Some exact sampling distributions for variogram estimators

For equally spaced observations from a one-dimensional, stationary, Gaussian random function, the characteristic function of the usual variogram estimator for a fixed lag k is derived. Because the characteristic function and the probability density function form a Fourier integral pair, it is possible to tabulate the sampling distribution of a function of a using either analytic or numerical methods. An example of one such tabulation is given for an underlying model that is simple transitive.     

Topological properties of random crack networks

The junctions of cracks in mudcrack, patterned ground, and columnar joint patterns can be categorized into Y, T,and Xtypes. The mean number of sides, ,to the polygonal areas in such nets is = 2(2J_T + 3J_Y + 4J_X)/(J_T + J_Y + 2J_X)where J_T, J_Y,and J_X are the proportions of T, Y,and Xjunctions, respectively.     

Tectonic effects of sea-floor spreading on the Arabian Shield

Paleogeographic evidence shows that the series of broad E-W anticlines and synclines on the Arabian Shield (Southern Hadramawt Arch, Wadi Hadramawt Syncline, Northern Hadramawt Arch, Rub Al Khali Syncline, Tuwaiq Homocline, Nafud Basin) are not old, inherited structures, but were formed in late Eocene and Oligocene times, as indicated by the warping of Middle Eocene sediments. The fold axes of these structures trend parallel to the Gulf of Aden, and their separation increases from S to N, i. e., with increasing distance from the Gulf of Aden. The most pronounced orogenic phase of the Toros mountain belt and the folding of the foreland belt (Lebanon, Antilebanon, Palmyra Arch, Jebel Sinjar, etc.) took place simultaneously with the warping of the shield. Furthermore, the early Tertiary Trap Volcanism occurs only in the neighborhood of the Gulf of Aden (Yemen, W-Aden Protectorate, Eritrea, Ethiopia, Somaliland). Geophysical-oceanographic research in the Gulf of Aden suggests that emplacement of basic magmatic material forms a quasi-oceanic crust (sea-floor spreading) in that rift trough. This apparently causes the displacement of the continental blocks. The close connections in time as well as in directional trends of epirogenic, orogenic and volcanic activities on the Arabian Shield to the sea-floor spreading in the Gulf of Aden indicates tectonic interrelations.This impression is still emphasized, if one considers the younger tectonic development on the shield. The young Tertiary Aden-Volcanics Belt (Miocene-Recent) extends from the East African Rift system over the West Arabian Shield all the way up to Turkey, that is to say its trend is more or less parallel to the Red Sea. Warping effects (Ras en Naqb Uplift, Jafr Depression, Bayir Uplift, Wadi Sirhan Depression, Rutba Dome and the Mesopotanian Basin) on the northern part of the Arabian Shield, where the earlier developed (Aden Gulf-related) structures die out, can be related in time and direction to the rifting in the Red Sea. Faulting along the Aqaba-Dead Sea System is of the same age and cuts the foreland belt. Finally the folding of the Zagros mountain belt is of Miocene age too.The Arabian Shield, bounded by still-active rifting structures of different direction and age, provides a classical example of the effect of sea-floor spreading on a shield area itself, and on its surrounding instable belt. The correct interpretation of these tectonic connections eventually may allow far reaching, basic conclusions.

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Zusammenfassung Die känozoische tektonische und vulkanologische Entwicklung auf und um den Arabischen Schild ist relativ jung und im Vergleich zu anderen Gegenden in ihrer Gesamtheit noch verhältnismäßig gut überschaubar. Sie bietet daher ein Beispiel, dessen Verständnis möglicherweise von grundlegender Bedeutung für die Interpretation gebirgsbildender Vorgänge werden kann.Der Arabische Schild ist im Süden und Südwesten umrahmt von den Rift-Systemen des Golfes von Aden und Roten Meeres, deren zentrale Teile durch quasi-ozeanische Kruste gekennzeichnet sind. Die Einschübe basischen magmatischen Materials (sea-floor spreading) in die Rifttröge verursachten offenbar eine Verdrängung der kontinentalen Blöcke (Bewegungssinn senkrecht zum Streichen der Zonen des aktiven sea-floor spreading). Jedenfalls läßt sich ein solcher Beanspruchungsplan von den verschiedenen tektonischen Teilvorgängen auf dem Arabischen Schild ableiten.Die Entwicklung des Golfes von Aden ist älter als die des Roten Meeres, und das gilt dementsprechend für die Eo- bis Oligozänen vulkanischen, epirogenen und orogenen Vorgänge, die räumlich und zeitlich Beziehungen zum Geschehen im Golf von Aden aufweisen (Trap-Vulkanismus, Verbiegungen des Süd- und Zentral-Arabischen Schildes und Auffaltung des Taurusgebirges und Palmyra-bogens). Alle Ereignisse, die räumliche Beziehungen zur Rotcn-Meer-Streichrichtung zeigen (Aden-Vulkanismus, epirogene Verbiegung des Nord-Arabischen Schildes und Auffaltung des Zagrosgebirges) sind jünger, d. h. seit dem Miozän besonders aktiv.

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Résumé L'évidence paléogéographique montre que, comme l'indique le gauchissement des sédiments de l'Eocéne Moyen, les séries des grands géanticlinaux et synclinaux, orientés est-ouest, sur le craton arabique (S. Hadramawt Arc, Wadi Hadramawt syncline, N. Hadramawt géanticline, Rub Al Khali syncline, Tuwaiq homocline, Nafud bassin) ne sont pas des vieilles structures antérieures, mais ont été formés durant l'Eocéne et l'Oligocène. Les axes de plissement de ces structures ont tendance à être parallèles au Golfe d'Aden. Leur séparation augmente du sud vers le nord, c'est à dire de la même manière que leur distance du Golfe d'Aden augmente. La phase orogénique la plus prononcée de la ceinture montagneuse de Toros et les prémontagnes de l'Arabie septentrionale (Lebanon, Antilebanon, Palmyra Arc, Jebel Sinjar) eurent lieu au même moment que le gauchissement du craton arabique. Bien plus, le «Trap»-volcanisme du Tertiaire Inférieur n'a lieu que dans le voisinage du Golfe d'Aden (Yemen, W-Aden Protectorat, Éritrea, Ethiopia, Somali). Des recherches géophysiques et océanographiques dans le Golfe d'Aden et la Mer Rouge suggèrent que des emplacements de matériaux d'origine magmatique forment une croûte quasi-océanique («Sea-floor Spreading») dans le fossé d'effondrement. Ceci est apparement la cause du déplacement des blocs continentaux. Les proches coïncidences aussi bien en époque qu'en direction des activités épirogéniques, orogéniques et volcaniques entre le craton arabique et le «Sea-floor Spreading» du Golfe d'Aden indiquent des correspendances tectoniques.Cette impression est encore plus renforcée, si l'on considère les développements plus récents du craton arabique. La jeune ceinture Tertiaire d'«Aden»-Volcanisme (Miocène-Recent) s'étend depuid le rift d'Afrique de l'est jusqu'en Turquie au travers du craton arabique de l'ouest. Elle se trouve de ce fait être plus ou moins parallèle à la Mer Rouge. Les gauchissements (Ras En Naqb, Jafr dépression, Bayir hautes plaines, Wadi Sirhan bassin, Rutba dome, Bassin Mésopotanien) de la partie septentrionale du craton arabique, où disparaissent des structures (identiques à celles du Golfe d'Aden) dévelopées au paravent, peuvent être associées en temps et direction au « rifting » de la Mer Rouge. Les failles le long du système Aquaba-Mer Morte sont du même âge et coupent les prémontagnes de l'Arabie septentrionale. Finalement le plissement de la ceinture montagneuse de Zagros appartient aussi au Miocène.Le craton arabique délimité par des structures d'âge et de directions différentes et toujours en cours de séparation, est un example classique de l'effet de la «Sea-floor Spreading» sur un craton et sur sa ceinture instable environnante. L'interprétation correcte de ces effets tectoniques resultera, le cas échéant, en des conclusions fondamentales très importantes.

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. . , , w . — - , - . , -, (seafloor-spreading) , . — , , ( , ). , , ( , ) ; .

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Formerly Southwest Center for Advanced Studied P. O. Box 30 365 Dallas Texas 75 230(Contribution No.81).     

Estimation of covariance matrix from geochemical data with observations below detection limits

Multivariate statistical analyses have been extensively applied to geochemical measurements to analyze and aid interpretation of the data. Estimation of the covariance matrix of multivariate observations is the first task in multivariate analysis. However, geochemical data for the rare elements, especially Ag, Au, and platinum-group elements, usually contain observations the below detection limits. In particular, Instrumental Neutron Activation Analysis (INAA) for the rare elements produces multilevel and possibly extremely high detection limits depending on the sample weight. Traditionally, in applying multivariate analysis to such incomplete data, the observations below detection limits are first substituted, for example, each observation below the detection limit is replaced by a certain percentage of that limit, and then the standard statistical computer packages or techniques are used to obtain the analysis of the data. If a number of samples with observations below detection limits is small, or the detection limits are relatively near zero, the results may be reasonable and most geological interpretations or conclusions are probably valid. In this paper, a new method is proposed to estimate the covariance matrix from a dataset containing observations below multilevel detection limits by using the marginal maximum likelihood estimation (MMLE) method. For each pair of variables, sayY andZ whose observations containing below detection limits, the proposed method consists of three steps: (i) for each variable separately obtaining the marginal MLE for the means and the variances, , , , and forY andZ: (ii) defining new variables by and and lettingA=C+D andB=C–D, and obtaining MLE for variances, and forA andB; (iii) estimating the correlation coefficient _YZ by and the covariance _YZ by . The procedure is illustrated by using a precious metal geochemical data set from the Fox River Sill, Manitoba, Canada.     

Colquiriit,ein neues Fluoridmineral aus der Zinnlagerstätte von Colquiri in Bolivien

Zusammenfassung Colquiriit tritt in Vergesellschaftung mit Ralstonit, Gearksutit, Zinkblende, Madocit und Pyrit im Bereich der Zinnlagerstätte von Colquiri in Bolivien auf. Das als selten zu betrachtende Mineral bildet maximal cm-große xenomorphe durchscheinende bis durch-sichtige Körner von weißlicher Farbe. Es zeigt keine Spaltbarkeit. Härte ca. 4; Dichte (gem.) 2,94, (ber.) 2,95 g/cm³;n 1,385±0.002,n 1,388±0,002, einachsig oder schwach zweiachsig, negativ. Colquiriit kristallisiert trigonal, Raumgruppe oderP31c,a ₀ 5,02,c ₀ 9,67 Å,Z=2. Stärkste Linien des Pulverdiagramms: 3,98(7) ; 3,23(10) ; 2,22(9) ; 1,736(8) . Eine chemische Analyse ergab: Li 3,1, Na 0,34, Mg 0,55, Ca 22,8, Al 13,4, F 58,0, Gewichtsverlust (105 °C) 0,5, Summe 98,69%, woraus sich die idealisierte Formel LiCaAlF₆ ableiten läßt. Beim Erhitzen wird das Gitter zwischen 800 und 900°C zerstört.

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Colquiriite, a new fluoride mineral from the Colquiri tin deposit in Bolivia

Summary Colquiriite occurs at the Colquiri tin deposit in Bolivia and is associated with ralstonite, gearksutite, sphalerite, madocite and pyrite. The mineral, which probably is a rare species, forms anhedral translucent to transparent white grains reaching up to 1 cm in size. No cleavage; hardness about 4; density (meas.) 2.94, density (calc.) 2.95 g/cm³;n 1.385±0.002,n 1.388±0.002, uniaxial or weakly biaxial, negative. Colquiriite is trigonal,a ₀ 5.02,c ₀ 9.67 Å, space group orP31c,Z=2. The strongest lines of the powder pattern are: 3.98(7) ; 3.23(10) ; 2.22(9) ; 1.736(8) . The chemical analysis gave: Li 3.1, Na 0.34, Mg 0.55, Ca 22.8, Al 13.4, F 58.0, weight loss (105 °C) 0.5, sum 98.69%, leading to the idealized formula LiCaAlF₆. Heating experiments show that the lattice breaks down between 800 and 900 °C. The new mineral and its name have been approved by the I.M.A. Commission on New Minerals and Mineral Names.

     

Stochastic modeling of gold mineralization in the Champion lode system of Kolar gold fields (India)

Stochastic modeling of gold mineralization in the Champion lode of Kolar gold fields was carried out using assay data taken from developmental headings. After dividing the lode into 71 horizontal and 18 vertical strata, autoregressive (AR), moving average (MA), and autoregressive and moving average (ARMA) models were developed and applied. The model selection with the acf and pacf for the various strata showed that in most of the cases, ARMA modeling of first-order would forecast gold headings with a reasonable degree of confidence. This was substantiated by comparing the coefficients of variation. From a parsimony point of view, AR (1) model may also be considered valid. The best overall models are: ARMA (1, 1), ; AR (1), , where a_t is N (0, _a ² ), x is in logarithms of in-dwt, and t is in block units of 100 ft. The applications of these models to a specific stratum are given. These models would also be helpful to describe the characteristics of the gold mineralization process of this lode.     

Stratigraphisch-Paläontologische Hinweise zum Ablauf tektonischer Ereignisse in den Ostalpen während der Kreidezeit

Zusammenfassung Im Hinblick auf den zeitlichen Ablauf orogener Ereignisse und ihre paläogeographischen Auswirkungen werden vorwiegend mikropaläontologische Resultate referiert, die ihren sehr raschen Ablauf während nur ein bis zwei Faunenzonen bzw. innerhalb einer Unterstufe wahrscheinlich machen. Dies gilt für die Austrische Phase innerhalb des Gault, die Vorgosauische Phase innerhalb des höheren Turon und eine baugeschichtlich sehr bedeutsame Intragosauische Phase im Unteren Ober-Campan. Im Verlaufe oder unmittelbar nach diesen tektonischen Ereignissen kommt es vorgosauisch und intragosauisch auch zur Verlandung, was durch Süßwasser-Fossilien und durch Landsaurier-Reste bewiesen werden kann. Die neu erfolgende marine Ingression bringt dann wieder marine Mikrofaunen, deren Altersunterschied zu jenen jüngsten marinen Faunen vor der jeweiligen tektonischen Phase erstaunlich gering ist. Es gibt jedoch in den Kreideschichten der Ostalpen kein Profil und keine Aufschlußfolge, wo all diese Umstände zusammen nachweisbar sind. Vielmehr bedarf es, infolge der Lückenhaftigkeit der Überlieferung, einer Kombination paläontologischer, stratigraphischer, paläogeographischer, petrographischer und tektonischer Studien in einem größeren Umkreis.

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The velocity of orogenetic events and their palaeogeographic effects are discussed from a point of view which is supported by micropalaeontological studies. These studies enable to prove the beginning and end of the orogenetic events within one or two faunistic zones or stratigraphic substages. This is demonstrated for the Austric orogenetic phase within the Gault (Late Aptian — Albian times), for the Pregosavian orogenetic phase within the Upper Turonian, and for an important Intragosavian orogenetic phase within early Upper Campanian times, too. During the movements of the Pregosavian and the Intragosavian phase or immediately following to them the seafloor emerged. Continental environments are confirmed by freshwater fossils and remains of terrestric reptiles. Succeeding new marine ingression brings new marine microfossils demonstrating that there is only a slight difference in geological age to the marine fauna living just before the gone orogenetic phase. Unfortunately there is no locality in the Eastern Alps, where all these events could be demonstrated in continuously sedimented Cretaceous beds. The fragmentarity of the geological evidence, however, enforces a combination of palaeontological, stratigraphical, palaeogeographical, petrological, and tectonical studies in more expanded areas.

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Résumé L'auteur, envisageant le déroulement temporel d'événements orogéniques et leurs répercussions paléogéographiques fait état avant tout de résultats micropaléontologiques qui rendent vraisemblable leur déroulement très rapide pendant seulement une à deux zones fauniques, c'est-à-dire à l'intérieur d'un sous-étage. Ceci s'applique à la phase Austrique pendant le Gault, à la phase pré-Gosau pendant le Turonien supérieur et à une phase Intra-Gosau, au début du Campanien supérieur, très importante du point de vue de l'histoire tectonique. Au cours de ces événements tectoniques ou immédiatement après, survient, au cours du pré-Gosau et de l'intra-Gosau, une émersion qui peut être prouvée par des fossiles limniques et par des restes de sauriens terrestres. L'ingression marine qui lui fait suite, ramène à nouveau des microfaunes marines, d'âge étonnament peu différent de celui des plus jeunes faunes marines qui ont vécu avant chaque phase tectonique. Toutefois, il n'existe, dans le Crétacé des Alpes orientales, aucun profil ni série d'affleurements où tous ces faits puissent être démontrés en même temps. Bien plus, le nourissage sédimentaire impliquant des lacunes, il faut combiner les études paléontologiques, stratigraphiques, paléogéographiques, pétrographiques et tectoniques dans une vue plus large.

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, , , . . - , , 1–2 . Austrische Gault'e, Vorgosauische Intragosauische . , , . , . , , . , , , .

     

Estimating relative bed-load contributions by lithology counts

In gravel-bedded streams where bed material of a tributary differs distinctly in lithology from that of the main stream, rock-type percentages can be used to estimate bed-load contributions of the two streams. The rock type that shows the greatest difference in abundance between the two streams is selected as the indicator lithology. Percentages of this lithology are estimated in both the main stream and tributary stream above their junction, and also in the main stream at a distance sufficiently downstream from the junction to allow complete mixing. The fraction of bed load contributed by the main stream, p,is estimated by ,where is an estimate of the proportion of indicator rock fragments in the bed of the main stream above the junction, is an estimate of the proportion in the bed of the tributary above the junction, and is an estimate of the proportion in the bed of the main stream below the junction. The variance of is obtained as var ( )= [p₁q₁(p_r – p₂)²/n(p₁ – p₂)⁴] + [p₂q₂(p_r – p₁)²/n(p₁ – p₂)⁴] + [p_rq_r/n(p₁ – p₂)²].Although no estimate of actual quantity of bed load is provided, the indicator rock technique supplies data that can serve as a check on data obtained by means of empirical formulas or actual transport measurements.     

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.     

Maximum entropy and shear strain of shear zone

The principle of maximum entropy can be used to determine the shear strain in natural shear zones. When the margin of a shear zone is assumed, the principle leads to the truncated exponential distribution of the shear strain. Ifx is the distance remote from the shear zone center, which possesses the maximum shear strain, the shear strain (x) is given by

Redox states of lithospheric and asthenospheric upper mantle

The oxidation state of lithospheric upper mantle is heterogeneous on a scale of at least four log units. Oxygen fugacities ( ) relative to the FMQ buffer using the olivine-orthopyroxene-spinel equilibrium range from about FMQ-3 to FMQ+1. Isolated samples from cratonic Archaean lithosphere may plot as low as FMQ-5. In shallow Proterozoic and Phanerozoic lithosphere, the relative is predominantly controlled by sliding Fe³⁺-Fe²⁺ equilibria. Spinel peridotite xenoliths in continental basalts follow a trend of increasing with increasing refractoriness, to a relative well above graphite stability. This suggests that any relative reduction in lithospheric upper mantle that may occur as a result of stripping lithosphere of its basaltic component is overprinted by later metasomatism and relative oxidation. With increasing pressure and depth in lithosphere, elemental carbon becomes progressively refractory and carbon-bearing equilibria more important for control. The solubility of carbon in H₂O-rich fluid (and presumably in H₂O-rich small-degree melts) under the P,T conditions of Archaean lithosphere is about an order of magnitude lower than in shallow modern lithosphere, indicating that high-pressure metasomatism may take place under carbon-saturated conditions. The maximum in deep Archaen lithosphere must be constrained by equilibria such as EMOG/D. If the marked chemical depletion and the orthopyroxene-rich nature of Archaean lithospheric xenoliths is caused by carbonatite (as opposed to komatiite) melt segregation, as suggested here, then a realistic lower limit may be given by the H₂O +C=CH₄+O₂ (C-H₂O) equilibrium. Below C –H₂O a fluid becomes CH₄ rather than CO₂-bearing and carbonatitic melt presumably unstable. The actual in deep Archaean lithosphere is then a function of the activities of CO₂ and MgCO₃. Basaltic melts are more oxidized than samples from lithospheric upper mantle. Mid-ocean ridge (MORB) and ocean-island basalts (OIB) range between FMQ-1 (N-MORB) and about FMQ +2 (OIB). The most oxidized basaltic melts are primitive island-arc basalts (IAB) that may fall above FMQ+3. If basalts are accurate probes of their mantle sources, then asthenospheric upper mantle is more oxidized than lithosphere. However, there is a wide range of processes that may alter melt relative to that of the mantle source. These include partial melting, melt segregation, shifts in Fe³⁺/Fe²⁺ melt ratios upon decompression, oxygen exchange with ambient mantle during ascent, and low-pressure volatile degassing. Degassing is not very effective in causing large-scale and uniform shifts, while the elimination of buffering equilibria during partial melting is. Upwelling graphite-bearing asthenosphere will decompress along -pressure paths approximately parallel to the graphite saturation surface, involving reduction relative to FMQ. The relative will be constrained to below the CCO equilibrium and will be a function of . Upwelling asthenosphere whose graphite content has been exhausted by partial melting, or melts that have segregated and chemically decoupled from a graphite-bearing residuum will decompress along -decompression paths controlled by continuous Fe³⁺-Fe²⁺ solid-melt equilibria. These equilibria will involve increases in relative to the graphite saturation surface and relative to FMQ. Melts that finally segregate from that source and erupt on the earth's surface may then be significantly more oxidized than their mantle sources at depth prior to partial melting. The extent of melt oxidation relative to the mantle source may be directly proportional to the depth of graphite exhaustion in the mantle source.     

A Coupled Riverine-Marine Fractionation Model for Dissolved Rare Earths and Yttrium

Fractionation of yttrium (Y) and the rare earth elements (REEs) begins in riverine systems and continues in estuaries and the ocean. Models of yttrium and rare earth (YREE) distributions in seawater must therefore consider the fractionation of these elements in both marine and riverine systems. In this work we develop a coupled riverine/marine fractionation model for dissolved rare earths and yttrium, and apply this model to calculations of marine YREE fractionation for a simple two-box (riverine/marine) geochemical system. Shale-normalized YREE concentrations in seawater can be expressed in terms of fractionation factors ( _ij ) appropriate to riverine environments ( ) and seawater ( ):

Bivariate normal distribution fitting on discontinuity orientation clusters

A bivariate normal density function has been used to represent discontinuity orientation cluster distributions. Goodness-of-fit tests should be performed in order to make decisions on the representation of discontinuity clusters by theoretical probability distributions. In the literature, graphical procedures are available to fit a bivariate normal distribution to discontinuity clusters. However, these procedures assume no correlation between the two orientation parameters. In this paper (a) a numerical procedure, and (b) a semigraphical procedure are given to perform a ² goodness-of-fit test for bivariate normal distributions having nonzero correlation coefficient between the two parameters. These procedures were applied to a selected discontinuity cluster. The semigraphical procedure was found to be a time-consuming process. On the other hand, rapid computation can be done with the computer program developed for the numerical method. Sensitivity of the ² test results of theIXJ grid setup was investigated. Mean orientation estimation for the cluster based on the equal area polar projection was compared with the estimation based on the moment estimate method. For the cluster analyzed, estimations of bivariate normal parameters and , based on the equal-area polar projection, and values based on the moment estimation method were found to be different up to about 6.7% of the values based on the moment estimation method.     

The role of CO2 in the genesis of olivine melilitite

The nature of the near-liquidus phases for a mantle-derived olivine melilitite composition have been determined at high pressure under dry conditions and with various water contents. Olivine and clinopyroxene occur on or near the liquidus and there are no conditions where orthopyroxene crystallizes in equilibrium with the olivine melilitite. We have determined the effect on the liquidus temperature and liquidus phases of substituting CO₂ for H₂O on a mole for mole basis at 30 kb, using olivine melilitite + 20 wt% H₂O at = 0 and = (CO₂)/(H₂+CO₂) (mole fraction) = 0.25, 0.5, 0.75 and 1.0 (i.e. olivine melilitite + 38 wt% CO₂). Experiments were buffered by the MH or NNO buffers. At 30 kb, CO₂ is only slightly less soluble than water for <0.5 as judged by the slight increase in liquidus temperature on mole-for-mole substitution of CO₂ for H₂O and at 30 kb, 1200° C, = = 0.5 the olivine melilitite contains 8.8 wt% H₂O and 21 wt% CO₂ in solution. For 1 the CO₂ saturated liquidus is depressed 70 ° C below the anhydrous liquidus and the magma dissolves approx. 17% CO₂ at 30kb, 1400 ° C, 1, 0. Infrared spectra of quenched glasses have absorption bands characteristic of CO ₃ ⁼ and OH- molecules and no evidence for HCO ₃ ^- . The effect of CO ₃ ⁼ molecules dissolved in the olivine melilitite at high pressure is to suppress the near-liquidus crystallization of olivine and clinopyroxene and bring orthopyroxene and garnet on to the liquidus. We infer that olivine melilitite magmas may be derived by equilibrium partial melting (<5%) of pyrolite at 30 kb, 1150–1200 ° C, provided that both H₂O and CO₂ are present in the source region in minor amounts. Preferred conditions are 0< <0.5, 0.5< <1, and at low oxygen fugacities (相似文献   

Oxygen isotope geochemistry of pyroclastic clinopyroxene monitors carbonate contributions to Roman-type ultrapotassic magmas

The oxygen isotope geochemistry and chemical composition of clinopyroxene crystals from Alban Hills pyroclastic deposits constrain the petrological evolution of ultrapotassic Roman-type rocks. Volcanic eruptions in the 560–35 ka time interval produced thick pyroclastic deposits bearing clinopyroxene phenocrysts with recurrent chemical characteristics. Clinopyroxenes vary from Si–Mg-rich to Al–Fe-rich with no compositional break, indicating that they were derived from a continuous process of crystal fractionation. Based on the ¹⁸O and trace element data no primitive samples were recovered: monomineralic clinopyroxene cumulates set the oxygen isotope composition of primary magmas in the range of uncontaminated mantle rocks (5.5), but their REE composition resulted from extensive crystal fractionation. Departing from these mantle-like ¹⁸O_Cpx values the effects of crustal contamination of clinopyroxene O-isotope composition were identified and used to monitor chemical variations in the parental magma. ¹⁸O values in Si–Mg-rich clinopyroxene are slightly higher than typical mantle values (5.9–6.2), and the low REE contents are representative of early stages of magmatic differentiation. ¹⁸O values as high as 8.2 are associated with Al–Fe³⁺-rich clinopyroxene showing high REE contents. These ¹⁸O values are characteristic of crystals formed during the late magmatic stages of each main eruptive phase. Geochemical modelling of ¹⁸O values vs. trace element contents indicates that these ultrapotassic magmas were derived from fractional crystallization plus assimilation of limited amounts of carbonate wall rocks starting from a primary melt, and from interaction with CO₂ derived from country rocks during crystal fractionation.     

Koritnigit,Zn[H2O|HOAsO3], ein neues Mineral aus Tsumeb,Südwestafrika

Zusammenfassung Das neue Mineral Koritnigit ist ein wasserhaltiges Zinkhydrogenarsenat der Formel Zn[H₂O|HOAsO₃]. Die chemische Analyse (Elektronenmikrosonde und T.G.A.) ergab: As₂O₅ 51,75%, ZnO 35,97% und H₂O 12,3%, Summe 100,0%. Die HOAsO₃-Ionen wurden IR-spektroskopisch nachgewiesen. Koritnigit ist löslich in kalter, verdünnter HCl und HNO₃.Die Gitterkonstanten sind:a ₀=7,948(2),b ₀=15,829(5),c ₀=6,668(2) Å, =90,86(2), =96,56(2), =90,05(2)^o,V=833,2(4)ų,V=8. Die Raumgruppe ist . Die stärksten Linien des Pulverdiagramms sind: 7,90(10) (020,100), 3,83(7) ( ), 3,16(9) ( ) 2,926(4) (150), 2,679(4) ( ), 2,461(6) ( ), 2,186(5) ( ), 1,969(4) (400), 1,649(3) (004).Koritnigit ist wasserklar bis durchscheinend weiß. Idiomorphe Kristalle sind nicht bekannt. Die Spaltbarkeit nach {010} ist ausgezeichnet und auf {010} sind Spaltspuren nach [001] und nach [100] erkennbar. Härte 2.G=3,54 g·cm^–3,D _x =3,56 g·cm^–3. Koritnigit ist optisch zweiachsig positiv, 2V70(5)^o. Die Werte der Lichtbrechung sind:n =1,632(5),n =1,652(3) undn =1,693(3).Koritnigit wurde auf der 31. Sohle der Tsumeb-Mine, Südwestafrika gefunden. Er kommt als Sekundärmineral in Paragenese mit Cu-Adamin, Stranskiit und drei weiteren, vorerst nicht identifizierten mineralen in Zersetzungshohlräumen von Tennantit vor.

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Koritnigite, Zn[H₂O|HOAsO₃], a new mineral from Tsumeb, South West Africa

Summary The new mineral koritnigite is a hydrated zinc hydrogen arsenate with the formula Zn[H₂O|HOAsO₃]. Chemical analysis (electron microprobe and t.g.a.) gave: As₂O₅ 51.75%, ZnO 35.97%, and H₂O 12.3%, total 100.0%. The HOAsO₃ ions were determined by IR spectroscopy. Koritnigite is soluble in cold diluted HCl and HNO₃. The unit cell dimensions are:a ₀=7.948(2),b ₀=15.829(5),c ₀=6.668(2)Å, =90.86(2), =96.56(2), =90.05(2)^o,V=833.2(4) ų,Z=8. The space group is . The strongest lines of the powder pattern are: 7.90(10) (020, 100), 3.83(7) ( ), 3.16(9) ( ), 2.926(4) (150), 2.679(4) ( ), 2.461(6) ( ), 2.186(5) ( ), 1.969(4)(400), 1.649(3) (004).

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Mit 2 Abbildungen

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Herrn Univ. Prof. Dr.H. Meixner zum 70. Geburtstag gewidmet.     

Titania precipitation in sapphire containing iron and titanium

Titania, TiO₂, precipitation in natural blue sapphire (Fe, Ti: -Al₂O₃) has been investigated using high resolution and analytical transmission electron microscopy. The structure and habit of the TiO₂ precipitate depends on both the Ti⁴⁺ concentration and the temperature at which the precipitate formed. Tetragonal TiO₂ (Rutile) grows at 1350° C but at 1150° C an orthorhombic non-equilibrium TiO₂ polymorph precipitates. Both TiO₂ polymorphs nucleate in the (0001)s plane as lens shaped discs twinned along their diameter. The crystallographic alignment of each type of TiO₂ precipitate with respect to the -Al₂O₃ host matrix provides a high degree of structural coherency with minimal lattice mismatch. Electron diffraction analysis established the following precipitate/host orientation relationships: tetragonal TiO₂: {011}r {11 07B;100}r(0001)s and 01 r10 0s twinned along the (011)r planeand orthorhombic TiO₂: {021}{11 0}s, {100}(0001)s and 0 2 10 0s twinned along the (021) plane.     

Zur Tektonik des andinen Bolivien

Zusammenfassung Es wird eine kurze Übersicht der neuen Erkenntnisse über die Tektonik des andinen Bolivien gegeben. Die wichtigsten Ergebnisse sind folgende:Das Präkambrium des brasilianischen Schildes reicht, direkt von mächtigem Alluvium bedeckt, NW Santa Cruz bis nahe an den Andenrand. Im Süden bricht es an einer Störung ab, die in 17° 30 S bis an den Andenrand reicht und als Schwächezone nach W bis zur Achse der Cordillera Real zu verfolgen ist. Diese teilt den geosynklinalen Raum in einen nördlichen, im Ostteil gehobenen und einen südlichen, tiefer liegenden Abschnitt.Der Andenblock ist ein Bruchfaltengebirge. Die Auf- und Abschiebungen der Blöcke sind zumeist in vertikalem Sinne erfolgt und nur im Subandin am Ostrande gegen Osten gerichtet. Stärkere epirogene Bewegungen haben gegen Ende des Perms stattgefunden. Mit ihnen ist die Intrusion der älteren Granite der Cordillera Real verknüpft. Epirogene Krustenbewegungen im Jura waren besonders stark im Raum von Potosi und südlicher, wo starke Faltungen und Diskordanzen beobachtet wurden. Die einzige starke Orogenese ist im Pliozän erfolgt, sie hat den gesamten Andenblock mitsamt Altiplano und Subandin einheitlich erfaßt. Die Plutone der Cordillera Quimsa Cruz, des Illimani und von Kari-Kari sind miozän und wohl als präorogen zu deuten. Der intensive Vulkanismus im post-geosynklinalen Raum und im Altiplano ist pliozän und postorogen.

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This paper presents new information concerning the tectonics of the Andean portion of Bolivia. The most important results are:In NW Santa Cruz, the Precambrian Brazilian shield extends westward nearly as far as to the Andean border; it is covered only with quaternary sediments. To the south it ends at a fault, which reaches the Andean border at 17° 30 S. This old tectonic zone of weakness extends west as far as to the axis of the Cordillera Real, and divides the Andean block into a northern portion, which is elevated in the east, and a southern portion in lower position.The Andes consist of a system of fractured folds. The movement of fault blocks was predominantly vertical, but in the Subandean belt at the eastern margin they were directed east. Epirogenic movements were relatively intensive at the end of the Permian; the intrusion of the older granites is related to these movements. Jurassic epirogenic movements were intensive in the area of Potosi and south, where intensive folding and unconformities were observed. The only intensive orogeny, which is of Pliocene age, affected the entire Andean block including Altiplano and Subandean belt. The granitic intrusions of the Cordillera Quimsa Cruz, of the Illimani, and of Kari-Kari of Miocene age are interpreted to be pre-orogenic. The intensive volcanism of the post-geosynclinal region and in Altiplano is post-orogenic and of Pliocene age.

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Résumé L'auteur donne un résumé des connaissances acquises sur la tectonique des Andes boliviennes à partir des travaux publiés ces dix dernières années. Les résultats les plus importantes sont les suivants:Le Précambrien du bouclier brésilien, qui a fortement influencé la tectonique du géosynclinal andin, s'étend, recouvert du Quaternaire, jusqu'au pied du massif andin. Le Précambrien se termine au Sud, le long d'une faille ancienne qui, à la latitude 17° 30, s'étend jusqu'au pied des Andes et se poursuit sous forme d'une zone de faiblesse jusqu'à l'axe de la Cordillera Real. Cette ligne ancienne divise l'aire geosynclinale en une partie septentrionale qui a été soulevée et une partie méridionale abaissée.Le massif andin est le résultat de soulèvements de blocs, généralement suivant la verticale, et de plissements asymétriques. Dans la zone subandine les mouvements tectoniques montrent un déversement vers l'Est. Généralement les terrains sont concordants depuis l'Ordovicien jusqu'au Tertiaire.Des mouvements epirogéniques se sont produits pour la première fois a la fin du Permien, en relacion avec les intrusions des massifs granitiques dans la Cordillera Real. Pendant le Jurassique se sont produits des mouvements de blocs plus intenses accompagnés de plissements, surtout dans la zone de Potosi et plus au Sud.Il y eut récemment, au Pliocène, une orogénèse qui a affecté l'ensemble du bloc andin, y compris l'Altiplano et la zone subandine. Les plutons de la Cordillera Quimsa Cruz, de l'Illimani et, au Sud, de la cordillère Kari-Kari sont miocènes; le volcanisme intense dans l'aire post-géosynclinale et dans l'Altiplano est d'âge pliocène et post-orogénique.

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. Santa Cruz , . , 17° 30 Cordillera Real. , , , . , . , Cordillera Real. Potosi , . , Cordillera Quimsa Cruz, Illimani Kari-Kari . . . - Altiplano , . . .