Visualization and modeling of sub-populations of compositional data: statistical methods illustrated by means of geochemical data from fumarolic fluids

Abstract

In the investigation of fluid samples of a volcanic system, collected during a given period of time, one of the main goals is to discover cause-effect relationships that allow us to explain changes in the chemical composition. They might be caused by physicochemical factors, such as temperature, pressure, or non-conservative behavior of some chemical constituents (addition or subtraction of material), among others. The presence of subgroups of observations showing different behavior is evidence of unusually complex situations, which might render even more difficult the analysis and interpretation of observed phenomena. These cases require appropriate statistical techniques as well as sound a priori hypothesis concerning underlying geological processes. The purpose of this article is to present the state of the art in the methodology for a better visualization of compositional data, as well as for detecting statistically significant sub-populations. The scheme of this article is to present first the application, and then the underlying methodology, with the aim of the first motivating the second. Thus, the first part has the goal to illustrate how to understand and interpret results, whereas the second is devoted to expose how to perform a study of this kind. The case study is related to the chemical composition of a fumarole of Vulcano Island (southern Italy), called F14. The volcanic activity at Vulcano Island is subject to a continuous program of geochemical surveillance from 1978 up to now and the large data set of observations contains the main chemical composition of volcanic gases as well as trace element concentrations in the condensates of fumarolic gases. Out of the complete set of measured components, the variables H 2 S, HF and As, determined in samples collected from 1978 to 1993 (As is not available in recent samples) are used to characterize two groups in the original population, which proved to be statistically distinct. The choice of the variables is motivated by the importance of investigating the behavior of well-known toxicity elements, which show, like As, a significant mobility under hydrothermal conditions. The statistical methodology used for this study is based on models devised for compositional data. They include (1) the perturbation approach for a better visualization; (2) cluster analysis to detect groups; (3) confidence regions for the center of the groups to obtain graphical evidence of differences between groups; and (4) tests of hypothesis about centers and covariance structures to obtain statistical evidence about differences between groups. The fact that only three components are used allows us to illustrate the results using ternary diagrams.

Compositional data analysis as a robust tool to delineate hydrochemical facies within and between gas‐bearing aquifers

“…The assessment of minor ion components can be challenging because of their relatively smaller concentration. One way of addressing this problem, when using ternary diagrams, is to center data to a common element (typically the inverse of the sample center) to better visualize data structure [ Pawlowsky‐Glahn and Buccianti , ; von Eynatten et al ., ].…”

Weighted principal component analysis for compositional data: application example for the water chemistry of the Arno river (Tuscany, central Italy)

“…The sample space for CoDa is the simplex with its natural geometry coherent with the concept of distance (Aitchison, 1986;Egozcue et al 2003;Buccianti et al, 2006;Buccianti, 2011;Buccianti and Magli, 2011). Consequently, CoDa have important and particular properties that preclude the application of standard statistical techniques to such data in their raw form (Pawlowsky-Glahn and Buccianti, 2002;Buccianti and Pawlowsky-Glahn, 2005). Thus, several multidimensional techniques have been adapted to analyze CoDa, including principal component analysis (PCA; Aitchison, 1983), partial least squares (Hinkle and Rayens, 1995;Gallo, 2003), discriminant partial least squares (Gallo, 2010), and hierarchical clustering (Martin-Fernandez et al, 1998), which are only some of the multivariate techniques proposed in literature.…”

VISUAL STATISTICAL CLASSIFICATION OF As Fe-RICH PRODUCTS OF ALTERATION OF TAILINGS FROM THE ENGUIALES TUNSGTEN MINE, FRANCE

“…For a three-element subcomposition, the CR can be displayed in a triangular diagram using the inverse ALR transformation (Weltje 2002). Pawlowsky-Glahn & Buccianti (2002) used this representation with data on fumaroles.…”

“…The Ward method of Hierarchical Clustering (HC) gives compact clusters and clear hierarchies (Martín-Fernández et al 1999, Martín-Fernández 2001. Pawlowsky-Glahn & Buccianti (2002) applied cluster analysis to the chemical composition of a fumarole on the Island of Vulcano, Italy. Mixture models also give excellent results, with overlapping groups (Barceló-Vidal et al 1999, Martín-Fernández et al 1997.…”