FRACTAL ANALYSIS OF ERUPTIVE ACTIVITY OF SOME BASALTIC VOLCANOS

The application of statistics to sequences of volcanic eruptions has been widely used by many authors. Generally, the distribution of repose time of volcanoes is submitted to different tests and a probability density function and the eruption rate are computed. These functions yield a maximum probability for the occurrence of eruptions at repose periods greater than a given interval of time. In this paper we apply a fractal analysis to the distributions of repose periods of some basaltic volcanoes; three of these are related to hotspots on oceanic lithosphere: Piton de la Fournaise on la Reunion, Mauna Loa and Kilauea on Hawaii. For comparison, the activity of Etna, a basaltic volcano, is analysed. A Cantor dust model in the time domain can be applied as N(i) the number of periods of length t(i) are tied to the relation N(i) = t-D. An estimated value of D, the fractal dimension of the distribution, is between 0 and 1.0 is the Euclidian dimension of a point, and 1 is a full segment. The fractal dimension describes the strength of clustering, the more isolated the clusters, the smaller the values of D. The main result obtained for the eruptive activity of hotspot volcanoes over a period of about 60 years is the evidence for a double-regime process with strong clustering of eruptions for the short intervals (D = 0.3) and more regular occurrence of eruptions on large intervals (D = 0.7). We obtained a single term for Etna, D = 0.75, which characterizes its regular activity. We discuss the interpretation of the observed double regime of activity of hotspot volcanoes in terms of two different processes of magmatic intrusion.