg)-carpholite₁+chlorite₁ (Fe,Mg)-carpholite_{1 2}+(Fe,Mg)-chloritoid_{1 2} +chlorite_1→2+quartz+H₂O ? (Fe,Mg)-chloritoid₂+chlorite₂+quartz+H₂O. This view is stipulated by the occurrence of ferrocarpholite-chloritoid schists in the southeastern part of central Crete. The assemblage chloritoid+ lawsonite recently recognized in western Crete provides evidence that the formation of chloritoid started well within the stability field of lawsonite.     

Tectono‐sedimentary evolution of lower to middle Miocene half‐graben basins related to an extensional detachment fault (western Crete,Greece)

Crustal extension in the overriding plate at the Aegean subduction zone, related to the rollback of the subducting African slab in the Miocene, resulted in a detachment fault separating high‐pressure/low‐temperature (HP‐LT) metamorphic lower from non‐metamorphic upper tectonic units on Crete. In western Crete, detachment faulting at deeper crustal levels was accompanied by structural disintegration of the hangingwall leading to the formation of half‐graben‐type sedimentary basins filled by alluvial fan and fan‐delta deposits. The coarse‐grained clastic sediments in these half‐grabens are exclusively derived from the non‐metamorphic units atop the detachment fault. Being in direct tectonic contact with HP‐LT metamorphic rocks of the lower tectonic units today, the basins must have formed in the period between c. 20 and 15 Ma, prior to the exposure of the HP‐LT metamorphic rocks at the surface, and juxtaposed with the latter during ongoing deformation.     

An appraisal of an iterative construction of the endmembers controlling the composition of deep-sea manganese nodules from the Central Indian Ocean Basin

This paper describes an estimation of endmember compositions followed by the assessment of those results by log-ratio variance analysis. As an appraisal, it deals only with the first objective of an endmember analysis namely, to identify endmembers if they exist by estimating their compositions. Following the creation of the endmember estimates, the computation of an array of log-ratio variances was a key innovation in this type of study. Log-ratio variances revealed intrinsic linear associations between the dominant elements on each of the estimated endmember compositions, largely confirming the endmember analysis. The dataset under study contained the concentrations of 16 elements in 93 samples of deep-sea manganese nodules from the Central Indian Ocean Basin. Many previous analyses of these nodules were undertaken to assess the economic potential of the deposits. This study by contrast, quantified the inter-element associations that account for the nodule compositions. Four endmembers were identified. The elements loaded on each were: (1) Mn, Zn, Ni, Cu, Mn-rich, (2) Fe, Ti, P, Co, Fe-rich, (3) Si, Al, Na, K, clay minerals, (3) Mg, ultramafic material, possibly including Mn, Cr, V, Ca, Na. These latter elements were also detected by their log-ratio variances to be associated with Mg on the 4th endmember.