Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

The hypogene iron oxide copper-gold mineralization in the Mantoverde District, Northern Chile

The Mantoverde iron oxide copper-gold (IOCC) district, northern Chile, is known for its Cu production from supergene ores. Recently, exploration outlined an additional hypogene ore resource of 440 Mt with 0.56 percent Cu, and 0.12 g/t An. The hypogene sulfide mineralization occurs mainly as chalcopyrite and pyrite, typically in specularite or magnetite-cemented breccias and associated stockworks. The host rocks underwent variably intense K feldspar alteration, chloritization, sericitization, silicification, and/or carbonatization. A district scale Na(-Ca) alteration is absent. The IOCC mineralization in the district shows a strong tectonic control by northwest- to north-northwest-trending brittle structures. Large Cu sulfide-rich veins or Cu sulfide-cemented breccias are absent. Therefore, head grades of 4 percent Cu are an exception. There is a positive correlation between Cu and An grades. Gold is probably contained mostly in chalcopyrite and pyrite. Elevated concentrations of light rare-earth elements (LREE) occur locally but are attributed to redistribution of LREE within the deposits rather than to derivation from external sources. The Cu-Au ores in the Mantoverde district are low in and have relatively low contents in heavy metals that are potentially hazardous to the environment, such as As (avg 14 ppm), Hg (<5 ppm), or Cd (<0.2 ppm). The sulfur isotope ratios of chalcopyrite from the IOCC deposits lie between -5.6 and 8.9 per mil delta(34)S(VCDT). They show systematic variations within the district, which are interpreted to reflect relative distance to inferred fluid conduits and the level of deposition within the hydrothermal system. Most initial (87)Sr/(86)Sr values of altered volcanic rocks and hydrothermal calcite from the Mantoverde district are between 0.7031 and 0.7060 and are similar to those of the igneous rocks of the region. Lead isotope ratios of chalcopyrite are consistent with Pb (and by inference Cu) derived from Early Cretaceous magmatism. The sulfur, strontium, and lead isotope data of chalcopyrite, calcite gangue, or altered host rocks, respectively, are compatible with a genetic model that involves cooling of metal and sulfur-bearing magmatic-hydrothermal fluids that mix with meteoric waters or seawater at relatively shallow crustal levels. An additional exotic sulfur input is likely, though not required, for the copper mineralization. Apart from the IOCC. deposits, there are a number of smaller magnetite(-apatite) bodies in the district. These are geologically similar to the Cu-Au-bearing magnetite bodies, but are related to splays of the north-south-trending Atacama fault zone and differ in alteration and texture.

Sulfur and strontium isotope composition of the Llobregat River (NE Spain): Tracers of natural and anthropogenic chemicals in stream waters

The use of sulfur and strontium isotopes as tracers for the source/s of water contaminants have been applied to the water of the Llobregat River system (NE Spain). Surface water samples from June 1997 were collected from the Llobregat River and its main tributaries and creeks. The chemistry of most stream waters are controlled mainly by the weathering of Tertiary chemical sediments within the drainage basin. The largest variation in delta(34)S values were found in the small creeks with values ranging from -9.9 to 15parts per thousand, whilst in the main river channels values ranged from 6.3 to 12.4parts per thousand. The Sr-87/Sr-86 ratio for dissolved strontium ranged from 0.70795 for a non-polluted site to 0.70882 for a polluted one. Most of the waters with high NO3 and low Ca/Na ratio converge to the same Sr-87/Sr-86 value, pointing to dominant pollutant end member contribution or a mixing of pollutants with an isotopic composition around 0.7083-0.7085. Although the concentration of the natural inputs in the river for sulfate and strontium are high, as a result of the sulfate outcrops within the geology of the basin, their isotopic characteristics suggest that they can be used as a discriminating device in water pollution problems. However to establish the detailed characteristics of the isotopes as geochemical tools, specific high-resolution case studies are necessary in small areas, where the inputs are well known.

Major-elements trends in cenozoic volcanites of Hungary

Hungary lies entirely within the Carpatho-Pannonian Region (CPR), a dominant tectonic unit of eastern Central Europe. The CPR consists of the Pannonian Basin system, and the arc of the Carpathian Mountains surrounding the lowlands in the north, east, and southeast. In the west, the CPR is bounded by the Eastern Alps, whereas in the south, by the Dinaridic belt. (...)

Bayesian tools for zero counts in compositional data

The log-ratio methodology makes available powerful tools for analyzing compositionaldata. Nevertheless, the use of this methodology is only possible for those data setswithout null values. Consequently, in those data sets where the zeros are present, aprevious treatment becomes necessary. Last advances in the treatment of compositionalzeros have been centered especially in the zeros of structural nature and in the roundedzeros. These tools do not contemplate the particular case of count compositional datasets with null values. In this work we deal with \count zeros" and we introduce atreatment based on a mixed Bayesian-multiplicative estimation. We use the Dirichletprobability distribution as a prior and we estimate the posterior probabilities. Then weapply a multiplicative modi¯cation for the non-zero values. We present a case studywhere this new methodology is applied.Key words: count data, multiplicative replacement, composition, log-ratio analysis

Discovering similarities in the time use patterns of the Spanish Autonomous Communities by Fuzzy techniques

In 2000 the European Statistical Office published the guidelines for developing theHarmonized European Time Use Surveys system. Under such a unified framework,the first Time Use Survey of national scope was conducted in Spain during 2002–03. The aim of these surveys is to understand human behavior and the lifestyle ofpeople. Time allocation data are of compositional nature in origin, that is, they aresubject to non-negativity and constant-sum constraints. Thus, standard multivariatetechniques cannot be directly applied to analyze them. The goal of this work is toidentify homogeneous Spanish Autonomous Communities with regard to the typicalactivity pattern of their respective populations. To this end, fuzzy clustering approachis followed. Rather than the hard partitioning of classical clustering, where objects areallocated to only a single group, fuzzy method identify overlapping groups of objectsby allowing them to belong to more than one group. Concretely, the probabilistic fuzzyc-means algorithm is conveniently adapted to deal with the Spanish Time Use Surveymicrodata. As a result, a map distinguishing Autonomous Communities with similaractivity pattern is drawn.Key words: Time use data, Fuzzy clustering; FCM; simplex space; Aitchison distance

Studies in stoichiometry with compositional data

Geochemical data that is derived from the whole or partial analysis of various geologic materialsrepresent a composition of mineralogies or solute species. Minerals are composed of structuredrelationships between cations and anions which, through atomic and molecular forces, keep the elementsbound in specific configurations. The chemical compositions of minerals have specific relationships thatare governed by these molecular controls. In the case of olivine, there is a well-defined relationshipbetween Mn-Fe-Mg with Si. Balances between the principal elements defining olivine composition andother significant constituents in the composition (Al, Ti) have been defined, resulting in a near-linearrelationship between the logarithmic relative proportion of Si versus (MgMnFe) and Mg versus (MnFe),which is typically described but poorly illustrated in the simplex.The present contribution corresponds to ongoing research, which attempts to relate stoichiometry andgeochemical data using compositional geometry. We describe here the approach by which stoichiometricrelationships based on mineralogical constraints can be accounted for in the space of simplicialcoordinates using olivines as an example. Further examples for other mineral types (plagioclases andmore complex minerals such as clays) are needed. Issues that remain to be dealt with include thereduction of a bulk chemical composition of a rock comprised of several minerals from which appropriatebalances can be used to describe the composition in a realistic mineralogical framework. The overallobjective of our research is to answer the question: In the cases where the mineralogy is unknown, arethere suitable proxies that can be substituted?Kew words: Aitchison geometry, balances, mineral composition, oxides

Possible solution of some essential zero problems in compositional data analysis

One of the tantalising remaining problems in compositional data analysis lies in how to deal with data sets in which there are components which are essential zeros. By anessential zero we mean a component which is truly zero, not something recorded as zero simply because the experimental design or the measuring instrument has not been sufficiently sensitive to detect a trace of the part. Such essential zeros occur inmany compositional situations, such as household budget patterns, time budgets,palaeontological zonation studies, ecological abundance studies. Devices such as nonzero replacement and amalgamation are almost invariably ad hoc and unsuccessful insuch situations. From consideration of such examples it seems sensible to build up amodel in two stages, the first determining where the zeros will occur and the secondhow the unit available is distributed among the non-zero parts. In this paper we suggest two such models, an independent binomial conditional logistic normal model and a hierarchical dependent binomial conditional logistic normal model. The compositional data in such modelling consist of an incidence matrix and a conditional compositional matrix. Interesting statistical problems arise, such as the question of estimability of parameters, the nature of the computational process for the estimation of both the incidence and compositional parameters caused by the complexity of the subcompositional structure, the formation of meaningful hypotheses, and the devising of suitable testing methodology within a lattice of such essential zero-compositional hypotheses. The methodology is illustrated by application to both simulated and real compositional data

U-Pb isotopic dating of fluid infiltration and metasomatism during Dalradian regional metamorphism in Connemara, western Ireland

A metasomatic diopside rock occurs at the top of the dolomitic Connemara Marble Formation of western Ireland and contains titanite and K-feldspar in addition to around 90% diopside (X(Mg) = 0.90-0.97). U-Pb isotopic measurements on this mineral assemblage show that the titanite is both unusually uranium-rich and isotopically concordant, with the result that a precise U-Pb age of 478 +/- 2.5 Ma can be determined. The age is identical within error to a less precise Rb-Sr age of diopside-K-feldspar of 483 +/- 6 Ma. Petrological evidence indicates that the assemblage crystallized at c. 620-degrees-C close to or below the closure temperature of titanite. The age thus provides a precise estimate of the time of metamorphism; this age is 11 +/- 3 Ma younger than the 490 Ma age for nearby gabbroic plutons which has previously been used to constrain the peak metamorphic age. This difference accords well with geological evidence that the gabbros were emplaced prior to the metamorphic peak. Analysis of minerals with high closure temperature from assemblages whose crystallization is unambiguously associated with a specific episode of fluid infiltration at the peak of metamorphism provides the basis for a new approach to dating metamorphism. The success of this approach is demonstrated by the results from Connemara.

Application of discriminant function analysis and change-point problem in dating volcanic ashes

The application of Discriminant function analysis (DFA) is not a new idea in the studyof tephrochrology. In this paper, DFA is applied to compositional datasets of twodifferent types of tephras from Mountain Ruapehu in New Zealand and MountainRainier in USA. The canonical variables from the analysis are further investigated witha statistical methodology of change-point problems in order to gain a betterunderstanding of the change in compositional pattern over time. Finally, a special caseof segmented regression has been proposed to model both the time of change and thechange in pattern. This model can be used to estimate the age for the unknown tephrasusing Bayesian statistical calibration

Monitoring procedures in environmental geochemistry and compositional data analysis theory

First discussion on compositional data analysis is attributable to Karl Pearson, in 1897. However, notwithstanding the recent developments on algebraic structure of the simplex, more than twenty years after Aitchison’s idea of log-transformations of closed data, scientific literature is again full of statistical treatments of this type of data by using traditional methodologies. This is particularly true in environmental geochemistry where besides the problem of the closure, the spatial structure (dependence) of the data have to be considered. In this work we propose the use of log-contrast values, obtained by asimplicial principal component analysis, as LQGLFDWRUV of given environmental conditions. The investigation of the log-constrast frequency distributions allows pointing out the statistical laws able togenerate the values and to govern their variability. The changes, if compared, for example, with the mean values of the random variables assumed as models, or other reference parameters, allow definingmonitors to be used to assess the extent of possible environmental contamination. Case study on running and ground waters from Chiavenna Valley (Northern Italy) by using Na+, K+, Ca2+, Mg2+, HCO3-, SO4 2- and Cl- concentrations will be illustrated

Grain size analyses in tin-lead glazes based on 2d-sections

A problem in the archaeometric classification of Catalan Renaissance pottery is the fact, thatthe clay supply of the pottery workshops was centrally organized by guilds, and thereforeusually all potters of a single production centre produced chemically similar ceramics.However, analysing the glazes of the ware usually a large number of inclusions in the glaze isfound, which reveal technological differences between single workshops. These inclusionshave been used by the potters in order to opacify the transparent glaze and to achieve a whitebackground for further decoration.In order to distinguish different technological preparation procedures of the single workshops,at a Scanning Electron Microscope the chemical composition of those inclusions as well astheir size in the two-dimensional cut is recorded. Based on the latter, a frequency distributionof the apparent diameters is estimated for each sample and type of inclusion.Following an approach by S.D. Wicksell (1925), it is principally possible to transform thedistributions of the apparent 2D-diameters back to those of the true three-dimensional bodies.The applicability of this approach and its practical problems are examined using differentways of kernel density estimation and Monte-Carlo tests of the methodology. Finally, it istested in how far the obtained frequency distributions can be used to classify the pottery

Statistical evidences of cyclic changes in volcanic gas chemistry composition by inverse modelling

The identification of compositional changes in fumarolic gases of active and quiescent volcanoes is one of the mostimportant targets in monitoring programs. From a general point of view, many systematic (often cyclic) and randomprocesses control the chemistry of gas discharges, making difficult to produce a convincing mathematical-statisticalmodelling.Changes in the chemical composition of volcanic gases sampled at Vulcano Island (Aeolian Arc, Sicily, Italy) fromeight different fumaroles located in the northern sector of the summit crater (La Fossa) have been analysed byconsidering their dependence from time in the period 2000-2007. Each intermediate chemical composition has beenconsidered as potentially derived from the contribution of the two temporal extremes represented by the 2000 and 2007samples, respectively, by using inverse modelling methodologies for compositional data. Data pertaining to fumarolesF5 and F27, located on the rim and in the inner part of La Fossa crater, respectively, have been used to achieve theproposed aim. The statistical approach has allowed us to highlight the presence of random and not random fluctuations,features useful to understand how the volcanic system works, opening new perspectives in sampling strategies and inthe evaluation of the natural risk related to a quiescent volcano

Modelling changes in stable isotope compositions of minerals during net transfer reactions in a contact aureole: Wollastonite growth at the northern Hunter Mountain Batholith (Death Valley National Park, USA)

One of the world's largest wollastonite deposits was formed at the contact of the northern Hunter Mountain Batholith (California, USA) in Paleozoic sediments. Wollastonite occurs as zones of variable thickness surrounding layers or nodules of quartzite in limestones. A minimum formation temperature of 650 degrees C is estimated from isolated periclase-bearing lenses in that area. Contact metamorphism of siliceous carbonates has produced mineral assemblages that are consistent with heterogeneous, and partly limited infiltration of water-rich fluids, compatible with O-18/O-16 and C-13/C-12 isotopic patterns recorded in carbonates. Oxygen isotope compositions of wollastonites in the study area may also not require infiltration of large quantities of externally-derived fluids that were out of equilibrium with the rocks. 8180 values of wollastonite are high (14.8 parts per thousand to 25.0 parts per thousand; median: 19.7 parts per thousand) and close to those of the host limestone (19.7 parts per thousand to 28 parts per thousand; median: 24.9 parts per thousand) and quartz (18.0 parts per thousand. to 29.1 parts per thousand; median: 22.6 parts per thousand). Isotopic disequilibrium exists at quartz/wollastonite and wollastonite/calcite boundaries. Therefore, classical batch/Rayleigh fractionation models based on reactant and product equilibrium are not applicable to the wollastonite rims. An approach that relies on local instantaneous mass balance for the reactants, based on the wollastonite-forming reaction is suggested as an alternative way to model wollastonite reaction rims. This model reproduces many of the measured delta O-18 values of wollastonite reaction rims of the current study to within +/- 1 parts per thousand, even though the wollastonite compositions vary by almost 10 parts per thousand. (C) 2011 Elsevier B.V. All rights reserved.

Indicator taxa of benthic diatom communities: a case study in Mediterranean streams

A key issue in the implementation of the Water Framework Directive is the classification of streams and rivers using biological quality parameters and type-specific reference conditions. Four groups of stream types were defined in NE Spain on the basis of 152 diatom samples by means of detrended correspondence analysis and classification techniques. Diatom analysis was restricted to epilithic taxa, and the sites included gradients ranging from near-natural streams to sites with poor ecological quality. The main gradient shows a clear separation of sites in relation to the degree of human influence: polluted streams (mainly located in the lowlands) differ from streams in mountainous areas and in the Pyrenees. A second gradient is related to physiographical features. Headwater streams can be distinguished by their catchment geology. The type-specific diatom taxa for the stream types studied were determined by using indicator species analysis (IndVal). The type-specific taxa from near-natural streams are coincident with the indicator taxa for high ecological status. Human impact reduced the typological heterogeneity of the diatom community composition. Overall, the diatom communities in NE Spain exhibit a regional distribution pattern that closely corresponds with that observed in river systems elsewhere. Physiographical differences are only evident in undisturbed sites, while nutrient enrichment and other human disturbances may mask the regional differences in the distribution of diatom communities