CrystalMom: a new model for the evolution of crystal size distributions in magmas with the quadrature-based method of moments

Nucleation and growth of crystals, and the resulting crystal size distribution, play a fundamental role in controlling the physical properties of magmas and consequently the dynamics of the eruptions. In the past decades, laboratory experiments demonstrated that size and shape of crystals strongly control the physical properties of magma and lava. Additionally, natural and experimental samples are usually characterized in terms of their crystal size distribution to link it with physical processes that are not directly observable, such as cooling or decompression mechanisms. In this paper, we present CrystalMoM, a new predictive model, based on the quadrature-based method of moments, developed for studying the kinetic of crystallization in volcanic systems. The quadrature-based method of moments, well established in the field of chemical engineering, represents a mesoscale modelling approach that rigorously simulates the space–time evolution of a distribution of particles, by considering its moments. The method is applied here, for the first time, for studying the equilibrium/disequilibrium crystallization in magma, modelling the temporal evolution of the moments of a crystal size distribution. The model, verified against numerical and experimental data, represents a valuable tool to infer the cooling and decompression rates from the crystal size distribution observed in natural samples.     

An image analysis method to determine crystal size distributions of olivine in kimberlite

Crystal size distributions (CSDs) are a standard method of describing populations of crystals within magmatic rocks. Olivine is the dominant phase in kimberlite (∼40–50% by volume) and features a diverse range of sizes, shapes and origins. CSDs of olivine provide a logical means of semi-quantitatively characterising kimberlite. The CSDs can then be used to distinguish or correlate between kimberlite bodies or to investigate processes related to ascent, emplacement and eruption. In this paper, we present an automatic image analysis technique that provides efficient quantification of olivine CSDs within digital images of polished slabs of kimberlite. This technique relies on a combination of algorithms for detecting regions of interest (ROI) and for segmentation of ROIs in order to identify individual olivine crystals that are used for size distribution datasets. The detection process identifies regions expected to be olivine using a model-based colour detection technique using Mahalanobis distance combined with texture analysis based on local standard deviation and greyscale foreground enhancement techniques. The segmentation process separates adjacent domains to identify individual crystals using an iterative marker-based watershed algorithm to separate adjoined structures of varying sizes. We demonstrate the utility of automatic image analysis by comparing CSDs for olivine derived from this method versus results from manual digitisation of olivine grains. The automatic detection system correctly identified ∼86% of the manually detected olivine domains; ∼88% of the automatically detected regions correctly correlate to manually defined olivine grains. Discrepancies between the two methods are mostly the result of oversimplification of crystal margins (i.e. rounding) by manual tracing whereas automatic boundary recognition shows clear advantages in identifying irregularities in crystal edges. Closer examination of the results shows that both methods suffer from under-representation of smaller crystals due to: (1) human subjectivity and error in manual tracing and (2) noise removal processes in automatic detection. Automatic detection of olivine grains is much more efficient than conventional manual tracing; manual detection requires ∼6 h per sample versus ∼1 min for automatic analysis of the same sample.     

An extension of the Saltykov method to quantify 3D grain size distributions in mylonites

The estimation of 3D grain size distributions (GSDs) in mylonites is key to understanding the rheological properties of crystalline aggregates and to constraining dynamic recrystallization models. This paper investigates whether a common stereological method, the Saltykov method, is appropriate for the study of GSDs in mylonites. In addition, we present a new stereological method, named the two-step method, which estimates a lognormal probability density function describing the 3D GSD. Both methods are tested for reproducibility and accuracy using natural and synthetic data sets. The main conclusion is that both methods are accurate and simple enough to be systematically used in recrystallized aggregates with near-equant grains. The Saltykov method is particularly suitable for estimating the volume percentage of particular grain-size fractions with an absolute uncertainty of ±5 in the estimates. The two-step method is suitable for quantifying the shape of the actual 3D GSD in recrystallized rocks using a single value, the multiplicative standard deviation (MSD) parameter, and providing a precision in the estimate typically better than 5%. The novel method provides a MSD value in recrystallized quartz that differs from previous estimates based on apparent 2D GSDs, highlighting the inconvenience of using apparent GSDs for such tasks.     

Prediction of in-situ block size distributions with reference to armourstone for breakwaters

Understanding a quarry in terms of its potential for breakwater construction materials presents a special challenge for the engineering geologist. Unlike blasting in aggregates and mining operations, optimisation of the extraction process has a focus on the potential for production of large blocks for armourstone. These blocks weighing many tonnes are used for cover layers to resist wave action. The quarry-run is used for breakwater core. If the quarry has been developed as a source of materials dedicated to a breakwater construction project, the success of the project depends greatly on the blasting and production of rock sizes that are required and the avoidance of leaving a massive quantity of unused materials behind in the quarry after project completion. Prediction of in-situ block sizes such as from joint spacing data, provides the most critical input for the prediction of the blast pile block size distribution (BBSD), which in turn is a vital early design input if the constructed breakwater is to be economical as well as effective.This paper is part of a series of papers that introduces the coastal engineering motivation for this work on engineering geology, giving reasons why the prediction of the fragmentation curve of the blast products in a dedicated quarry is of such economic importance for breakwater projects. The first step towards blasted block size distribution (BBSD) prediction is the prediction of the in-situ block sized distribution (IBSD), the main subject of this paper. Drawing together research methods from the 1990s and the rock mechanics principles of discontinuity analysis, a practical step by step methodology for IBSD assessment that includes approaches that are not reliant on specialised computer software is presented. Continuing on the practical theme, a new extension of the volumetric joint count approach is suggested for IBSD prediction for the case when sparse borehole data is all that is available. A case study of IBSD assessment and the associated BBSD and blast assessment is presented from a Carboniferous limestone quarry. For clarity, details of blast design and yield curve prediction that are recommended for use in the context of armourstone production, have been presented in a companion paper. The Rosin-Rammler equation is used as an example form for the BBSD prediction of a dedicated quarry and the potential for breakwater project optimisation is illustrated. The final section sets out a method for directly comparing yield curves together with the demand for materials set by the breakwater design. On the same plot, sizes where there is a relative shortfall in production can be identified. The dependence of effective breakwater design on accurate quarry yield prediction and quarry blasting performance is discussed.     

The role of fluorine in the evolution of ultrapotassic magmas

Summary The distribution of F and, to a lesser extent, Cl between phlogopite, amphibole, apatite, and glass in kamafugites from the West Eifel, Germany, and South-West Uganda, and from lamprophyres (minettes) from Hopi-Navajo, Arizona has been determined. In addition, these elements have been analyzed in the same phases from mantle-derived xenoliths from the kamafugitic rocks. All halogen determinations were made using a JEOL 8600 electron microprobe. The F contents and trends in the minerals and glass in the kamafugites and lamprophyres are very similar to those reported for lamproites (Edgar and Charbonneau, 1991). The results indicate that F in the minerals of ultrapotassic magmas is much greater then that found in the xenoliths that are believed to represent likely source regions for such magmas. Chlorine is present in much lower amounts and in the same phases. The discrepancy between F in the xenoliths and in the lavas, and the preference for F to be incorporated in solid phases suggest that F is insufficient to account for the F found in ultrapotassic magmas or to provide for the reduced fluid conditions proposed by Foley (1988) for the genesis of such magmas. Based on these results, the genesis of ultrapotassic magmas may occur if they are partial melts of a mantle source that has been further enriched in F by repeated partial melting of mantle-derived xenoliths such as those of southwest Uganda. Alternatively the slightly higher Cl in the minerals of the xenoliths relative to the magmas suggests that Cl has been lost during degassing of the ascending magma. This may enrich the magmas in F by a dilution effect that may take place prior to the formation of phenocrystal F-rich phlogopites that are often present in ultrapotassic magmas.

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Die Rolle von fluor in der evolution ultrapotassischer magmen

Zusammenfassung Die Verteilung von Fluor and untergeordnet von Chlor zwischen Phlogopit, Amphibol, Apatit and Glas wurde an Kamafugiten aus der westlichen Eifel, Deutschland and aus Südwest-Uganda sowie an Lamprophyren (Minetten) aus Hopi-Navajo, Arizona bestimmt. Außerdem wurde der Gehalt an diesen Elementen in den gleichen Mineralphasen von Mantel-Xenolithen aus kamafugitischen Gesteinen analysiert. Die Halogenbestimmungen wurden an einer JEOL 8600 Mikrosonde durchgeführt. Die Gehalte und Verteilungstrends von Fluor in den Mineralphasen und im Glas der Kamafugite und Lamprophyre sind vergleichbar mit jenen aus Lamproiten (Edgar und Charbonneau, 1991). Die Resultate deuten an, daß der Fluorgehalt in Mineralen ultrapotassischer Magmen viel höher ist als in Xenolithen, die als Repräsentanten der Herkunftsregion derartiger Magmen gelten. Chlor tritt in den selben Mineralphasen in viel geringeren Mengen auf. Das unterschiedliche Auftreten von Fluor in den Xenolithen und in den Laven sowie der bevorzugte Einbau von Fluor in feste Mineralphasen lassen vermuten, daß dieser Gehalt an Fluor nicht ausreicht, um den hohen Fluorgehalt in ultrapotassischen Magmen und die reduzierenden Fluida-Bedingungen, wie sie von Foley (1988) für die Genese von solchen Magmen angenommen worden sind, zu erklären. Auf der Basis dieser Ergebnisse können ultrapotassische Magmen nur dann entstehen, wenn das Mantelmaterial als Herkunft für die partielle Schmelze zum Beispiel durch wiederholtes Teilaufschmelzen von Mantelxenolithen wie jenen aus Südwest-Uganda an Fluor angereichert worden ist. Als Alternative wird angenommen, daß die leicht höheren Chlorgehalte in den Mineralen der Xenolithe verglichen mit dem der Magmen durch Chlorverlust während Entgasung beim Aufstieg des Magmas zustande gekommen sind. Dadurch kam es zu einem Verdünnungseffekt, der zu einer Anreicherung von Fluor führt, vor der Bildung von F-reichem Phlogopit als Phenokristall, Kristalle, die häufig in ultrapotassischen Magmen auftreten.

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With 9 Figures     

Interfacial energy effects and the evolution of pore size distributions during quartz precipitation in sandstone

Pore size is usually thought to control the rate of crystal growth in porous geological media by determining the ratio of mineral surface area to fluid volume. However, theory suggests that in micron-scale to nanometer scale pores, interfacial energy (surface energy) effects can also become important. Interfacial energy typically increases the solubility of very small crystals growing in tiny pores, and when the fluid is close to equilibrium - as is often the case in geological systems - mineral precipitation could occur in relatively large pores, while in very small adjacent pores crystal growth might be suppressed. Such a mechanism would effectively restrict the reactive surface area of the porous medium, thereby reducing the bulk reaction rate. We investigated the pore size distributions in naturally cemented sandstone adjacent to an isolated stylolite and found that quartz precipitation was inhibited in pores smaller than 10 μm in diameter. Furthermore, we demonstrate that kinetic formulations which assume constant solubility cannot reproduce the observed pore size patterns in mineralized samples; by contrast, excellent fits with the data are obtained when interfacial energy effects are taken into account. Reaction rates in geological media determined in field studies can be orders of magnitude lower than those measured in laboratory experiments, and we propose that reduced reaction rates in porous media with micron and submicron-scale porosity could account for much of the apparent paradox.     

Major element evolution of basaltic magmas: a comparison of the information in CMAS and ALFE projections

Basalt petrologists disagree as to whether the commonly used projection, forsterite-diopside-silica, in the system CMAS (CaO-MgO-Al₂O₃-SiO₂), can adequately resolve differences in basaltic glass compositions for purposes of petrogenetic modelling. Here, we suggest than an analogous plot, the aluminium-factor diagram (ALFE) of Nesbitt and Cramer (1981), has greater diagnostic value than Fo-Di-Sil. A plot of molar (Al₂O₂-CaO-Na₂O-K₂O)/(FeO + MgO) vs FeO/(FeO + MgO), it produces more coherent patterns both for experimental basalt glasses, and for natural lavas. It is, like Fo-Di-Sil, a projection through plagioclase, but has the advantage that it monitors changes in Fe/(Fe + Mg) in melts and associated crystalline phases, and is particularly useful in assessing the timing of clinopyroxene crystallization in a suite of lavas. The diagram owes its greater resolving power to the fact that the computation of its coordinates is less sensitive to analytical uncertainty than for Fo-Di-Sil. In the latter diagram, normative quartz is calculated as a residual and thus manifests the uncertainties in all the major elements.     

Contribution of enclave studies to the understanding of origin and evolution of granitic magmas

Enclaves give important information on the origin and evolution of granitic magmas.The presence in a granite of surmicaceous enclaves (restites) is good evidence of continental crust contribution to magma genesis. The presence of dark microgranular enclaves is an indication of mantle contribution. The joint presence in the same granite of the two types of enclaves indicates that its magma has probably more than one source.Dark microgranular enclaves, and their host granites as well, are hybridized rocks resulting from incomplete mixing (or mingling) of more acidic and basic components. Enclave studies allow one to specify mixing conditions.When mixing occurs relatively early with respect to granite crystallization, only earlier-formed granitic minerals (zircon, apatite ...) may be incorporated in the basic magma. When mixing occurs later all granitic minerals may be involved.When all the dark microgranular enclaves of a granite are similar, the intervention of a single mixing event can be assumed. On the contrary, when several chemically and mineralogically contrasted varieties occur, several mixing events can be assumed. The order of these events may be deduced from the nature of the granitic minerals present in the enclaves (early of late minerals) or sometimes by observation of double enclaves.Enclave shapes bring information on the distance between the place of mixing and the place of observation. Enclaves with irregular or crenulated margins, or with chilled margins as well, always occur near mixing places. The enclave transport in the magma makes these characteristics disappear.In spite of hybridization processes, the primitive composition of the basic component of the mixture may sometimes be recognized. A systematic identification of this component in the different granites from the same orogen should allow to understand the space and time evolution of basic magmatism in an orogen.Magma mixing is a cause of heterogeneity in granites, but it is also an important factor of homogenization as the thermal contribution of the basic magma produces new mingling of the components and sometimes new intrusive processes.

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Zusammenfassung Einschlüsse in Graniten geben wichtige Auskünfte über die Herkunft und Entwicklung der granitischen Magmen.Das Vorkommen restitischer glimmerreicher Einschlüsse (»enclaves surmicacées«) beweist die Teilnahme kontinentaler Kruste an der Magmenbildung. Die kleinkörnigen dunklen Einschlüsse dagegen sind Hinweise auf die Beteiligung von Mantelmaterial. Das Auftreten beider Arten von Einschlüssen ist ein starkes Argument für das Zusammenwirken beider Prozesse.Die kleinkörnigen dunklen Einschlüsse und der sie einschlie\ende Granit sind hybride Gesteine, sie entstehen durch unvollständige Mischung eines basischen und eines sauren Magmas. Durch genauere Untersuchung der Einschlüsse lassen sich die Vorgänge der Vermischung noch weiter erschlie\en.Wenn die Vermischung in einem Zustand eintritt, in welchem die Magmen noch wenig kristallisiert sind, dann werden nur die frühesten Mineralbildungen des Granits (Zirkon, Apatit) in die Einschlüsse aufgenommen. In späteren Stadien können alle jeweils schon kristallisierten Mineralphasen ausgetauscht werden. Tritt nur ein Typ basischer Einschlüsse in einem Granit auf, so ist dies ein Argument für nur einen Akt der Magmenmischung. Kommen dagegen mehrere Arten basischer Einschlüsse in einem Granit vor, die chemisch und mineralogisch deutlich verschieden sind, dann kann mit mehreren Vermischungsphasen gerechnet werden. Ihre Abfolge kann aus der Natur der ausgetauschten Minerale (Frühbis Spätausscheidungen) oder gegebenenfalls aus »doppelten« Einschlüssen abgeleitet werden.Die Gestalt der basischen Einschlüsse hängt von dem Abstand zwischen dem Ort der ersten Magmenvermischung und dem jetzt erreichten Ort im Granitkörper ab. Einschlüsse mit unregelmä\igen oder gekräuselten (crenulated) Rändern befinden sich stets noch in der Nähe des Ortes der Vermischung. Einschlüsse mit glatten Umrissen und ovoidaler Gestalt haben einen mehr oder weniger weiten Transport hinter sich.Gelegentlich kann noch die ursprüngliche Zusammensetzung des basischen Magmas ermittelt werden. Die Kenntnis dieser Magmenanteile in allen Graniten eines Orogens könnte die Entwicklung der basischen Magmen während der Orogenese erkennen lassen.Die Vermischung mit basischem Magma ist zwar eine Ursache der Heterogenität von Granitkörpern, auf der anderen Seite bewirkt aber die Wärmezufuhr durch den basischen Anteil und der damit verbundene »Rühreffekt« eine Homogenisierung und Belebung des Intrusionsvorganges.

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Résumé Les enclaves donnent d'importantes informations sur l'origine et l'évolution des magmas granitiques.La présence dans un granite d'enclaves surmicacées (restites) est une preuve de participation de la croûte continentale à la genèse de son magma. Celle d'enclaves microgrenues sombres est une preuve de contribution mantellique. La présence des deux types d'enclaves dans le mÊme granite est un fort argument pour une origine double.Les enclaves microgrenues sombres et le granite qui les entoure sont des roches hybrides résultant du mélange incomplet de magmas plus acides et plus basiques. L'étude des enclaves permet de préciser les conditions de mélange.Quand le mélange intervient à un stade où les magmas sont encore peu cristallisés, seuls les minéraux précoces (zircon, apatite) du granite sont incorporés dans les enclaves. Quand il se produit plus tardivement, toutes les phases minérales peuvent Être échangées.La présence d'un seul type d'enclaves basiques dans un granite est un argument pour l'intervention d'un seul stade de mélange. Au contraire, l'existence de plusieurs familles d'enclaves basiques, chimiquement et minéralogiquement bien différentes, témoigne de l'existence de plusieurs stades. L'ordre de ces événements peut Être déduit de la nature des minéraux échangés (précoces ou tardifs) ou parfois grâce à l'existence d'enclaves doubles.La forme des enclaves basiques renseigne sur la distance entre lieu de mélange et lieu d'observation. Les enclaves à bords irréguliers ou crénelés, ou avec bordures figées sont toujours proches du lieu de mélange. Les enclaves ovoÏdes, aux formes régulières, ont subi un transport plus ou moins long.La composition originale des magmas basiques mélangés peut parfois Être identifiée. Cette identification dans tous les granites d'un mÊme orogène permettrait de connaÎtre la distribution et l'évolution du magmatisme basique au cours de l'orogenèse.Les mélanges de magmas sont assurément une cause d'hétérogénéité des granites, mais ils sont aussi un important facteur d'homogénéisation car l'apport thermique des magmas basiques favorise le brassage magmatique et la reprise du mécanisme intrusif.

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Crystallization conditions of leucite-bearing magmas and their implications on the magmatological evolution of ultrapotassic magmas: the Vico Volcano, Central Italy

Summary Mineral compositions in leucite-bearing and leucite-free rocks from Vico volcano are reported. FeO/MgO partitioning (Kd_ol/liq) between olivine and latite (0.14–0.22), and between olivine and trachyte (0.06–0.10) indicates a lack of equilibrium between mineral and host rock. This suggests that mingling and/or mixing between magmas was a leading process during magmatic differentiation. In addition, a phono-tephrite olivine population with high (0.84) and equilibrium (0.23–0.29) Kd_ol/liq values has been produced by the interaction of differently evolved magmas. Zoning in clinopyroxene and plagioclase from these rocks recorded the same processes. In addition, resorbed quartz xenocrysts with coronas of clinopyroxene microlites indicate that digestion of crustal rocks occurred during the residence of magma in a shallow level reservoir. Increasing Fe coupled with decreasing Ca in diopside crystals from some phonolites, together with the petrographic and trace element data, indicate that polybaric fractional crystallisation also may be involved in the genesis of magmas of the second period of Vico activity. Leucite-free trachybasalts erupted in a late stage contain highly forsteritic olivine phenocrysts (forsterite 84–88 mol.%) in-equilibrium (Kd_ol/liq = 0.24–0.35) with the host rock, which indicate that they did not suffer chemical modification at low pressure. Received November 28, 2000; revised version accepted September 27, 2001     

Changes in fine sediment size distributions due to interactions with streambed sediments

In the classical view of fine sediment transport and deposition in streams, particles are expected to be removed from flowing water simply by direct sedimentation onto the streambed. However, recent research has demonstrated that fine sediments can propagate into pore spaces in the streambed due to hyporheic exchange and be removed by a combination of physical and chemical processes. This behaviour can significantly alter fine sediment size distributions during in-stream sediment transport because the physical transport of fine particles and their attachment to bed sediment grains are both a function of the particle size. Herein, we present model simulations for deposition of suspended sediments with a bimodal size distribution. We also applied this approach to analyse the results of laboratory flume observations of suspended sediment deposition. Results from model simulations and flume experiments clearly show that the rate of particle deposition increases with increasing particle size. Thus, the larger particles are preferentially removed from mixtures and there is a fining of the mixed suspensions over time. Both particle deposition mechanisms, i.e. particle sedimentation and filtration, contribute to the fining of the mixed fine particle suspensions over time, and their effects are clearly demonstrated using the fundamental process-based model. These results clearly demonstrate the effects of stream-subsurface exchange on the temporal evolution of the suspended fine sediment size distribution in downstream transport.     

Basic magmas in the early evolution of the Southernmost Patagonian Batholith,Chile

Basic magmas played an important role in the early evolution of a segment of the Patagonian Batholith (141 to 34 m.y.) exposed south of Tierra del Fuego, Chile. The basic magmatism lasted 40 m.y. to possibly 60 m.y. (141 to 84 m.y.). It is represented by early gabbros and hornblendites (141 to 103 m.y.) and by synplutonic dikes and some of the numerous basic inclusions in the granitoids of a Cretaceous (113 to 84 m.y.) plutonic group. Some of the inclusions are interpreted as the disrupted portions of synplutonic dikes.Available data indicate that basaltic to rhyolitic volcanism which took place in the area during the Early Cretaceous was contemporaneous with the basic magmatism reported here and during its latest stage, with granitoid magmas. Therefore, gabbros apparently formed part of the roots of the island arc during the early stages of its evolution, whilst granitoids may have had a greater participation at a later stage in the root system.

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Zusammenfassung Basische Magmen spielten eine bedeutende Rolle bei der frühen Entwicklung eines Abschnittes des Patagonischen Batholithen (141-34 Mio. J.), der südlich Tierra del Fuego, Chile, aufgeschlossen ist. Der basische Magmatismus dauerte 40 bis etwa 60 Millionen Jahre (141-84 Mio. J.). Er besteht aus frühen Gabbros und Hornblenditen (141-103 Mio. J.) und aus synplutonischen Gängen und einigen der zahlreichen basischen Einschlüsse in dem Granitkomplex der kretazischen Plutonit-Gruppe (113-84 Mio. J.). Einige der Einschlüsse werden als isolierte Anteile von synplutonischen Gängen gedeutet.Die zur Verfügung stehenden Daten belegen, daß der basaltische bis rhyolitische Vulkanismus, der sich in diesem Gebiet während der frühen Kreide ereignete, gleichzeitig mit dem hier vorgestellten basischen Magmatismus und in dessen letztem Stadium zusammen mit granitischen Magmen ereignete. Daher waren offensichtlich Gabbros an den Wurzeln des Inselbogens während der frühen Entwicklungsstadien beteiligt, während Granotioide mit größerem Anteil an dem späterem Stadium des Wurzelsystems beteiligt waren.

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Resumen Magmas básicos tuvieron un importante rol en la historia temprana del segmento del Batolito Patagónico (141 a 34 M a) que se expone al sur de Tierra del Fuego, Chile. El magmatismo básico tuvo una duración de unos 40 Ma y hasta unos 60 Ma (141 a 84 Ma). Este magmatismo está representado por gabros y hornblenditas (141 a 103 Ma), por diques sinplutónicos y por algunas de las numerosas inclusiones básicas en los granitoides pertenecientes a un grupo plutónico del Cretácico (113 a 84 Ma). Algunas de las inclusiones se interpretan como partes de diques sinplutónicos.La información existente permite indicar que el volcanismo basáltico y riolítico que tuvo lugar en la región, durante el Cretácico Inferior, fue contemporáneo con el magmatismo básico del que se informa en este artículo. Aparentemente, la etapa final de este volcanismo habría sido coetáneo con un importante magmatismo granítico. En consecuencia, aparentemente, en las etapas iniciales de la evolución de la cadena volcánica, los gabros habrían constituído parte de su raíz, mientras que posteriormente habría habido mayor participación de granitoides.

     

The central Kenya peralkaline province: Insights into the evolution of peralkaline salic magmas

The central Kenya peralkaline province comprises five young (< 1 Ma) volcanic complexes dominated by peralkaline trachytes and rhyolites. The geological and geochemical evolution of each complex is described and issues related to the development of peralkalinity in salic magmas are highlighted. The peralkaline trachytes may have formed by fractionation of basaltic magma via metaluminous trachyte and in turn generated pantellerite by the same mechanism. Comenditic rhyolites are thought to have formed by volatile-induced crustal anatexis and may themselves have been parental to pantelleritic melts by crystal fractionation. The rhyolites record very low temperatures of equilibration (≤ 700 °C) at low fO₂ (≤ FMQ). The development of compositional zonation within the magma reservoirs has been ubiquitous, involving up to tens of cubic km of magma at timescales of 10³–10⁴ years. Magma mixing has also been commonplace, sometimes between adjacent centres. Isotopic evidence relating to rates and timescales of pre-eruptive residence times and crystal fractionation processes is summarized.     

Modelling Nd-isotopes with a coarse resolution ocean circulation model: Sensitivities to model parameters and source/sink distributions

The neodymium (Nd) isotopic composition (?_Nd) of seawater is a quasi-conservative tracer of water mass mixing and is assumed to hold great potential for paleoceanographic studies. Here we present a comprehensive approach for the simulation of the two neodymium isotopes ¹⁴³Nd, and ¹⁴⁴Nd using the Bern3D model, a low resolution ocean model. The high computational efficiency of the Bern3D model in conjunction with our comprehensive approach allows us to systematically and extensively explore the sensitivity of Nd concentrations and ?_Nd to the parametrisation of sources and sinks. Previous studies have been restricted in doing so either by the chosen approach or by computational costs. Our study thus presents the most comprehensive survey of the marine Nd cycle to date.Our model simulates both Nd concentrations as well as ?_Nd in good agreement with observations. ?_Nd covaries with salinity, thus underlining its potential as a water mass proxy. Results confirm that the continental margins are required as a Nd source to simulate Nd concentrations and ?_Nd consistent with observations. We estimate this source to be slightly smaller than reported in previous studies and find that above a certain magnitude its magnitude affects ?_Nd only to a small extent. On the other hand, the parametrisation of the reversible scavenging considerably affects the ability of the model to simulate both, Nd concentrations and ?_Nd. Furthermore, despite their small contribution, we find dust and rivers to be important components of the Nd cycle. In additional experiments, we systematically varied the diapycnal diffusivity as well as the Atlantic-to-Pacific freshwater flux to explore the sensitivity of Nd concentrations and its isotopic signature to the strength and geometry of the overturning circulation. These experiments reveal that Nd concentrations and ?_Nd are comparatively little affected by variations in diapycnal diffusivity and the Atlantic-to-Pacific freshwater flux. In contrast, an adequate representation of Nd sources and sinks is crucial to simulate Nd concentrations and ?_Nd consistent with observations. The good agreement of our results with observations paves the way for the evaluation of the paleoceanographic potential of ?_Nd in further model studies.     

A stepwise method for determining the number of component distributions in a mixture

This paper considers the problem of estimatingm, the number of components in a finite mixture of distributions from a parametric family. A step-up procedure using the bootstrap method is proposed. Some properties of the procedure are illustrated with simulation studies. An example of the method, applied to orientation of beach clasts, is given.     

Four cultures: the evolution of a parsimonious model

Cultural theory works with a parsimonious model of four cultural types, each emanating from a specific form of organisation. The four types are identified as attitudes and values that justify the organisation. The hierarchical type, with its ranked levels and symmetrical branchings, depends on the adoption of hierarchical values and the expression of matching judgements. Likewise for the enclavist culture, the individualist culture and that of the isolates. There is no assumption of fixity, on the contrary, the four types are represented in any community, and social life is in permanent tension and flux. This article gives a summary of the early history of the theory. This revised version was published online in August 2006 with corrections to the Cover Date.     

A simple thermodynamic model for estimating the solubility of H2O in magmas

A symmetrical, strictly regular solution model is used to estimate H₂O solubilities in silicate melts. The standard state chemical potential of dissolved H₂O and the adjustable parameter in the activity coefficient are determined by least squares analyses of data on H₂O solubility in silicate melts. The adjustable parameter in the expression for the activity coefficient (In) is a function only of the anhydrous melt composition and eleven values are provided for melts ranging in composition from picrite to rhyolite. At the 95% confidence level, the model should estimate H₂O contents to within 4.8% of the amount present if the amount present is less than 10 wt.%. This compares to the reproducibility of 2.25% of the amount present for experimental determinations. To apply the model to rocks and magmas estimates ofT, P, and the fugacity of H₂O are required.Variation of the H₂O content of the melt changes the activity of other components. Knowledge of this variation removes the requirement that the fugacity of H₂O be estimated. Application of the properties of exact differentials to the Gibbs function for the hydrous melt provides an expression relating the chemical potential of a feldspar component to the H₂O content of the melt. This expression contains a second adjustable parameter which depends on the anhydrous melt composition. Using this second expression, the H₂O content can be estimated ifT, P, and feldspar composition are known. Data are too meagre to evaluate the quantitative success of the second method.     

Geochemical variations in lavas from Kahoolawe volcano,Hawaii: evidence for open system evolution of plume-derived magmas

The Kahoolawe shield volcano produced precaldera and caldera-filling tholeiites and mildly alkalic post-caldera lavas that petrographically and compositionally resemble such lavas from other Hawaiian shield volcanoes. However, Kahoolawe tholeiites display wide ranges in incompatible trace element ratios (e.g., Nb/Th=9–24, Th/Ta=0.6–1.3), ⁸⁷Sr/⁸⁶Sr (0.70379–0.70440), ¹⁴³Nd/¹⁴⁴Nd (0.51273–0.51298), and ²⁰⁶Pb/²⁰⁴Pb (17.92–18.37). The isotopic variation exceeds that at any other Hawaiian shield volcano, and spans about half the range for all Hawaiian tholeiites. Quasi-cyclic temporal evolution of Kahoolawe tholeiites is consistent with combined fractional crystallization and periodic recharge by primitive magmas. Ratios of highly incompatible trace elements and Sr, Nd, and Pb isotopic ratios from coherent sub-trends that reflect recurrent interactions between variably evolved magmas and two other mantle components whose compositions are constrained by intersections between these trends. The most MgO-rich Kahoolawe tholeiites are partial melts of a high Nb/Th (23.5) ascending plume, possibly comprising ancient subducted oceanic lithosphere. Slightly evolved tholeiites experienced combined crystal fractionation and assimilation (AFC) of material derived from a distinct reservoir (Nb/Th 9) of asthenospheric derivation. The most evolved tholeiites display compositional shifts toward a third component, having mid ocean ridge basalt-like isotopic ratios but enriched OIB-like trace element ratios, representing part of the lithospheric mantle (or melts thereof). Periodic recurrence of all three magma variants suggests that eruptions may have tapped coeval reservoirs distributed over a large depth range. Kahoolawe provides new evidence concerning the nature of the Hawaiian plume, the distribution of compositional heterogeneities in the suboeanic mantle, and the processes by which Hawaiian tholeiites form and evolve.