Z. Petrillo has deep knowledge in statistical treatment of data. Particularly, he managed, in the first period of his research, with magnetotelluric data which are multivariate (electric and magnetic channels) and generally contaminated by random and correlated noise. He worked on the attempt to separate the plane wave contribution (MT tensor) from the coherent noise (near field tensor). The aim of the research was to recover the structural asset (by the resistivity distribution) of the Apennines and principally of the main Italian volcanoes. On a 3D model (permeability porosity) of the Plegrean field caldera, the participant applied the tough2 code to explain the pattern of temperature and the flux of hot water and CO2 measured during volcanic monitoring activities by the Osservatorio Vesuviano team. The linearization of the multiphase transport equation, allowed to use a linear approach, based on the Green’s function, which give, in quasi real time, the injected fluid in the hydrothermal system estimated via the deformation pattern at Campi Flegrei caldera. In the very recent period the participant has analyzed the Campi Flegrei geochemical (multicomponents) compositional data using principal component in order to compare the main compositional invariant ratios with geophysical data (number of earthquakes deformations etc.). The aim is an attempt to describe in terms of a common pattern the complex volcanic phenomenon.