Dynamical similarity of explosions at Stromboli volcano

Abstract

We analyse Strombolian explosions recorded with broadband seismometers to quantify the degree of similarity among explosions. First, we construct the trajectory space. This reconstruction is analogous to that of phase space but, unlike the phase space which relies on the analysis of a single trajectory of a dynamic system, the trajectory space takes into account many trajectories of the dynamic process to study the overlapping properties. Based on the scaling of distances between each pair of histories, it is possible to evaluate the dimension of the trajectory space. We consider the different explosions as different trajectories and, after normalizing all the records, we find that the scaling region is spread over less than one order of magnitude. This absence of scaling implies that all the trajectories cover the same attractor in the trajectory space, and that the trajectories are generated by the same dynamic system. Accordingly, we conclude that all the events are very similar to each other. This result is confirmed by the energy distribution of these events. Standard techniques of energy estimation are inadequate in this case, and we propose an evaluation method based on a quantity that is proportional to energy. The distribution function of this quantity, calculated on 580 events, displays a log-normal behaviour with very low variability (less than two orders of magnitude in energy). These results provide quantitative support for the observation that there is a great degree of similarity among Strombolian explosions and support the idea that a dynamic model underlying these events can be elaborated through the study of just one event. © 2004 RAS.