Session 5: Applications to geology and environmenthttp://hdl.handle.net/10256/6292016-05-25T13:13:43Z2016-05-25T13:13:43ZMajor-elements trends in cenozoic volcanites of HungaryMartín Fernández, Josep AntoniBarceló i Vidal, CarlesPawlowsky-Glahn, VeraKovács, L.Ó.Kovács, G.P.http://hdl.handle.net/10256/6792012-11-19T08:56:18Z2003-10-16T00:00:00ZMajor-elements trends in cenozoic volcanites of Hungary
Martín Fernández, Josep Antoni; Barceló i Vidal, Carles; Pawlowsky-Glahn, Vera; Kovács, L.Ó.; Kovács, G.P.
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
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. (...)
2003-10-16T00:00:00ZA Factor analysis of hidrochemical composition of Llobregat river basinOtero Pérez, NeusTolosana Delgado, RaimonSoler i Gil, Alberthttp://hdl.handle.net/10256/6782012-12-20T10:36:49Z2003-10-16T00:00:00ZA Factor analysis of hidrochemical composition of Llobregat river basin
Otero Pérez, Neus; Tolosana Delgado, Raimon; Soler i Gil, Albert
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
Hydrogeological research usually includes some statistical studies devised to elucidate mean background state, characterise relationships among different hydrochemical parameters, and show the influence of human activities. These goals are achieved either by means of a statistical approach or by mixing models
between end-members. Compositional data analysis has proved to be effective with the first approach, but there is no commonly accepted solution to the end-member problem in a compositional framework.
We present here a possible solution based on factor analysis of compositions illustrated with a case study.
We find two factors on the compositional bi-plot fitting two non-centered orthogonal axes to the most representative variables. Each one of these axes defines a subcomposition, grouping those variables that
lay nearest to it. With each subcomposition a log-contrast is computed and rewritten as an equilibrium equation. These two factors can be interpreted as the isometric log-ratio coordinates (ilr) of three hidden
components, that can be plotted in a ternary diagram. These hidden components might be interpreted as end-members.
We have analysed 14 molarities in 31 sampling stations all along the Llobregat River and its tributaries, with a monthly measure during two years. We have obtained a bi-plot with a 57% of explained total
variance, from which we have extracted two factors: factor G, reflecting geological background enhanced by potash mining; and factor A, essentially controlled by urban and/or farming wastewater. Graphical
representation of these two factors allows us to identify three extreme samples, corresponding to pristine waters, potash mining influence and urban sewage influence. To confirm this, we have available analysis
of diffused and widespread point sources identified in the area: springs, potash mining lixiviates, sewage, and fertilisers. Each one of these sources shows a clear link with one of the extreme samples, except
fertilisers due to the heterogeneity of their composition.
This approach is a useful tool to distinguish end-members, and characterise them, an issue generally difficult to solve. It is worth note that the end-member composition cannot be fully estimated but only characterised through log-ratio relationships among components. Moreover, the influence of each endmember in a given sample must be evaluated in relative terms of the other samples. These limitations are
intrinsic to the relative nature of compositional data
2003-10-16T00:00:00ZKriging coordinates: what does that mean?Tolosana Delgado, RaimonPawlowsky-Glahn, Verahttp://hdl.handle.net/10256/6762012-06-28T12:30:36Z2003-10-16T00:00:00ZKriging coordinates: what does that mean?
Tolosana Delgado, Raimon; Pawlowsky-Glahn, Vera
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
Kriging is an interpolation technique whose optimality criteria are based on normality assumptions either for observed or for transformed data. This is the case of normal, lognormal and multigaussian kriging.
When kriging is applied to transformed scores, optimality of obtained estimators becomes a cumbersome concept: back-transformed optimal interpolations in transformed scores are not optimal in the original sample space, and vice-versa. This lack of compatible criteria of optimality induces a variety of problems in both point and block estimates. For instance, lognormal kriging, widely used to interpolate positive
variables, has no straightforward way to build consistent and optimal confidence intervals for estimates.
These problems are ultimately linked to the assumed space structure of the data support: for instance, positive values, when modelled with lognormal distributions, are assumed to be embedded in the whole real space, with the usual real space structure and Lebesgue measure
2003-10-16T00:00:00ZNew insights on river water chemistry by using non-centred simplicial principal component analysis: a case studyBuccianti, AntonellaVaselli, OrlandoNisi, Barbarahttp://hdl.handle.net/10256/6752012-06-28T12:30:36Z2003-10-16T00:00:00ZNew insights on river water chemistry by using non-centred simplicial principal component analysis: a case study
Buccianti, Antonella; Vaselli, Orlando; Nisi, Barbara
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
The use of perturbation and power transformation operations permits the investigation of linear processes in the simplex as in a vectorial space. When the investigated geochemical processes can be constrained by the use of well-known starting point, the eigenvectors of the covariance matrix of a non-centred principal
component analysis allow to model compositional changes compared with a reference point.
The results obtained for the chemistry of water collected in River Arno (central-northern Italy) have open new perspectives for considering relative changes of the analysed variables and to hypothesise the relative effect of different acting physical-chemical processes, thus posing the basis for a quantitative modelling
2003-10-16T00:00:00ZMonitoring procedures in environmental geochemistry and compositional data analysis theoryBuccianti, AntonellaVaselli, OrlandoNisi, BarbaraMinissale, AngeloTassi, Francohttp://hdl.handle.net/10256/6742012-11-30T09:23:15Z2003-10-16T00:00:00ZMonitoring procedures in environmental geochemistry and compositional data analysis theory
Buccianti, Antonella; Vaselli, Orlando; Nisi, Barbara; Minissale, Angelo; Tassi, Franco
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
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 a
simplicial principal component analysis, as LQGLFDWRUV of given environmental conditions. The investigation of the log-constrast frequency distributions allows pointing out the statistical laws able to
generate 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 defining
monitors 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
2003-10-16T00:00:00ZExploration of geological variability and possible processes through the use of compositional data analysis: an example using scottish metamorphosedThomas, C.W.Aitchison, Johnhttp://hdl.handle.net/10256/6732012-06-28T12:30:36Z2003-10-16T00:00:00ZExploration of geological variability and possible processes through the use of compositional data analysis: an example using scottish metamorphosed
Thomas, C.W.; Aitchison, John
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
Developments in the statistical analysis of compositional data over the last two
decades have made possible a much deeper exploration of the nature of variability,
and the possible processes associated with compositional data sets from many
disciplines. In this paper we concentrate on geochemical data sets. First we explain
how hypotheses of compositional variability may be formulated within the natural
sample space, the unit simplex, including useful hypotheses of subcompositional
discrimination and specific perturbational change. Then we develop through standard
methodology, such as generalised likelihood ratio tests, statistical tools to allow the
systematic investigation of a complete lattice of such hypotheses. Some of these tests are simple adaptations of existing multivariate tests but others require special
construction. We comment on the use of graphical methods in compositional data
analysis and on the ordination of specimens. The recent development of the concept
of compositional processes is then explained together with the necessary tools for a
staying- in-the-simplex approach, namely compositional singular value decompositions. All these statistical techniques are illustrated for a substantial compositional data set, consisting of 209 major-oxide and rare-element compositions of metamorphosed limestones from the Northeast and Central Highlands of Scotland.
Finally we point out a number of unresolved problems in the statistical analysis of
compositional processes
2003-10-16T00:00:00Z