Measuring the change under compositional data analysis (CoDA): Insight on the dynamics of geochemical systems

Geochemical systems are complex and the analysis of the shape of the frequency distribution of elements and chemical species often informs about the variability and dispersion related to the underlying dynamics. However, when compositional data are used it is incorrect to investigate concentrations in the Euclidean space. Distribution analysis is aimed at focusing on real coordinates, which can be obtained by applying some appropriate log-ratio transformation. In particular, distributional analysis for compositional data can be applied to isometric coordinates, called balances, obtained through partition of a multi-element data set. As an alternative the same investigation can be performed on indices such as the robust Mahalanobis distance after having ranked log-ratio compositions with respect to some reference composition (i.e. average Earth crust) and having obtained a sort of "measure of change". By considering this second new perspective, the chemical composition of topsoils of the Campania Region (Southern Italy) was investigated by analysing the concentrations of Al, As, B, Ba, Ca, Co, Cr, Cu, Fe, K, La, Mg, Mn, Mo, Na, Ni, P, Pb, Sr, Th, Ti, V and Zn, in mg/kg, determined on > 3500 samples. Results reveal the presence of complex processes governed by interaction-dominant dynamics where self-organisation appears to play some role.