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Outliers are encountered in all practical situations of data analysis, regardless of the discipline of application. However, the term outlier is not uniformly defined across all these fields since the differentiation between regular and irregular behaviour is naturally embedded in the subject area under consideration. Generalized approaches for outlier identification have to be modified to allow the diligent search for potential outliers. Therefore, an overview of different techniques for multivariate outlier detection is presented within the scope of selected kinds of data frequently found in the field of geosciences. In particular, three common types of data in geological studies are explored: spatial, compositional and flat data. All of these formats motivate new outlier concepts, such as local outlyingness, where the spatial information of the data is used to define a neighbourhood structure. Another type are compositional data, which nicely illustrate the fact that some kinds of data require not only adaptations to standard outlier approaches, but also transformations of the data itself before conducting the outlier search. Finally, the very recently developed concept of cellwise outlyingness, typically used for high-dimensional data, allows one to identify atypical cells in a data matrix. In practice, the different data formats can be mixed, and it is demonstrated in various examples how to proceed in such situations. [ABSTRACT FROM AUTHOR]

A compositional multivariate approach was used to analyse regional-scale soil geochemical data obtained as part of the Tellus Project generated by the Geological Survey of Northern Ireland. The multi-element total concentration data presented comprise X-ray fluorescence (XRF) analyses of 6862 rural soil samples collected at 20-cm depth on a non-aligned grid at one site per 2km2. Censored data were imputed using published detection limits. Each soil sample site was assigned to the regional geology map, resulting in spatial data for one categorical variable and 35 continuous variables comprised of individual and amalgamated elements. This paper examines the extent to which soil geochemistry reflects the underlying geology or superficial deposits. Since the soil geochemistry is compositional, log-ratios were computed to adequately evaluate the data using multivariate statistical methods. Principal component analysis (PCA) and minimum/maximum autocorrelation factors (MAF) were used to carry out linear discriminant analysis (LDA) as a means to discover and validate processes related to the geologic assemblages coded as age bracket. Peat cover was introduced as an additional category to measure the ability to predict and monitor fragile ecosystems. Overall prediction accuracies for the age bracket categories were 68.4 % using PCA and 74.7 % using MAF. With inclusion of peat, the accuracy for LDA classification decreased to 65.0 and 69.9 %, respectively. The increase in misclassification due to the presence of peat may reflect degradation of peat-covered areas since the creation of superficial deposit classification. [ABSTRACT FROM AUTHOR]

The so-called Air Quality Index (AQI), expresses the quality of atmospheric air. The overall AQI is determined from the AQIs of some reference air pollutants, which are calculated by a transform of the respective concentrations. Concentrations of air pollutants are compositional data; they are expressed as part of mass of each pollutant in a total air volume or mass. Therefore, air pollution concentration data, as compositional data, just provide ratio information between concentrations of pollutants. Operations involved in the computation of overall AQI are not admissible operations in the framework of compositional data analysis, as they destroy the original ratio information. Consequently, the standard methodology should be reviewed for such calculations, taking into account the principles and operations of compositional data analysis. The objective of this article is to present a first approach to incorporate compositional perspective to air quality expression. For this, it is proposed to use a balance log-contrast of concentrations expressed in $$\upmu $$ g/m $$^3$$ to define a new kind of air quality indicator. Furthermore, the geometric mean of the concentrations is applied to obtain a new and simple scale air quality index, avoiding definition of piecewise linear interpolations used in the standard AQI computation. As an illustrative example, statistical analysis of atmospheric pollution data series (2004-2013) of the city of Madrid (Spain) has been carried out. [ABSTRACT FROM AUTHOR]

A comparative study of Last Glacial to Holocene planktonic foraminiferal assemblages obtained from $$>$$ 150 to $$>$$ 106 $$\upmu $$ m size fractions of a Tyrrhenian sea core was carried out by means of compositional data analysis methods. The results show a major loss of small-sized species in the $$>$$ 150 $$\upmu $$ m size fraction, resulting in underdetection limit values for several Holocene samples. Statistical tests, performed by means of contrast and bootstrap, indicate that the assemblages obtained differ statistically. Nevertheless, despite the drawbacks of the analysis based on the $$>$$ 150 $$\upmu $$ m fraction, these differences do not imply, in the compositional data analysis approach, a significant change in covariance structure. Under compositional data analysis, covariance-based analysis should give similar results regardless of the size fraction adopted, while distance-based ones may give partly different results. The $$>$$ 106 $$\upmu $$ m size fraction, in which both large and small-sized species are sufficiently represented, is proposed for adoption in future studies focussing on palaeoclimatic reconstruction. [ABSTRACT FROM AUTHOR]

Mathematicians and geochemists have long realized that compositional data intrinsically exhibit a structure prone to spurious and induced correlations. This paper demonstrates, using the Na-Cl-Br system, that these mathematical problems are exacerbated in the study of sedimentary basin brines by such processes as the evaporation or dissolution of salts owing to their high salinities. Using two published datasets of Na-Cl-Br data for fluids from the Appalachian Basin, it is shown that log concentration and Na/Br versus Cl/Br methods for displaying solute chemistry may lead to misinterpretation of mixing trends between meteoric waters (for example shallow drinking water aquifers) and basinal brines, partially due to spurious mathematical relationships. An alternative approach, based on the isometric log-ratio transformation of molar concentration data, is developed and presented as an alternative method, free from potential numerical problems of the traditional methods. The utility, intuitiveness, and potential for mathematical problems of the three methods are compared and contrasted. Because the Na-Cl-Br system is a useful tool for sourcing solutes and investigating the evolution of basinal brines, results from this research may impact such critical topics as evaluating sources of brine contamination in the environment (possibly related to oil and gas production), evaluating the behavior of fluids in the reservoir during hydraulic fracturing, and tracking movement of fluids as a result of geologic CO sequestration. [ABSTRACT FROM AUTHOR]