Multifractal analysis of Vesuvius volcano eruptions

The standard statistical analysis of volcanic eruptions could be not very useful tools to describe temporal variations of the volcanic events clustering due to the shortness of the catalogues. A more appropriate approach is the multifractal analysis. If interevent times between eruptions are fractally distributed, they have a scale invariant structure and the behaviour of the catalogue can be described in terms of Poissonian or stationary clustered distribution. On the contrary, if a multifractal distribution is observed, the clustering cannot be considered constant. We analyse the catalogue of occurrence times of Vesuvius eruptions from 1631 to 1944 that can be considered complete. We fmd a multifractal distribution. Such a result implies a clustering degree that varies in time. At small scales a weak clustering is observed, while at large scale the catalogue can be considered Poissonian. This implies that the correlation between the events of the volcanic activity cycles is very weak and that the dynamics evolves at the same time scales within a given cycle and between cycles.