A new treatment of compositional data The Stromboli, Italy case
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Traditional methods used to interpret and process geochemical data are inherently awed since they rely on a statistical foundation that was created to deal with unconstrained data. Geochemical data are usually presented closed (to 100% or ppm) and therefore carry relative information in the form of only (constrained) positive values. Although the coordinates of a given geochemical analysis carry only relative information, the ratios between them are absolute values, hence this work invloves testing the idea to transform the data into a non-Euclidean space in order to take advantage of the absolute information carried by the ratios. A set of geochemical data from Stromboli volcano, Italy was selected in order to test this new methodology, compared with the traditional methods used in igneous petrology. The main goal was to assess whether more information can be retrieved using the new methodology from a very well studied geochemical data set. The data was processed using Principal Component Analysis (PCA), which allowed for the visualization of the data from the volcano as a whole rather than by each chemical species (as in a set of variation diagrams). A logratio transformation was then applied to the data, in order to transform such data and take advantage of the information within the ratios and avoid the problems associated with constrained data. Principal component analysis was then applied to the transformed data. In order to quantify PCA in both cases, a method for drawing a confidence ellipse of the data was created and used as aid in visualization and applied to both PCA projections. The results of the study show that there are differences between the results of the Principal component analyses of the untransformed data and the transformed data. These differences arise because of an extremely high variance related to a component of the untransformed data which overshadowed the variance of the others. The logratio transformation proved useful in eliminating this issue. The transformed and visualized data show promise in relating the total chemistry from one period of Stromboli volcano to another as well as identification of trends in the chemistry. Moreover, the traditional methods used for the interpretation of geochemical trends proved to still be useful and valid despite the inherent errors associated with closure of the data. Thus, valuable information can still be gained from the study of variation diagrams by a trained individual.