Oxygen isotope thermometry in carbonatites, Fuerteventura, Canary Islands, Spain

Crystallization temperatures of the oceanic carbonatites of Fuerteventura, Canary Islands, have been determined from oxygen isotope fractionations between calcite, silicate minerals (feldspar, pyroxene, biotite, and zircon) and magnetite. The measured fractionations have been interpreted in the light of late stage interactions with meteoric and/or magmatic water. Cathodoluminescence characteristics were investigated for the carbonatite minerals in order to determine the extent of alteration and to select unaltered samples. Oxygen isotope fractionations of minerals of unaltered samples yield crystallization temperatures between 450 and 960degreesC (average 710degreesC). The highest temperature is obtained from pyroxene-calcite pairs. The above range is in agreement with other carbonatite thermometric Studies. This is the first study that provides oxygen isotope data coupled with a CL study on carbonatite-related zircon. The CL pictures revealed that the zircon is broken and altered in the carbonatites and in associated syenites. Regarding geological field evidences of syenite-carbonatite relationship and the close agreement of published zircon U/Pb and whole rock and biotite K/Ar and Ar-Ar age data, the most probable process is early zircon crystallization from the syenite magma and late-stage reworking during magma evolution and carbonatite segregation. The oxygen isotope fractionations between zircon and other carbonatite minerals (calcite and pyroxene) support the assumption that the zircon would correspond to the early crystallization of syenite-carbonatite magmas.

The tectonically controlled emplacement of a vertically sheeted gabbro-pyroxenite intrusion: Feeder-zone of an ocean-island volcano (Fuerteventura, Canary Islands)

The Miocene PX1 gabbro-pyroxenite pluton, Fuerteventura, Canary Islands, is a 3.5 x 5.5 km shallow-level intrusion (0.15-0.2 GPa and 1100-1120 degrees C), interpreted as the feeder-zone to an ocean-island volcano. It displays a vertical magmatic banding expressed in five 50 to 100 metre-wide NNE-SSW trending alkaline gabbro sequences alternating with pyroxenites. This emplacement geometry was controlled by brittle to ductile shear zones, generated by a regional E-W extensional tectonic setting that affected Fuerteventura during the Miocene. At a smaller scale, the PX1 gabbro and pyroxenite bands consist of metre-thick differentiation units, which suggest emplacement by periodic injection of magma pulses as vertical dykes that amalgamated, similarly to a sub-volcanic sheeted dyke complex. Individual dykes underwent internal differentiation following a solidification front parallel to the dyke edges. This solidification front may have been favoured by a significant lateral/horizontal thermal gradient, expressed by the vertical banding in the gabbros, the fractionation asymmetry within individual dykes and the migmatisation of the wall rocks. Pyroxenitic layers result from the fractionation and accumulation of clinopyroxene +/- olivine +/- plagioclase crystals from a mildly alkaline basaltic liquid. They are interpreted as truncated differentiation sequences, from which residual melts were extracted at various stages of their chemical evolution by subsequent dyke intrusions, either next to or within the crystallising unit. Compaction and squeezing of the crystal mush is ascribed to the incoming and inflating magma pulses. The expelled interstitial liquid was likely collected and erupted along with the magma flowing through the newly injected dykes. Clinopyroxene mineral orientation - as evidenced by EBSD and micro X-ray tomography investigations - displays a marked pure-shear component, supporting the interpretation of the role of compaction in the generation of the pyroxenites. Conversely, gabbro sequences underwent minor melt extraction and are believed to represent crystallised coalesced magma batches emplaced at lower rates at the end of eruptive cycles. Clinopyroxene orientations in gabbros record a simple shear component suggesting syn-magmatic deformation parallel to observed NNE-SSW trending shear zones induced by the regional tensional stress field. This emplacement model implies a crystallisation time of 1 to 5 years for individual dykes, consistent with PX1 emplacement over less than 0.5 My. A minimum amount of approximately 150 km(3) of magma is needed to generate the pluton, part of it having been erupted through the Central Volcanic Centre of Fuerteventura. If the regional extensional tectonic regime controls the PX1 feeder-zone initiation and overall geometry, rates and volumes of magma depend on other, source-related factors. High injection rates are likely to induce intrusion growth rates larger than could be accommodated by the regional extension. In this case, dyke intrusion by propagation of a weak tip, combined with the inability of magma to circulate through previously emplaced and crystallised dykes could result in an increase of non-lithostatic pressure on previously emplaced mushy dyke walls; thus generating strong pure-shear compaction within the pluton feeder-zone and interstitial melt expulsion. These compaction-dominated processes are recorded by the cumulitic pyroxenite bands. (C) 2010 Elsevier B.V. All rights reserved.

Modeling of in-situ crystallization processes in the Permian mafic layered intrusion of Mont Collon (Dent Blanche nappe, western Alps)

The Mont Collon mafic complex is one of the best preserved examples of the Early Permian magmatism in the Central Alps, related to the intra-continental collapse of the Variscan belt. It mostly consists (> 95 vol.%) of ol+hy-nonnative plagioclase-wehrlites, olivine- and cpx-gabbros with cumulitic structures, crosscut by acid dikes. Pegmatitic gabbros, troctolites and anorthosites outcrop locally. A well-preserved cumulative, sequence is exposed in the Dents de Bertol area (center of intrusion). PT-calculations indicate that this layered magma chamber emplaced at mid-crustal levels at about 0.5 GPa and 1100 degrees C. The Mont Collon cumulitic rocks record little magmatic differentiation, as illustrated by the restricted range of clinopyroxene mg-number (Mg#(cpx)=83-89). Whole-rock incompatible trace-element contents (e.g. Nb, Zr, Ba) vary largely and without correlation with major-element composition. These features are characteristic of an in-situ crystallization process with variable amounts of interstitial liquid L trapped between the cumulus mineral phases. LA-ICPMS measurements show that trace-element distribution in the latter is homogeneous, pointing to subsolidus re-equilibration between crystals and interstitial melts. A quantitative modeling based on Langmuir's in-situ crystallization equation successfully duplicated the REE concentrations in cumulitic minerals of all rock facies of the intrusion. The calculated amounts of interstitial liquid L vary between 0 and 35% for degrees of differentiation F of 0 to 20%, relative to the least evolved facies of the intrusion. L values are well correlated with the modal proportions of interstitial amphibole and whole-rock incompatible trace-element concentrations (e.g. Zr, Nb) of the tested samples. However, the in-situ crystallization model reaches its limitations with rock containing high modal content of REE-bearing minerals (i.e. zircon), such as pegmatitic gabbros. Dikes of anorthositic composition, locally crosscutting the layered lithologies, evidence that the Mont Collon rocks evolved in open system with mixing of intercumulus liquids of different origins and possibly contrasting compositions. The proposed model is not able to resolve these complex open systems, but migrating liquids could be partly responsible for the observed dispersion of points in some correlation diagrams. Absence of significant differentiation with recurrent lithologies in the cumulitic pile of Dents de Bertol points to an efficiently convective magma chamber, with possible periodic replenishment, (c) 2005 Elsevier B.V. All rights reserved.

Contact metamorphism and emplacement of the western Adamello tonalite

The geodynamic forces acting in the Earth's interior manifest themselves in a variety of ways. Volcanoes are amongst the most impressive examples in this respect, but like with an iceberg, they only represent the tip of a more extensive system hidden underground. This system consists of a source region where melt forms and accumulates, feeder connections in which magma is transported towards the surface, and different reservoirs where it is stored before it eventually erupts to form a volcano. A magma represents a mixture of melt and crystals. The latter can be extracted from the source region, or form anywhere along the path towards their final crystallization place. They will retain information of the overall plumbing system. The host rocks of an intrusion, in contrast, provide information at the emplacement level. They record the effects of thermal and mechanical forces imposed by the magma. For a better understanding of the system, both parts - magmatic and metamorphic petrology - have to be integrated. I will demonstrate in my thesis that information from both is complementary. It is an iterative process, using constraints from one field to better constrain the other. Reading the history of the host rocks is not always straightforward. This is shown in chapter two, where a model for the formation of clustered garnets observed in the contact aureole is proposed. Fragments of garnets, older than the intrusive rocks are overgrown by garnet crystallizing due to the reheating during emplacement of the adjacent pluton. The formation of the clusters is therefore not a single event as generally assumed but the result of a two-stage process, namely the alteration of the old grains and the overgrowth and amalgamation of new garnet rims. This makes an important difference when applying petrological methods such as thermobarometry, geochronology or grain size distributions. The thermal conditions in the aureole are a strong function of the emplacement style of the pluton. therefore it is necessary to understand the pluton before drawing conclusions about its aureole. A study investigating the intrusive rocks by means of field, geochemical, geochronologi- cal and structural methods is presented in chapter three. This provided important information about the assembly of the intrusion, but also new insights on the nature of large, homogeneous plutons and the structure of the plumbing system in general. The incremental nature of the emplacement of the Western Adamello tonalité is documented, and the existence of an intermediate reservoir beneath homogeneous plutons is proposed. In chapter four it is demonstrated that information extracted from the host rock provides further constraints on the emplacement process of the intrusion. The temperatures obtain by combining field observations with phase petrology modeling are used together with thermal models to constrain the magmatic activity in the immediate intrusion. Instead of using the thermal models to control the petrology result, the inverse is done. The model parameters were changed until a match with the aureole temperatures was obtained. It is shown, that only a few combinations give a positive match and that temperature estimates from the aureole can constrain the frequency of ancient magmatic systems. In the fifth chapter, the Anisotropy of Magnetic Susceptibility of intrusive rocks is compared to 3D tomography. The obtained signal is a function of the shape and distribution of ferromagnetic grains, and is often used to infer flow directions of magma. It turns out that the signal is dominated by the shape of the magnetic crystals, and where they form tight clusters, also by their distribution. This is in good agreement with the predictions made in the theoretical and experimental literature. In the sixth chapter arguments for partial melting of host rock carbonates are presented. While at first very surprising, this is to be expected when considering the prior results from the intrusive study and experiments from the literature. Partial melting is documented by compelling microstructures, geochemical and structural data. The necessary conditions are far from extreme and this process might be more frequent than previously thought. The carbonate melt is highly mobile and can move along grain boundaries, infiltrating other rocks and ultimately alter the existing mineral assemblage. Finally, a mineralogical curiosity is presented in chapter seven. The mineral assemblage magne§site and calcite is in apparent equilibrium. It is well known that these two carbonates are not stable together in the system Ca0-Mg0-Fe0-C02. Indeed, magnesite and calcite should react to dolomite during metamorphism. The presented explanation for this '"forbidden" assemblage is, that a calcite melt infiltrated the magnesite bearing rock along grain boundaries and caused the peculiar microstructure. This is supported by isotopie disequilibrium between calcite and magnesite. A further implication of partially molten carbonates is, that the host rock drastically looses its strength so that its physical properties may be comparable to the ones of the intrusive rocks. This contrasting behavior of the host rock may ease the emplacement of the intrusion. We see that the circle closes and the iterative process of better constraining the emplacement could start again. - La Terre est en perpétuel mouvement et les forces tectoniques associées à ces mouvements se manifestent sous différentes formes. Les volcans en sont l'un des exemples les plus impressionnants, mais comme les icebergs, les laves émises en surfaces ne représentent que la pointe d'un vaste système caché dans les profondeurs. Ce système est constitué d'une région source, région où la roche source fond et produit le magma ; ce magma peut s'accumuler dans cette région source ou être transporté à travers différents conduits dans des réservoirs où le magma est stocké. Ce magma peut cristalliser in situ et produire des roches plutoniques ou alors être émis en surface. Un magma représente un mélange entre un liquide et des cristaux. Ces cristaux peuvent être extraits de la source ou se former tout au long du chemin jusqu'à l'endroit final de cristallisation. L'étude de ces cristaux peut ainsi donner des informations sur l'ensemble du système magmatique. Au contraire, les roches encaissantes fournissent des informations sur le niveau d'emplacement de l'intrusion. En effet ces roches enregistrent les effets thermiques et mécaniques imposés par le magma. Pour une meilleure compréhension du système, les deux parties, magmatique et métamorphique, doivent être intégrées. Cette thèse a pour but de montrer que les informations issues de l'étude des roches magmatiques et des roches encaissantes sont complémentaires. C'est un processus itératif qui utilise les contraintes d'un domaine pour améliorer la compréhension de l'autre. Comprendre l'histoire des roches encaissantes n'est pas toujours aisé. Ceci est démontré dans le chapitre deux, où un modèle de formation des grenats observés sous forme d'agrégats dans l'auréole de contact est proposé. Des fragments de grenats plus vieux que les roches intru- sives montrent une zone de surcroissance générée par l'apport thermique produit par la mise en place du pluton adjacent. La formation des agrégats de grenats n'est donc pas le résultat d'un seul événement, comme on le décrit habituellement, mais d'un processus en deux phases, soit l'altération de vieux grains engendrant une fracturation de ces grenats, puis la formation de zone de surcroissance autour de ces différents fragments expliquant la texture en agrégats observée. Cette interprétation en deux phases est importante, car elle engendre des différences notables lorsque l'on applique des méthodes pétrologiques comme la thermobarométrie, la géochronologie ou encore lorsque l'on étudie la distribution relative de la taille des grains. Les conditions thermales dans l'auréole de contact dépendent fortement du mode d'emplacement de l'intrusion et c'est pourquoi il est nécessaire de d'abord comprendre le pluton avant de faire des conclusions sur son auréole de contact. Une étude de terrain des roches intrusives ainsi qu'une étude géochimique, géochronologique et structurale est présente dans le troisième chapitre. Cette étude apporte des informations importantes sur la formation de l'intrusion mais également de nouvelles connaissances sur la nature de grands plutons homogènes et la structure de système magmatique en général. L'emplacement incrémental est mis en évidence et l'existence d'un réservoir intermédiaire en-dessous des plutons homogènes est proposé. Le quatrième chapitre de cette thèse illustre comment utiliser l'information extraite des roches encaissantes pour expliquer la mise en place de l'intrusion. Les températures obtenues par la combinaison des observations de terrain et l'assemblage métamorphique sont utilisées avec des modèles thermiques pour contraindre l'activité magmatique au contact directe de cette auréole. Au lieu d'utiliser le modèle thermique pour vérifier le résultat pétrologique, une approche inverse a été choisie. Les paramètres du modèle ont été changés jusqu'à ce qu'on obtienne une correspondance avec les températures observées dans l'auréole de contact. Ceci montre qu'il y a peu de combinaison qui peuvent expliquer les températures et qu'on peut contraindre la fréquence de l'activité magmatique d'un ancien système magmatique de cette manière. Dans le cinquième chapitre, les processus contrôlant l'anisotropie de la susceptibilité magnétique des roches intrusives sont expliqués à l'aide d'images de la distribution des minéraux dans les roches obtenues par tomographie 3D. Le signal associé à l'anisotropie de la susceptibilité magnétique est une fonction de la forme et de la distribution des grains ferromagnétiques. Ce signal est fréquemment utilisé pour déterminer la direction de mouvement d'un magma. En accord avec d'autres études de la littérature, les résultats montrent que le signal est dominé par la forme des cristaux magnétiques, ainsi que par la distribution des agglomérats de ces minéraux dans la roche. Dans le sixième chapitre, une étude associée à la fusion partielle de carbonates dans les roches encaissantes est présentée. Si la présence de liquides carbonatés dans les auréoles de contact a été proposée sur la base d'expériences de laboratoire, notre étude démontre clairement leur existence dans la nature. La fusion partielle est documentée par des microstructures caractéristiques pour la présence de liquides ainsi que par des données géochimiques et structurales. Les conditions nécessaires sont loin d'être extrêmes et ce processus pourrait être plus fréquent qu'attendu. Les liquides carbonatés sont très mobiles et peuvent circuler le long des limites de grain avant d'infiltrer d'autres roches en produisant une modification de leurs assemblages minéralogiques. Finalement, une curiosité minéralogique est présentée dans le chapitre sept. L'assemblage de minéraux de magnésite et de calcite en équilibre apparent est observé. Il est bien connu que ces deux carbonates ne sont pas stables ensemble dans le système CaO-MgO-FeO-CO.,. En effet, la magnésite et la calcite devraient réagir et produire de la dolomite pendant le métamorphisme. L'explication présentée pour cet assemblage à priori « interdit » est que un liquide carbonaté provenant des roches adjacentes infiltre cette roche et est responsable pour cette microstructure. Une autre implication associée à la présence de carbonates fondus est que la roche encaissante montre une diminution drastique de sa résistance et que les propriétés physiques de cette roche deviennent comparables à celles de la roche intrusive. Cette modification des propriétés rhéologiques des roches encaissantes peut faciliter la mise en place des roches intrusives. Ces différentes études démontrent bien le processus itératif utilisé et l'intérêt d'étudier aussi bien les roches intrusives que les roches encaissantes pour la compréhension des mécanismes de mise en place des magmas au sein de la croûte terrestre.

Evolution of an Archean greenstone belt in the Stormy Lake - Kawashegamuk Lake area (stratigraphy, structure and geochemistry) - Western Wabigoon Subprovince, Northwest Ontario /

330 km 2 of the easter-n part of the Archean Manitou Lakes - Stormy Lake metavolcanic - metasedimentary belt have been mapped and sampled. A large number of rocks ~.vere analyzed for the major and trace constituents including the rare-earth elements (REE). The Stormy Lake - Kawashegamuk Lake area may be subdivided into four major lithological groups of supracrustal rocks 1) A north-facing mafic assemblage, consisting of pillowed tholeiitic basalts and gabbro sills characterized by flat REE profiles, is exposed in the south part of the map area and belongs to a 8000 m thick homoclinal assemblage outside the map area. Felsic pyroclastic rocks believed to have been issued from a large central vent conformably overlie the tholeiites. 2) A dominantly epiclastic group facing to the north consists of terrestrial deposits interpreted to be an alluvial fan deposit ; a submarine facies is represented by turbiditic sediments. 3) The northeastern part of the study area consists of volcanic rocks belonging to two mafic - felsic cycles facing to the southuest ; andesitic flows with fractionated REE patterns make up a large part of the upper cycle, whereas the lower cycle has a stronger chemical polarity being represented by tholeiitic flows, with flat REE, which a r e succeeded by dacitic and rhyolitic pyroclasti cs. iii 4) A thick monotonous succession of tholeiitic pillmled basalt f lows and gabbro sills with flat REE represent the youngest supracrustal rocks. TIle entire belt underwent folding, faulting and granitic plutonism during a tectono-thermal event around 2700 Ma ago. Rocks exposed in the map area were subjected to regional greenschist facies metamorphism, but higher metamorphic grades are present near late granitic intrusions. Geochemical studies have been useful in 1) distinguishing the various rock units ; 2) relating volcanic and intrusive rocks 3) studying the significance of chemical changes due to post magmatic processes 4) determining the petrogenesis of the major volcanic rock types. In doing so, two major volcanic suites have been recognized : a) a tholeiitic suite, mostly represented by mafic rocks, was derived from partial melting of upper mantle material depleted in Ti, K and the light REE ; b) a calc-alkalic suite which evolved from partial melting of amphibolite in the lower crust. The more differentiated magma types have been produced by a multistage process involving partial melting and fractional crystallization to yield a continuum of compos i t i ons ranging from basaltic andesite to rhyolite. A model for the development of the eastern part of the Manitou Lakes - Stormy Lake belt has been proposed.

Geology of the Rankin Inlet area, Northwest Territories /

The Rankin Inlet area, on the west shore of Hudson Bay in the Northwest Territories, is in the Churchill Structural Province. Metamorphosed volcanic and sedimentary rocks, previously mapped as Archean and part of the Kaminak Group, underlie most of the area. The Rankin Inlet Group consists of greywacke, with minor conglomeratic greywacke, quartzite and dolomite, overlain by massive and pillowed basaltic flows. Gabbro sills intrude the sediments near the base of the volcanic sequence and three serpentinite sills outcrop at the base of the volcanic sequence. The sediments are in fault-contact with quartz monzonite to the south and were intruded by granitic rocks to the northwest. Two periods of folding were defined by the mapping. The first generation folds are recumbent isoclinal folds, with northwest-trending and northeast-dipping axial planes, formed through gravitational sliding. The second generation folds are symmetrically disposed about the axis of the granitic intrusion and have east-southeast trending and nearly vertical axial planes. Whole-rock analysis of 64 rock samples indicates that metasomatic alteration accompanied the intrusion of both the granitic rocks and the serpentinite. The volcanic rocks, gabbro and serpentinite were derived from a magma of oceanic tholeiitic affinities. The stratigraphic sequence and chemistry of the volcanic rocks of the Rankin Inlet Group indicate that this assemblage is correlative with the Hurwitz Group rather than the Kaminak Group and is therefore Aphebian in age.

A reconnaissance study of the metamorphic petrology and volcanic geochemistry of a portion of the Island Lake greenstone belt, Manitoba /

The Island Lake greenstone belt is one of the major Archean supracrustal exposures in the northwestern part of the Superior Province of the Canadian Shield. This belt is subdivided into two units: 1) a lower sequence characterised by pillowed to massive, locally pyroclastic, basalt to andesite with a thin central zone of felsic derivatives, all of which are interbedded with and overlain by thick sequences of turbidite facies rock; 2) the upper unit which consists of thick stratified conglomerate overlain by thickly bedded arkose and feldspathic greywacke. Reconnaissance sampling traverses were completed across both the strike of the belt and along its margins with adjacent granitoids. Most of the belt is within the greenschist metamorphic f acies with amphibolite facies occurring in certain areas near t he margins. A post-tectonic, low pressure thermal event may be responsible for the development of a unit of cordierite schi s t which stretches southeastwards from the east end of Cochrane Bay. Volcanism is cyclical in nature changing from tholeiitic to calc-alkaline. There is a general progression in the character of the lavas from mafic t o felsic with stratigraphic height. Chemica l d a ta sugges t that h i gh level fractionation of a mantle- derived ' dry' magma i s t he s ource of the thole i iti c lavas. Contamination of this magma with 'we t' sia l and subsequent fractionation may be r esponsi b l e for the calcalkaline phases .Observations of stratigraphic relationships (in particular the contact between the supracrustals and the granitoids) coupled with the metamorphic and chemical studies, allow the construction of a preliminary model for the evolution of the Island Lake greenstone belt. The following sequential development is suggested: 1) a platform stage characterised by the subaqueous effusion of mafic to intermediate lavas of alternating tholeiitic and calc-alkaline affinities; 2) an edifice stage marked by the eruption of felsic calc-alkaline rocks; 3) an erosional stage characterised by the deposit~on of thick sequences of turbidite facies rocks; 4) the impingement of granitic masses into the margins of the greenstone belt, which was probably related to a downward warping of the supracrustal pilei 5) the erosion of sialic massifs surrounding and within the greenstone belt and of early supracrustal piles, to give the clastic upper unit.

Petrography, geochemistry and structure of the Timmins area, Ontario

Regional structural analysis of the Timmins area indicates four major periods of tectonic deformation. The DI deformation is characterized by a series of isoclinal FI folds which are outlined in the study area by bedding, pillow tops and variolitic flows. The D2 deformation developed the Porcupine Syncline and refolded the Fl folds about a NE. axis. A pervasive S2 foliation developed during low grade (greenschist) regional metamorphism associated with the D2 deformation. The S2 foliation developed south of the Destor-Porcupine Break. The third phase of tectonic D3 deformation is recognized by the development of a S3 sub-horizontal crenulation cleavage which developed on the plane of the S2 foliation. No meso scopic folds are associated with this deformation. The 8 3 crenulation cleavage is observed south of the Destor-Porcupine Break. The D4 tectonic deformation is recorded as a subvertical S4 crenulation cleavage which developed on the plane of the S2 foliation and also offsets the S3 crenulation cleavage. Macroscopic F4 folds have refolded the F2 axial plane. No metamorphic recrystallization is associated with this deformation. The S4 crenulation cleavage is observed south of the Destor-Porcupine Break. Petrographic evidence indicates that the Timmins area has been subjected to pervasive regional low grade (greenschist) metamorphism which has recrystallized the original mineralogy. South of the study are~ the Donut Lake ultramafic lavas have been subjected to contact medium grade (amphibolite facies) metamorphism associated with the intrusion of the Peterlong Lake Complex. The Archean volcanic rocks of the Timmins area have been subdivided into komatiitic, tholeiitic and calcalkaline suites based on Zr, Ti0 2 and Ni. The three elements were used because of their r e lative immobility during subsequent metamorphic events. Geochemical observations in the Timmins area indicates that the composition of the Goose Lake and Donut Lake Formations are a series of peridotitic, pyroxenitic and basaltic komatiites. The Lower Schumacher Formation is a sequence of basaltic komatiites while the upper part of the Lower Schumacher Formation is an intercalated sequence of basaltic komatiites and low Ti0 2 tholeiites. The variolitic flows are felsic tholeiites in composition and geochemical evidenc e sugg ests that they developed as a n immiscible splitting of a tholeiitic magma. The Upper Schumacher Formation is a sequence of tholeiitic rocks dis p laying a mild iron enrichment. The Krist and Boomerang Formations are the felsic calc-alkaline rocks of the study area which are characteristically pyroclastic. The Redstone Fo rmation is dominantly a calc-alkali ne sequence of volcani c rocks whose minor mafic end me mbers exposed in 1t.he study hav e basaltic komatiitic compositions. Geochemical evidence sugges ts that the Keewatin-type se dimentary rocks have a composition similar to a quartz diorite or a granodiorite. Fi e l d obs ervations and petrographic evidence suggests that they were derived fr om a distal source and now repr esent i n part a turbidite sequence. The Timiskaming-type sedimentary rocks approach the c omp osi t ion of the felsic calc-alkaline rocks of the study area . The basal conglomerate in the study are a sugge s ts that th e uni t was derived fr om a proximal source. Petrographic and ge ochemical evidence suggests that the peridotitic and pyroxenitic komatiites originated as a 35-55% partial melt within the mantle, in excess of 100 Km. depth. The melt ros e as a diapir with the subsequent effusion of the ultramafic lavas, The basaltic komatiites and tholeiitic rocks originated in the mantle from lesser degrees of partial melting and fractionated in low pressure chambers. Geochemical evidence suggests a "genetic link" between the basaltic komatiites and tholeiites, The calc-alkaline rocks developed as a result of the increa.se In PO in the magma chamber. The felsic calcalkaline rocks are a late stage effusion possibly the last major volcanic eruptions in the area.

Physical volcanology, sedimentology, stratigraphy and petrochemistry of the Berry Creek metavolcanics: an Archean calc-alkaline complex, Lake of the Woods, Ontario

The steeply dipping, isoclinally folded early Precambrian (Archean) Berry Creek Metavolcanic Complex comprises primary to resedimented pyroclastic, epiclastic and autoclastic deposits. Tephra erupted from central volcanic edifices was dumped by mass flow mechanisms into peripheral volcanosedimentary depressions. Sedimentation has been essentially contemporaneous with eruption and transport of tephra. The monolithic to heterolithic tuffaceous horizons are interpreted as subaerial to subaqueous pumice and ash flows, secondary debris flows, lahars, slump deposits and turbidites. Monolithic debris flows, derived from crumble breccia and dcme talus, formed during downslope collapse and subsequent gravity flowage. Heterolithic tuff, lahars and lava flow morphologies suggest at least temporary emergence of the edifice. Local collapse may have accompanied pyroclastic volcanism. The tephra, produced by hydromagmatic to magmatic eruptions, were rapidly transported, by primary and secondary mechanisms, to a shallow littoral to deep water subaqueous fan developed upon the subjacent mafic metavolcanic platform. Deposition resulted from traction, traction carpet, and suspension sedimentation from laminar to turbulent flows. Facies mapping revealed proximal (channel to overbank) to distal facies epiclastics (greywackes, argillite) intercalated with proximal vent to medial fan facies crystal rich ash flows, debris flows, bedded tuff and shallow water to deep water lava flows. Framework and matrix support debris flows exhibit a variety of subaqueous sedimentary structures, e.g., coarse tail grading, double grading, inverse to normal grading, graded stratified pebbly horizons, erosional channels. Pelitic to psammitic AE turbidites also contain primary stru~tures, e.g., flames, load casts, dewatering pipes. Despite low to intermediate pressure greenschist to amphibolite grade metamorphism and variably penetrative deformation, relicts of pumice fragments and shards were recognized as recrystallized quartzofeldspathic pseudomorphs. The mafic to felsic metavolcanics and metasediments contain blasts of hornblende, actinolite, garnet, pistacitic epidote, staurolite, albitic plagioclase, and rarely andalusite and cordierite. The mafic metavolcanics (Adams River Bay, Black River, Kenu Lake, Lobstick Bay, Snake Bay) display _holeiitic trends with komatiitic affinities. Chemical variations are consistent with high level fractionation of olivine, plagioclase, amphibole, and later magnetite from a parental komatiite. The intermediate to felsic (64-74% Si02) metavolcanics generally exhibit calc-alkaline trends. The compositional discontinuity, defined by major and trace element diversity, can be explained by a mechanism involving two different magma sources. Application of fractionation series models are inconsistent with the observed data. The tholeiitic basalts and basaltic andesites are probably derived by low pressure fractionation of a depleted (high degree of partial melting) mantle source. The depleted (low Y, Zr) calc-alkaline metavolcanics may be produced by partial melting of a geochemically evolved source, e.g., tonalitetrondhjemite, garnet amphibolite or hydrous basalt.

Les tiers, vecteurs du réseau social. Les personnes et les biens dans le Code civil du Québec.

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Computation of locally free class groups

We show that the locally free class group of an order in a semisimple algebra over a number field is isomorphic to a certain ray class group. This description is then used to present an algorithm that computes the locally free class group. The algorithm is implemented in MAGMA for the case where the algebra is a group ring over the rational numbers.

Computing Generators of Free Modules over Orders in Group Algebras

Let E be a number field and G be a finite group. Let A be any O_E-order of full rank in the group algebra E[G] and X be a (left) A-lattice. We give a necessary and sufficient condition for X to be free of given rank d over A. In the case that the Wedderburn decomposition E[G] \cong \oplus_xM_x is explicitly computable and each M_x is in fact a matrix ring over a field, this leads to an algorithm that either gives elements \alpha_1,...,\alpha_d \in X such that X = A\alpha_1 \oplus ... \oplusA\alpha_d or determines that no such elements exist. Let L/K be a finite Galois extension of number fields with Galois group G such that E is a subfield of K and put d = [K : E]. The algorithm can be applied to certain Galois modules that arise naturally in this situation. For example, one can take X to be O_L, the ring of algebraic integers of L, and A to be the associated order A(E[G];O_L) \subseteq E[G]. The application of the algorithm to this special situation is implemented in Magma under certain extra hypotheses when K = E = \IQ.

Computations in Relative Algebraic K-Groups

Let G be finite group and K a number field or a p-adic field with ring of integers O_K. In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K_0(O_K[G],K) as an abstract abelian group. We solve the discrete logarithm problem, both in K_0(O_K[G],K) and the locally free class group cl(O_K[G]). All algorithms have been implemented in MAGMA for the case K = \IQ. In the second part of the manuscript we prove formulae for the torsion subgroup of K_0(\IZ[G],\IQ) for large classes of dihedral and quaternion groups.

Ein Algorithmus zur numerischen Verifikation der äquivarianten Tamagawazahlvermutung für eine Familie von Zahlkörpererweiterungen

Sei $N/K$ eine galoissche Zahlkörpererweiterung mit Galoisgruppe $G$, so dass es in $N$ eine Stelle mit voller Zerlegungsgruppe gibt. Die vorliegende Arbeit beschäftigt sich mit Algorithmen, die für das gegebene Fallbeispiel $N/K$, die äquivariante Tamagawazahlvermutung von Burns und Flach für das Paar $(h^0(Spec(N), \mathbb{Z}[G]))$ (numerisch) verifizieren. Grob gesprochen stellt die äquivariante Tamagawazahlvermutung (im Folgenden ETNC) in diesem Spezialfall einen Zusammenhang her zwischen Werten von Artinschen $L$-Reihen zu den absolut irreduziblen Charakteren von $G$ und einer Eulercharakteristik, die man in diesem Fall mit Hilfe einer sogenannten Tatesequenz konstruieren kann. Unter den Voraussetzungen 1. es gibt eine Stelle $v$ von $N$ mit voller Zerlegungsgruppe, 2. jeder irreduzible Charakter $\chi$ von $G$ erfüllt eine der folgenden Bedingungen 2a) $\chi$ ist abelsch, 2b) $\chi(G) \subset \mathbb{Q}$ und $\chi$ ist eine ganzzahlige Linearkombination von induzierten trivialen Charakteren; wird ein Algorithmus entwickelt, der ETNC für jedes Fallbeispiel $N/\mathbb{Q}$ vollständig beweist. Voraussetzung 1. erlaubt es eine Idee von Chinburg ([Chi89]) umzusetzen zur algorithmischen Berechnung von Tatesequenzen. Dabei war es u.a. auch notwendig lokale Fundamentalklassen zu berechnen. Im höchsten zahm verzweigten Fall haben wir hierfür einen Algorithmus entwickelt, der ebenfalls auf den Ideen von Chinburg ([Chi85]) beruht, die auf Arbeiten von Serre [Ser] zurück gehen. Für nicht zahm verzweigte Erweiterungen benutzen wir den von Debeerst ([Deb11]) entwickelten Algorithmus, der ebenfalls auf Serre's Arbeiten beruht. Voraussetzung 2. wird benötigt, um Quotienten aus den $L$-Werten und Regulatoren exakt zu berechnen. Dies gelingt, da wir im Fall von abelschen Charakteren auf die Theorie der zyklotomischen Einheiten zurückgreifen können und im Fall (b) auf die analytische Klassenzahlformel von Zwischenkörpern. Ohne die Voraussetzung 2. liefern die Algorithmen für jedes Fallbeispiel $N/K$ immer noch eine numerische Verifikation bis auf Rechengenauigkeit. Den Algorithmus zur numerischen Verifikation haben wir für $A_4$-Erweiterungen über $\mathbb{Q}$ in das Computeralgebrasystem MAGMA implementiert und für 27 Erweiterungen die äquivariante Tamagawazahlvermutung numerisch verifiziert.

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