Palaeozoic flysch series in the Coastal Cordillera of Northern Chile

A discontinuous outcrop of Palaeozoic rhythmic clastites appears in the North Chilean Coastal Cordillera. The Formación El Toco (21°15–22°15S) whose scarce flora points to a presumably Upper Devonian age forms the northernmost part of the outcrop. It is discordantly overlain by Lower Jurassic volcanics (Fm. La Negra), its base, however, is not exposed. Hercynian heteromorphous deformation led to predominantly NW trending folds strongly inclined mostly to the SW. Chevron-like folds of 0.1 to 30 m occur locally and seem to display properties transitional between synsedimentary-gravitational and early tectonic deformation.The series which is at least 2300 m thick consists of proximal, in parts pebbly turbidites with non-turbiditic finegrained intercalations. Incomplete BOUMA-sequences frequently begin with A-beds of grey to green immature, badly sorted coarse sandstones of up to 6 m thickness containing isolated quartz- and pelite-clasts.Measurements of flute casts and f oresets show palaeocurrents which came from NW and NNE. Along with petrographic observations they indicate southward directed transport of detritus from low metamorphic sedimentary and magmatic source areas into an Upper Devonian nonvolcanic basin.

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Zusammenfassung Die Formación El Toco ist der nördlichste Aufschluß einer Kette von Vorkommen paläozoischer rhythmischer Klastite in der nordchilenischen Küstenkordillere. Diese Formation (21°15–22°15S), deren spärliche Flora vorbehaltlich dem Oberdevon zuzuordnen ist, wird diskordant von unterjurassischen Vulkaniten (Fm. La Negra) überlagert —das Liegende ist nicht aufgeschlossen. Variszische heteromorphe Deformation führte zu vorherrschend NW-streichender Faltung, die meist starke SW-Vergenz zeigt. Lokal tritt eine scharfe Verfaltung im 0,1 bis 30 m-Bereich hinzu, die sowohl synsedimentär-gravitative als auch frühtektonische Deformationsmerkmale zeigt.Die mindestens 2300 m mächtige Serie ist ein proximaler Flysch mit z. T. kiesführenden Turbiditen, in die nichtturbiditische feinkörnige Partien eingeschaltet sind. Die unvollständigen BOUMA-Sequenzen beginnen häufig mit einer aus grauen bis grünen unreifen und schlechtsortierten Grobsandsteinen bestehenden A-Division von bis zu 6 m Mächtigkeit, die isolierte Quarz- und Pelitklasten enthalten kann.Flute cast- und Foreset-Messungen weisen auf Paläoströmungsrichtungen aus NW und NNO hin. Zusammen mit petrographischen Analysen läßt sich daraus ein südwärts gerichteter Transport von schwachmetamorphsedimentärem und magmatischem Detritus in ein oberdevonisches nicht-vulkanisches Becken ableiten.

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Résumén Ritmitas clásticas de edad paleozoica forman afloramientos discontinuos en la Cordillera de la Costa del Norte de Chile. La Formación El Toco (21°15–22°15S), que contiene una flora escasa de probable edad Devónico Superior, constituye la parte más septentrional de estos afloramientos. La base no se conoce, mientras que el techo infrayace discordantemente a volcanitas jurásicas inferiores (Fm. La Negra). Deformaciones hercínicas heteromórficas llevan a la formación de pliegues orientados predominantemente al NW inclinados fuertemente al SW. Localmente aparecen pliegues en forma de chevron de un tamano de 0.1 a 30 m que muestran caracteristicas de deformación transicional entre sinsedimentana-gravitativa y tectónica temprana.La serie que tiene una potencia de por lo menos 2300 m consiste en turbiditas proximales parcialmente con gravas e intercalaciones finas no-turbidíticas. Secuencias incompletas de BOUMA empiezan frecuentemente con capas de la division A (espesor maximo 6 m) los cuales se componen con frecuencia de areniscas gruesas gris-verdes, composicionalmente inmaduras y mal seleccionadas, con clastos aislados de cuarzo y pelita.Medidas de flute casts y foresets muestran paleocorrientes provenientes de NW y NNE. Junto con observaciones petrográficas, las paleocorrientes indican un transporte de material detrítico, originado de áreas con rocas sedimentarias, metamórficas de bajo grado e ígneas, dirigido al sur hacia una cuenca no volcánica de edad Devónico Superior.

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Fazieswechsel und Metamorphose in der westlichen Serra Negra (Espinhaço-Zone,Minas Gerais,Brasilien)

Zusammenfassung Es wird eine Übersichtskarte für die Serra Negra (Ostrand der Espinhaço-Zone) im Maßstab 1250 000 vorgelegt.Lithologische Faziesübergänge und das Vorkommen ultrabasischer bis basischer Gesteine belegen einen mio-/eugeosynklinalen Übergangsbereich der Minas-Geosynklinale. In der jüngeren, die Minas-Serie diskordant überlagernde São-Francisco-Serie (Macaúbas-Fazies) wurden erstmals magmatische Gesteine nachgewiesen.Die metamorphen Mineralneubildungen in der Minas-Serie weisen auf eine nach Osten zunehmende Regionalmetamorphose hin. Der größte Teil des Arbeitsgebietes liegt im Übergangsbereich Grünschiefer-/Amphibolit-Fazies.

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A regional study of the Serra Negra (eastern region of the Serra do Espinhaço) was carried out at the scale 1250 000.Lithologic facies changes and occurences of ultrabasic and basic rocks allow to delimit a mio/eugeosynclinal transition within the Precambrian Minas-Geosyncline. Within a post-Minas sequence (Macaúbas-Facies of the São Francisco Series) magmatic rocks have been encountered for the first time.Regional metamorphism within the Minas-Series is increasing to the east. The major part of the area belongs to a transitional zone between the greenshist- and amphibolite-Facies.

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Resumo Foi mapeada a região da Serra Negra (margem oriental da Serra do Espinhaço) na escala 1250 000.Mudanças de fácies, ocorrênicias de rochas ultrabásicas e básicas permitiram delimitar uma região de transição entre condições mio- e eugeossinclinais na Série Minas. Dentro da fácies Macaúbas, na Série São Francisco, discordante da Série Minas, foram reconhecidas rochas magmáticas pela primeira vez.O metamorflsmo regional da Série Minas cresce em direção leste. A maior parte da área em estudo situa-se na região de transição entre a fácies xisto verde e a anfibolítica.

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Polar ice sheets: Developments since Wegener

Wegener's expeditions pioneered many measurements that are now essential for computer modelling of ice sheets. Advances in knowledge of accumulation, thickness, temperature, crystal fabric and surface mapping of ice sheets and of impurities, gas content and isotopic ratios of ice cores from these ice sheets are outlined before computer modelling work is discussed. The value of such studies in providing large scale tests of geophysical concepts is emphasized. The paper concludes by suggesting that the drag of continental ice sheets on the top of continental blocks might be of comparable magnitude and tend to balance forces on the base of these blocks by motion of the asthenosphere. Apart from providing a possible reason for the aseismic nature of the Antarctic and Greenland land masses, the hypothesis provides a suitable link for this volume between Wegener's interest in continental ice sheets and continental drift.

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Zusammenfassung Wegeners Expeditionen haben viele Messungen angeregt, die zu Ergebnissen geführt haben, die nunmehr reif sind für Computer-Modelle von Eisdecken. Es werden die Fortschritte in der Kenntnis von Akkumulationsraten, Mächtigkeit, Temperatur, Kristallstruktur, Oberflächenkartierung von Eisdecken und Verunreinigungen umrissen. Danach wird die Arbeit mit dem Computer-Modell diskutiert. Der Wert solcher Untersuchungen für großmaßstäbliche Tests geophysikalischer Konzepte wird betont. Die Ergebnisse lassen erwarten, daß die Schubkräfte der kontinentalen Eisdecken auf dem Top der kontinentalen Blöcke in derselben Größenordnung liegen könnten wie die aus der Bewegung der Asthenosphäre an der Basis dieser Blöcke. Letztere könnten damit kompensiert werden.Unabhängig davon, daß die aufgestellte Hypothese mögliche Argumente für die aseismische Natur der Antarktischen und Grönland-Massen aufzeigt, verbindet sie im Rahmen dieses Bandes Wegeners Interesse an kontinentalen Eisdecken mit der Kontinentaldrift.

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Résumé Les expéditions de Wegener ont suscité de nombreuses mesures qui ont fourni des données aujourd'hui mûres pour établir des modèles de couvertures glaciaires par la voie de calculatrices. Mais avant de discuter ce procédé, mention est faite des progrès accomplis dans la connaissance de l'accumulation, de l'épaisseur, de la température, de la structure cristalline et de la cartographie des couvertures glaciaires ainsi que de leurs impuretés, leur teneur en gas et les rapports d'isotopes dans les carottes qui y ont été prélevées, études dont il convient de souligner la valeur par les données à grande échelles qu'elles ont fourni à l'appui de concepts géophysiques. Le mémoire conclut sur la suggestion que les forces d'entrainement des couvertures glaciaires continentales sur la surface des blocs continentaux doit être d'un ordre comparable aux forces agissant à la base de ces blocs dans leur mouvement sur l'asthénosphère et qu'ils tendent à égaler. Outre qu'elle donne une raison possible de la nature asismique du continent antactique et du Groenland, cette hypothèse, dans ce volume, forme un trait d'union dans les intérêts que Wegener a portés aux couvertures glaciaires continentales et à la dérive des continents.

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Etude des images Landsat de la zone transformante Rhin-Saône (France)

Résumé L'étude des images Landsat de la zone transformante entre les fossés de la Saône et du Rhin donne un échantillonage significatif de la facturation réparti sur une grande surface, et révèle l'existence de plusieurs linéaments. Ceux-ci sont interprétés comme des accidents profonds délimitant, au Paléogène, un couloir de cisaillement sénestre transformant N 80°, au dessus duquel la couverture se fracture selon un système de Riedel. On reconnait également en surface des failles hercyniennes de direction varisque et des failles »rhénanes« subméridiennes liées à l'ouverture des fossés.

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Landsat imagery of the transform fault zone between the Saône and Rhine grabens indicates a significant fracture pattern distributed over a large area, and reveals many lineaments. These latter are interpreted as basement faults delimiting, during Paleogene time, a N 80° sinistral transform fault zone, above which the cover breaks in series of Riedel shears. Other faults can be recognized on the surface: Hercynian faults of Variscan trend as well as approximately N-trending faults due to the opening of the rifts.

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Zusammenfassung Die Auswertung von Satellitenbildern Landsat der transform fault zone zwischen dem Saône- und dem Rhein-Graben ergibt ein signifikatives Bild der über eine ausgedehnte Oberfläche verteilten Bruchtektonik; es läßt sich daraus auf das Vorhandensein von mehreren Lineamenten schließen. Diese werden als krustale Störungen interpretiert, welche im Paleogen eine enge Scherungszone (senestre, N 80° transform fault zone) begrenzten, deren Bedeckung dem System von Riedel folgend aufbrach. Es lassen sich außerdem an der Oberfläche zwei verschiedene Bruchsysteme erkennen: einerseits herzynische Störungen variskischer Richtung, andererseits die mit der Öffnung des Rheingrabens verbundenen Bruchlinien submeridianer Richtung.

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Statistical Properties of Ideal Rock Textures: Relationship Between Crystal Size Distribution and Spatial Correlation of Minerals

The concept of an ideal rock texture, in which crystals are distributed randomly in space, is proposed for use in general analysis of rock textures. The spatial correlation function for the ideal rock texture was examined and the function, a specific kind of spatial correlation function, is related to crystal size distribution and to some extent to crystal boundaries. The function is unity at distance zero, and monotonically decreases with increasing distance for the ideal texture. This behavior of the function is observed for any size distribution. In an ideal texture, the function is directly related to crystal size distribution and crystal shape. It is important in stereology because the crystal size distribution in three dimensions may be deduced from analyzing a function that is obtained from analyzing two-dimensional section images. Crystal shape is also related to the function. If crystals are concave in shape, or have inclusions of other phases, the function may show a hump or plateau when plotted against distance. However, the crystal shape effect cannot produce values smaller than zero. If values become negative, the texture is no longer considered ideal. The ideal textures for two model size distributions—step and delta functions—are considered. The rate of decrease of values is more strongly dependent on size distribution than on system dimension.     

Generalized Sequential Gaussian Simulation on Group Size ν and Screen-Effect Approximations for Large Field Simulations

The modelling of spatial uncertainty in attributes of geological phenomena is frequently based on the stochastic simulation of Gaussian random fields. This paper presents a generalization of the sequential Gaussian simulation method founded upon the group decomposition of the posterior probability density function of a stationary and ergodic Gaussian random field into posterior probability densities of a set of groups of nodes of size . The method, which is termed generalized sequential Gaussian simulation on group size , relies computationally on sharing the neighborhood of adjacent nodes and simulates groups of nodes at a time, instead of the traditional node-by-node simulation. The new method is computationally efficient and suitable for simulation on large grids of nodes. Results suggest that, in terms of computing cost (time), an optimal size of a group is about 80% of the optimal neighborhood used for sequential Gaussian simulation and that computation can be up to 50 times faster than the regular sequential Gaussian method, with little loss in accuracy. The effectiveness of the method is assessed by using a general measure of accuracy, screen-effect approximation loss (SEA loss), defined herein as the mean-square difference between the simulated value posterior to the information in the neighborhood and the simulated value posterior to all information, and shown to be determined by the corresponding posterior variances. The results presented show that both the exponential and the spherical models perform well and can meet the less-than 5% relative SEA loss requirement for any grid setup using a relatively small neighborhood. The Gaussian covariance model was found to have a relatively high relative SEA loss in most cases.     

Stability relations of chromium kyanite at high pressures and temperatures

The pseudobinary section Al₂SiO₅-Cr₂SiO₅ of the system Al₂O₃-Cr₂O₃-SiO₂ has been investigated at 20 and 30 kb pressure in the temperature range 1,000–1,600° C. The solubility of Cr₂SiO₅ in kyanite (Al₂SiO₅) extends up to 24 mole % Cr₂SiO₅ at 20 kb and 31 mole % at 30 kb. The extent of this solid solution is not notably dependent on temperature in the range studied. The stability of kyanite is increased by the substitution Cr Al by about 80° C at 20 kb as compared to Cr-free kyanite. Cr-poor sillimanite and Cr-rich kyanite can stably coexist in a temperature interval of up to 80° C at 20 kb and about 150° C at 25 kb.     

Estimation of the probability of success in petroleum exploration

A probabilistic model for oil exploration can be developed by assessing the conditional relationship between perceived geologic variables and the subsequent discovery of petroleum. Such a model includes two probabilistic components, the first reflecting the association between a geologic condition (structural closure, for example) and the occurrence of oil, and the second reflecting the uncertainty associated with the estimation of geologic variables in areas of limited control. Estimates of the conditional relationship between geologic variables and subsequent production can be found by analyzing the exploration history of a training area judged to be geologically similar to the exploration area. The geologic variables are assessed over the training area using an historical subset of the available data, whose density corresponds to the present control density in the exploration area. The success or failure of wells drilled in the training area subsequent to the time corresponding to the historical subset provides empirical estimates of the probability of success conditional upon geology. Uncertainty in perception of geological conditions may be estimated from the distribution of errors made in geologic assessment using the historical subset of control wells. These errors may be expressed as a linear function of distance from available control. Alternatively, the uncertainty may be found by calculating the semivariogram of the geologic variables used in the analysis: the two procedures will yield approximately equivalent results. The empirical probability functions may then be transferred to the exploration area and used to estimate the likelihood of success of specific exploration plays. These estimates will reflect both the conditional relationship between the geological variables used to guide exploration and the uncertainty resulting from lack of control. The technique is illustrated with case histories from the mid-Continent area of the U.S.A.This paper was presented at Symposium 116.3, Quantitative Strategy for Exploration, held as part of the 25th International Geological Congress, Sydney, Australia, August 1976.     

Conditional Simulation of Nongaussian Random Functions

This paper presents a conditional simulation procedure that overcomes the limits of gaussian models and enables one to simulate regionalized variables with highly asymmetrical histograms or with partial or total connectivity of extreme values. The philosophy of the method is similar to that of sequential indicator technique, but it is more accurate because it is based on a complete bivariate model by means of an isofactorial law. The resulting simulations, which can be continuous or categorical, not only honor measured values at data points, but also reproduce the mono and bivariate laws of the random function associated to the regionalized variable, that is, every one or two-point statistic: histogram, variogram, indicator variograms. The sequential isofactorial method can also be adapted to conditional simulation of block values, without resorting to point–support simulations.     

Métamorphisme hydrothermal en faciès salins et pénésalins sur l'exemple du complexe salifère de l'extrême Nord Tunisien

Résumé Les roches sédimentaires des formations salifères de l'extrême Nord tunisien ont fréquemment subies une recristallisation ou une dolomitisation notable, à laquelle se superpose souvent un envahissement de minéraux automorphes, quartz et feldspaths principalement. L'étude des inclusions fluides de ces cristaux conduit à des conditions thermométriques de genèse qui dépassent le stade d'une simple diagenèse. Les transformations subies relèvent davantage d'un épimétamorphisme, en milieu aquifère hypersalin, lié à des anomalies thermiques vraisemblablement en rapport avec des manifestations volcaniques.

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Hydrothermal low grade metamorphism within saline and penesaline facies with reference to the saliferous complex in Northern Tunisia

The sedimentary rocks of saliferous formations in the tunisian far North have gone through frequent recrystallization or a notable dolomitization which an invading of idiomorph minerals mainly made up of quartz and feldspar crystals is frequently added to. Studies carried out on fluid inclusions from these crystals lead thermometric figures clearly exceeding the range of values met with in diagenesis. New paragenesis are best related to low grade metamorphism in aquiferous hypersalted medium bearing relation with thermal anomalies likely connected to volcanism.

     

Foundation analysis of an arch dam. Comparison of two modelling techniques: No tension and jointed rock material

Summary The paper describes the application of a recently developed joint element to the analysis of a jointed rock foundation of an arch dam. The most relevant joint system and the concrete-rock interfaces were simulated by means of joint elements. Parameters for the constitutive behaviour of the joints were derived from large scale in situ shear tests. The analysis showed the suitability of the jointed model to predict not only stresses and deformations but also the shape of the failure surface al ultimate conditions. This allows an easy determination of conventional safety factors. A parallel no tension analysis incorporating a cohesion threshold was also carried out. The comparison of both approaches indicates that the no tension hypothesis is a crude approximation of the rock response to dam loads and may lead to unsafe estimates of stability and stress conditions.The analysis performed also showed the relevance of initial stress conditions inside the rock mass in controlling the overall foundation response.     

Estimating work-magnitude associations in earth surface processes

Magnitude-frequency concepts in earth surface processes have found widespread application following the publication of the well-known paper Wolman and Miller. Of particular interest in such studies is the determination of those event magnitudes which make the most important long-term contributions to the total work of a given process. However, there has been little discussion to date concerning an appropriate estimator of the parameter , where is the long-term work achieved by events within a specified magnitude range, expressed as a proportion of the long-term work achieved by events of all magnitudes. The estimation of is straightforward for the time-independent case where short-duration events occur randomly in time, and event magnitudes are independent random variables from a common distribution. For this model, exists as a true parameter which can be estimated by , where is the sample proportion of work contributed by events within the specified magnitude range. This estimator is biased, but it is almost median-unbiased for large samples. An approximate expression for var ( ) can be obtained from standard results. A similar approach to the estimation of can be applied to estimating the long-term work contribution of the largest events in consecutiveR-year periods. An example is presented using riverbank erosion data. Within the constraints of the time-independent model, the estimation procedure is quite general and can be applied with or without prior specification of the probability distribution of event magnitudes. In some situations, estimation can also be achieved indirectly by using a sample of the causal events which generate the individual work events. This indirect estimation is particularly simple if work magnitude is a power transformation of causal magnitude, and the distribution of causal event magnitudes can be approximated by a lognormal distribution or a Weibull distribution. The relative work achieved by events within ever-smaller magnitude ranges leads in the limit to the work intensity function,P(y). A plot of this function shows the relative importance ofy—magnitude events with respect to their long-term work contributions. Estimation ofP(y) is carried out by first fitting a probability distribution to a sample of event magnitude data. The functionP(y) is unimodal with respect to the following probability distributions of event magnitudes: lognormal, Weibull, unimodal beta, gamma, and inverse Gaussian. A lognormal distribution of event magnitudes produces the maximum work intensity at the lognormal median. In a strict mathematical sense, the long-term work contribution of very large and very small events is insignificant. However, little can be deduced concerning the pattern of work intensity between these two extremes. In particular, there appears no reason to suppose that the maximum work intensity will coincide with work magnitudes classified as intermediate.     

A robust-symmetric mean: A new way of mean calculation for environmental data

Environmental data seldom follow normal distributions, so how to calculate their means is a very important problem. Commonly used methods for mean calculation, such as arithmetic mean, geometric mean, and median, were evaluated. Arithmetic means should only be used when datasets follow normal distributions. Geometric means are suitable for datasets which follow log-normal distributions. Medians are a kind of robust treatment. However, their efficiency is very low. Based on the methods described, two new ideas are developed: robust and symmetric, for calculating means. As far as the symmetric feature is concerned, Box-Cox power transformation is better than logarithmic transformation. Robust statistics and Box-Cox transformation are combined to produce the robust-symmetric mean. As environmental data often follow log-normal or skewed distributions, this method is better than the previous ones and also is appropriate.     

Cristallochimie de l'owyheeite: nouvelles données

Résumé L'étude chimique comparée, à la microsonde électronique, d'owyheeite de treize gisements différents a révélé des fluctuations sensibles des teneurs en éléments majeurs, en liaison avec la nature des sulfosels associés, ainsi que la présence occasionnelle de différents éléments mineurs: Cu et As (très fréquents), Sn et Bi (moins fréquents), Tl et Se (exceptionnels). Compte tenu du mode de substitution de ces éléments mineurs, la projection des analyses dans le système Pb₂S₂–Ag₂S–Sb₂S₃ délimite un champ restreint de solution solide dont l'allongement s'accorde avec la substitution 2 Pb²⁺Ag⁺+Sb³⁺. Ce champ de solution solide englobe la composition de la variété téremkovite, mais exclue la formule donnée initialement parShannon. La formule Pb_10–2x Sb_11+x Ag_3+x S₂₈ (–0,13x+0,20) rend compte des termes à la résolution de la Ag/Sb maximal; l'obtention d'une formule plus générale reste subordonée à la résolution de la structure cristalline. Aucun élément mineur ne peut jouer à lui seul le rôle de stabilisateur de la structure, mais ce même rôle peut être joué complémentairement par différents éléments, tels que Cu et Sn. Les clichés de microdiffraction électronique montrent des phénomènes de sur-structure plus ou moins prononcés, en liaison avec la concentration en (Ag+Cu), ou avec le degré de finesse du maclage complexe spécifique de l'owyheeite.

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Crystal chemistry of owyheeite: New data

Summary Comparative electron microprobe study of owyheeite from thirteen ore deposits shows significant variations in the concentration of major elements. These can be correlated with the chemical composition of the associated sulfosalts. Sometimes, some minor elements may be present: Cu and As (very frequent), Sn and Bi (less frequent), Tl and Se (exceptional). Considering certain substitution rules for minor elements, the analyses plotted in the Pb₂S₂–Ag₂S–Sb₂S₃ system show a limited solid-solution field, the elongation of which follows the substitution 2 Pb²⁺Ag⁺+Sb³⁺. This solid-solution field includes the composition of the variety teremkovite, but excludes the initial formula for owyheeite proposed byShannon. The formula Pb_10–2x Sb_11+x Ag_3+x S₂₈ (–0.13x+0.20) describes compositional variation of members with the highest Ag/Sb ratio; a more general formula would require the determination of the crystal structure. No individual minor element appears to be responsible for stabilizing owyheeite. The stabilization may be due to a combined effect of two elements, such as Cu and Sn. Electron diffraction patterns show superstructure reflections which are related to the (Ag+Cu) concentration, as well as to the scale of the complex twinning characteristic of owyheeite.

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Avec 3 Figures     

On the condition number of covariance matrices in kriging, estimation, and simulation of random fields

The numerical stability of linear systems arising in kriging, estimation, and simulation of random fields, is studied analytically and numerically. In the state-space formulation of kriging, as developed here, the stability of the kriging system depends on the condition number of the prior, stationary covariance matrix. The same is true for conditional random field generation by the superposition method, which is based on kriging, and the multivariate Gaussian method, which requires factoring a covariance matrix. A large condition number corresponds to an ill-conditioned, numerically unstable system. In the case of stationary covariance matrices and uniform grids, as occurs in kriging of uniformly sampled data, the degree of ill-conditioning generally increases indefinitely with sampling density and, to a limit, with domain size. The precise behavior is, however, highly sensitive to the underlying covariance model. Detailed analytical and numerical results are given for five one-dimensional covariance models: (1) hole-exponential, (2) exponential, (3) linear-exponential, (4) hole-Gaussian, and (5) Gaussian. This list reflects an approximate ranking of the models, from best to worst conditioned. The methods developed in this work can be used to analyze other covariance models. Examples of such representative analyses, conducted in this work, include the spherical and periodic hole-effect (hole-sinusoidal) covariance models. The effect of small-scale variability (nugget) is addressed and extensions to irregular sampling schemes and higher dimensional spaces are discussed.     

An effect of closure on the structure of principal components

The principal components transformation generates, from any data array, a new set of variables—the scores of the components—characterized by a total variance exactly equal to that of the initial set. It is in this sense that the transformed variables are said to contain, preserve, or account for, the variance of the original set. The scores, however, are uncorrelated. In the course of the transformation, what becomes of the strong interdependence of variance and covariance so characteristic of closed arrays? The question seems to have attracted little attention; we are aware of no study of it in the earth sciences. Experimental work reported here shows quite clearly that the overall equivalence of variance and covariance imposed by closure, though absent from the component scores,may emerge in relations between the coefficientsof each of the lower-order components; if the raw data are complete rock analyses, the sum of all the covariances of the coefficients of such a component is negative, and is very nearly equal to the sum of all the variances in absolute value. (In all cases so far examined, the absolute value of the first sum is a little less than that of the second.) The principal components transformation provides an elegant escape from closure correlation if a petrographic problem can be restated entirely in terms of component scores, but not if a physical interpretation of the component vectors is required.     

Tridymite: Effect of hydrostatic pressure to 6 kbar on temperatures of two rapidly reversible transitions

Trajectories of two reversible phase transitions in a low-Na synthetic tridymite have been determined to 6 kbar by differential thermal analysis (DTA) in hydrostatic apparatus using Ar or CO₂. The temperature of the lower transition increases from 111 ° C at 1 bar linearly with pressure with slope 1₅ deg kbar^–1. Pressure raises the temperature of the upper transition from 157 ±2 ° or 159 ° C (independently determined) at 1 bar wit a slope of 53 deg kbar^–1, up to 0.7 kbar; for the data above that pressure, the initial slope is 64 deg kbar^–1. Above 2–1/2 kbar, the variation is linear with slope 70 deg kbar^–1. No evidence for other transitions was found at any of the apparent changes of slope. Hystereses for both transitions decreased at high pressures compared to 1-bar. Preferred values for the transition enthalpies, together with these slopes and the Clausius-Clapeyron equation, yield estimates for the volume changes at the transitions of 0.01 (lower) and 0.15 to 0.25 (upper) cm³ gfw^–1. These calculated volume changes are not consonant with many of the high temperature volumetric data on tridymites of varying origins.     

Shear resistance of en-echelon jointed rock masses in joint direction

Summary A criterion for determining normal stress levels of shear failure of rock masses is developed, then the shear resistance of the rock mass, based upon the geometric model of en-echelon jointed rock masses, can be evaluated for low normal stress levels or high normal stress levels respectively by using the method proposed in this paper. Finally, a procedure generating joint patterns which are described with individual joint geometry parameter or multi-joint geometry parameter is discussed.     

The anthracite smokers of eastern pennsylvania: PS2 (g)P_{S_2 (g)} -T stability diagram by TL analysis

Coal seams and culm banks associated with mine fires in the anthracite region of eastern Pennsylvania have been burning for decades. Many of the fires may have ignited by spontaneous combustion or by the burning of trash. Minerals associated with the combustion of anthracite form by the condensation of gas exhaled through surficial gas vents or anthracite smokers. A Pressure-Temperature (P-T) stability diagram is constructed for the condensation of orthorhombic sulfur from anthracite gas using Thermodynamic Loop Analysis (TL analysis). This method of analyzing chemical systems incorporates Kirchhoff's Law into a four step procedure structured around a closed thermodynamic cycle or thermodynamic loop. The four steps, referred to us The Four S S of Thermodynamic Loop Analysis, include: (1) Set Up—graphical characterization of the problem. (2) Sum—the application of thermodynamic principles. (3) Substitute—the use of materials data available from the literature, and (4) Solve—computation of one or more variables. The example presented demonstrates that thermodynamic loops can incorporate any number of polymorphic phase transformations. In addition, thermodynamic loop analysis is applicable to any geologic process involving the condensation of minerals from a gas. The stability diagram derived by TL analysis may have applicability in monitoring the release of sulfur gas into the atmosphere.     

Dispersive Particle Transport: Identification of Macroscale Behavior in Heterogeneous Stratified Subsurface Flows

Dispersive mass transport processes in naturally heterogeneous geological formations (porous media) are investigated based on a particle approach to mass transport and on its numerical implementation using LPT3D, a Lagrangian Particle Tracking 3D code. We are currently using this approach for studying microscale and macroscale space–time behavior (advection, diffusion, dispersion) of tracer plumes, solutes, or miscible fluids, in 1,2,3-dimensional heterogeneous and anisotropic subsurface formations (aquifers, petroleum reservoirs). Our analyses are based on a general advection-diffusion model and numerical scheme where concentrations and fluxes are discretized in terms of particles. The advection-diffusion theory is presented in a probabilistic framework, and in particular, a numerical analysis is developed for the case of advective transport and rotational flows (numerical stability of the explicit Euler scheme). The remainder of the paper is devoted to the behavior of concentration, mass flux density, and statistical moments of the transported tracer plume in the case of heterogeneous steady flow fields, where macroscale dispersion occurs due to geologic heterogeneity and stratification. We focus on the case of perfectly stratified or multilayered media, obtained by generating many horizontal layers with a purely random transverse distribution of permeability and horizontal velocity. In this case, we calculate explicitly the exact mass concentration field C(x, t), mass flux density field f(x, t), and moments. This includes spatial moments and dispersion variance ² _x (t) on a finite domain L, and temporal moments on a finite time scale T, e.g., the mass variance of arrival times ² _T (x). The moments are related to flux concentrations in a way that takes explicitly into account finite space–time scales of analysis (time-dependent tracer mass; spatially variable flow through mass). The multilayered model problem is then used in numerical experiments for testing different ways of recovering information on tracer plume migration, dispersion, concentration and flux fields. Our analyses rely on a probabilistic interpretation that emerges naturally from the particle approach; it is based on spatial moments (particle positions), temporal moments (mass weighted arrival times), and probability densities (both concentrations and fluxes). Finally, as an alternative to direct estimations of the flux and concentration fields, we formulate and study the Moment Inverse Problem. Solving the MIP yields an indirect method for estimating the space–time distribution of flux concentrations based on observed or estimated moments of the plume. The moments may be estimated from field measurements, or numerically computed by particle tracking as we do here.