Frequency Distributions of Geochemical Data, Scaling Laws, and Properties of Compositions

Abstract—Many random processes occur in geochemistry. Accurate predictions of the manner in which elements or chemical species interact with each other are needed to construct models able to treat the presence of random components. Although modelling of frequency distributions with some probabilistic models (for example Gaussian, log-normal, Pareto) has been well discussed in several fields of application, little attention has been devoted to the features of compositional data and, in particular, to their multivariate nature. In this contribution an approach coherent with the properties of compositional information is proposed and used to investigate the shape of the frequency distribution of geochemical indices obtained by robust multivariate analysis. The purpose is to understand data-generation processes from the perspective of compositional theory. The approach is based on use of transformations of the log-ratio family, each with peculiar theoretical and practical advantages, depending on the statistical methods adopted. Accordingly, because, in compositional data, all the relevant information about one term (xi) of a D-part composition is contained in the ratios to each of the remaining parts x2,…, xD, analysis of single variables is abandoned. The proposed methodology directs attention to modelling of the frequency distribution of more complex indices, linking all the terms of the composition to better represent the dynamics of geochemical processes. An example of its application is presented and discussed on the basis of consideration of the chemistry of 616 ocean floor basaltic (OFB) glasses from the abyssal volcanic glass data file (AVGDF) of the Smithsonian Institution.