1,721,103 research outputs found
Grain-size control on petrographic composition of sediments: compositional regression and rounded zeroes
Full text linkIt is well-known that sediment composition strongly depends on grain size. A number of studies have tried to quantify this relationship focusing on the sand fraction, but only very limited data exists covering wider grain size ranges. Geologists have a clear conceptual model of the relation between grain size and sediment petrograpic composition, typically displayed in evolution diagrams. We chose a classical model covering grain sizes from fine gravel to clay, and distinguishing five types of grains (rock fragments, poly- and mono crystalline quartz, feldspar and mica/clay). A compositional linear process is fitted here to a digitized version of this model, by (i) applying classical regression to the set of all pairwise log-ratios of the 5-part composition against grain size, and (ii) looking for the compositions that best approximate the set of estimated parameters, one acting as slope and one as intercept. The method is useful even in the presence of several missing values. The linear fit suggests that the relative influence of the processes controlling the relationship between grain size and sediment composition is constant along most of the grain size spectrum.Postprint (published version
Simplifying compositional multiple regression: Application to grain size controls on sediment geochemistry
No full textModern geochemical data sets have typically around 20-30 compositional variables measured on some tens or hundreds of samples. A statistical analysis of data sets with so many variables should take as a priority the reduction of dimensionality of the model, in order to increase its reliability and enhance its interpretation. In the framework of compositional data analysis with multiple regression, such simplification can be achieved taking some geometric concepts into account. First, the sample space of compositions, the simplex, is given an Euclidean space structure by the compositional operations of perturbation, powering and Aitchison inner product. Then, given some qualitative information on which subcompositions might depend on each explanatory variable, one can decompose the simplex in a set of orthogonal subspaces, in such a way that the composition projected onto each subspace is independent of a subset of the explanatory variables. This is achieved with a series of singular value decomposition computations. The method is applied to a data set of 88 observations of six major oxides in molar proportions, from modern glacial and fluvio-glacial sediments, with grain size ranging from coarse sand to clay. The goal is to assess the influence of chemical weathering processes (expected to impose a linear relation of composition and grain size) against purely physical processes (expected to show step-wise functions following the largest characteristic crystal sizes of specific minerals in the source rock). We exhaustively explore all patterns of uncorrelation of the composition with three explanatory variables: grain size in 4, scale, and two step functions for the silt and clay domains. The best pattern, chosen with a likelihood ratio test, has only a smooth trend of (Mg,Fe) vs. (Al,K,Ca+Na) enrichment towards finer grain sizes explained as differential mechanical behaviour of phyllosilicates vs. feldspar and coefficients for the two step functions related to the sharp decrease of quartz in silt fractions, and the sudden enrichment of mafic accessory minerals, alteration products and mechanically unstable phyllosilicates in the clay fraction. We could thus be confident that weathering is almost absent in this data set. (C) 2010 Elsevier Ltd. All rights reserved
Kriging regionalized positive variables revisited: Sample space and scale considerations
No full textFrequently, regionalized positive variables are treated by preliminarily applying a logarithm, and kriging estimates are back-transformed using classical formulae for the expectation of a lognormal random variable. This practice has several problems (lack of robustness, non-optimal confidence intervals, etc.), particularly when estimating block averages. Therefore, many practitioners take exponentials of the kriging estimates, although the final estimations are deemed as non-optimal. Another approach arises when the nature of the sample space and the scale of the data are considered. Since these concepts can be suitably captured by an Euclidean space structure, we may define an optimal kriging estimator for positive variables, with all properties analogous to those of linear geostatistical techniques, even for the estimation of block averages. In this particular case, no assumption on preservation of lognormality is needed. From a practical point of view, the proposed method coincides with the median estimator and offers theoretical ground to this extended practice. Thus, existing software and routines remain fully applicable
Correction to: Garnet major-element composition as an indicator of host-rock type: a machine learning approach using the random forest classifier
No full text"compositions": A unified R package to analyze compositional data
No full textThis contribution presents a new R package, called "compositions". It provides tools to analyze amount or compositional data sets in four different geometries, each one associated with an R class: rplus (for amounts, or open compositions, in a real, classical geometry), aplus (for amounts in a logarithmic geometry), rcomp (for closed compositions in a real geometry) and acomp (for closed compositions in a logistic geometry, following a log-ratio approach). The package allows to compare results obtained with these four approaches, since an analogous analysis can be performed according to each geometry, with minimal and straightforward modifications of the instructions. Beside these grounding classes, the package also includes: the most-basic features such as data transformations (e.g. logarithm, or additive logistic transform), basic statistics (both the classical ones, and those developed in the log-ratio framework of compositional analysis), high-level graphics (like ternary diagram matrix and scatter-plots) and high-level analysis (e.g. principal components or cluster analysis). Results of these functions and analysis are also provided in a consistent way among the four geometries, to ease their comparison. (C) 2007 Elsevier Ltd. All rights reserved
Sediment generation in modern glacial settings: Grain-size and source-rock control on sediment composition
No full textClastic sediment generation is controlled by physical and chemical processes acting in concert in most geological settings. In glacial settings, however, it is possible investigating the sole impact of mechanical processes such as comminution on sediment composition, as chemical processes are thought to be negligible in this environment. Comminution is a selective process in the sense that minerals behave differently under mechanical forcing and has yet not been thoroughly investigated under strict grain-size control. We sampled sediment from modem front and side moraines from six retreating glaciers in the Alps, that drain and erode either pure felsic crystalline rocks (granites, granodiorites, orthogneisses) or largely pure metamafic rocks (amphibolites and hornblende-rich gneisses). Samples were split in up to eleven grain-size fractions from very coarse sand to clay. Grain-size fractions were analysed for major and trace elements using X-ray fluorescence. Mineralogical composition was determined by X-ray diffraction and endmember modelling of geochemical data. Results reveal in general strong grain-size control on sediment composition and strikingly similar patterns for both source lithologies. Significant influence of chemical weathering and hydrodynamic sorting is ruled out. Zr/Zn ratio is found as a valuable proxy for grain size while Cr/Rb constitutes one of the rare discriminants between the two cases over the entire grain-size range. Most trace elements, however, are not suitable for source rock discrimination across grain size grades even in glacial environment and extreme proximity to the source. Consequently, bulk sediment geochemistry has only limited benefit in provenance studies unless the samples were analysed under strict grain-size control. The data can be modelled by linear regression with two components: (i) a linear trend describing preferential enrichment of phyllosilicates at the expense of quartz and feldspar towards finer fractions, and (ii) some breaks at certain grain-size thresholds. Due to the observed step functions the model describes a four-step enrichment-depletion pattern that is largely similar for the two source-rock cases: feldspar is highest in the very coarse to medium sand fraction; quartz is highest in very fine sand; epidote, garnet, hornblende, apatite are highest and plagioclase is relatively high in the silt range; sheet silicates (chlorite, biotite, muscovite) are highest in the clay fraction. The observed pattern describes the process of comminution, i.e. the impact of mechanical forces on minerals with contrasting durability: the most durable minerals like quartz are concentrated close to their inherited grain-sizes while less durable minerals are enriched in silt fractions, and least durable minerals (i.e. sheet silicates) are enriched in the very fine silt to clay fractions. The latter, not chemical weathering causes an increase in chemical index of alteration (CIA) values up to similar to 63 at the finest grain-size grades. The model provides a quantitative description of the composition to grain-size relations and is thought to form a valuable module for building comprehensive sediment generation models that describe the entire network of sediment production processes from source to sink. (C) 2012 Elsevier B.V. All rights reserved.German Research Foundation (DFG) [EY23/11
Simplicial indicator kriging
No full textIndicator kriging (IK) is a spatial interpolation technique devised for estimating a conditional cumulative distribution function at an unsampled location. The result is a discrete approximation, and its corresponding estimated probability density function can be viewed as a composition in the simplex. This fact suggested a compositional approach to IK which, by construction, avoids all its standard drawbacks (negative predictions, not-ordered or larger than one). Here, a simple algorithm to develop the procedure is presented
Constructing modal mineralogy from geochemical composition: A geometric-Bayesian approach
No full textModal mineralogical composition is known to carry more information than major element geochemistry, though the latter is far easier to determine in the lab. Constructing mineral compositions from geochemistry can be seen as a typical end-member problem, where one assumes that some rnultivariate observations are generated by a convex linear mixture of a few pure end-members: these end-member characteristics as well as the coefficients of the linear mixture for the observations can be then estimated from geochemical data. We propose a mixed geometric-probabilistic solution to this problem. First, we assume known end-members, in number and properties, and study the set of solutions from a purely geometric perspective. Second, we discuss how to select representative solutions from this space, in particular under some distributional assumptions. Third, we allow the end-member properties to randomly vary in a controlled, interpretable fashion. Finally we build a Bayesian model, with a parsimonious parametrization characterizing each of these three steps, that can be treated by conventional Markov-Chain Monte Carlo techniques. In the illustration case study, we apply the method to reconstruct the mineralogy of a set of fluvio-glacial monomictic sediments from an Alpine granitoid massif. Results suggest a trend of enrichment in chlorite, muscovite and Ti-bearing minerals, along with depletion in quartz and feldspar. This is tentatively interpreted as an effect of comminution combined with differential mechanical properties. Moreover, mineral chemistry is estimated to exhibit very low Na in muscovite, Fe-rich garnet, Na-rich plagioclase. K-feldspar with up to 10% Na-component (albite), and biotite with Mg > Fe. The reconstructed modal mineralogy stays in a reasonable agreement with quantitative XRD phase analyses. (C) 2010 Elsevier Ltd. All rights reserved
Indicator Kriging without Order Relation Violations
No full textIndicator kriging (IK) is a spatial interpolation technique aimed at estimating the conditional cumulative distribution function (ccdf) of a variable at an unsampled location. Obtained results form a discrete approximation to this ccdf, and its corresponding discrete probability density function (cpdf) should be a vector, where each component gives the probability of an occurrence of a class. Therefore, this vector must have positive components summing up to one, like in a composition in the simplex. This suggests a simplicial approach to IK, based on the algebraic-geometric structure of this sample space: simplicial IK actually works with log-odds. Interpolated log-odds can afterwards be easily re-expressed as the desired cpdf or ccdf. An alternative but equivalent approach may also be based on log-likelihoods. Both versions of the method avoid by construction all conventional IK standard drawbacks: estimates are always within the (0,1) interval and present no order-relation problems (either with kriging or co-kriging). Even the modeling of indicator structural functions is clarified
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