Poisson-distributed patterns of explosive eruptive activity

The study of patterns of eruption occurrence could lead to a better understanding of the physics behind the volcanic process. However, various attempts to find a single statistical distribution that describes the occurrences of volcanic eruptions have not been successful. Global data show that, if the energies of point events in time (eruptions) are properly accounted above a certain noise level, the stochastic process — whose realization consists of explosive volcanic events — can be well represened by a Poisson point process, though not necessarily stationary. Many previous attempts to describe patterns of eruption occurrences were hampered by counting events with all levels of explosivity in the same category. When eruptions are separated by their sizes, the occurrence patterns of the higher magnitude eruptions become clearly Poissonian. In this study eruptions are classified by size using the Volcanic Explosivity Index (Newhall and Self 1982). Further analysis of the magnitude-characterized eruption data shows direct relations among the energy of eruptions, mean rate of occurrences and distribution of repose intervals between eruptions. An important result from the analysis of energy and mean rate of occurrence data is that, for global data, the product of those parameters is a constant. Simple load-and-discharge models provide an explanation of the random features of the volcanic processes. These considerations lead to the definition of a constinuous magnitude scale for volcanic eruptions which can consistently measure the energy and the rate-of-occurrence of eruptions over a wide range of values.