Predictive regions for geochemical compositional data of volcanic systems

In this contribution, the theoretical basis to define predictive regions on multivariate compositional data is applied to, volcanological, geochemical data. The method defines a predictive region based on the calculation of the eigenvalues and eigenvectors of the covariance matrix of a logratio-transformed data set to circumvent the issue of singularity of the covariance matrix of the raw data due to the closure problem. Principal components have been used to reduce dimensionality and produce a 2-D display of the transformed data and the confidence ellipse.The method was tested in a well studied volcanic sequence from Stromboli volcano (The Vancori period) and in the tholeiitic differentiation of Thingmuli volcano represented in the AFM diagram. Results of the first example are strongly consistent with previous works, suggesting that the methodology reproduces the conventional patterns and potentially could help in the search of hidden patterns in noisy data. Results of the second example depict a useful approach for the treatment of volcanic geochemical data when plotted in a ternary diagram.