A Brownian Model for Recurrent Volcanic Eruptions: an Application to Miyakejima Volcano (Japan)

The definition of probabilistic models as mathematical structures to describe the response of a volcanic system is a plausible approach to characterize the temporal behavior of volcanic eruptions, and constitutes a tool for long-term eruption forecasting. This kind of approach is motivated by the fact that volcanoes are complex systems in which a completely deterministic description of the processes preceding eruptions is practically impossible. To describe recurrent eruptive activity we apply a physically-motivated probabilistic model based on the characteristics of the Brownian passage-time (BPT) distribution; the physical process defining this model can be described by the steady rise of a state variable from a ground state to a failure threshold; adding Brownian perturbations to the steady loading produces a stochastic load-state process (a Brownian relaxation oscillator) in which an eruption relaxes the load state to begin a new eruptive cycle. The Brownian relaxation oscillator and Brownian passage-time distribution connect together physical notions of unobservable loading and failure processes of a point process with observable response statistics. The Brownian passage-time model is parameterized by the mean rate of event occurrence, μ , and the aperiodicity about the mean, α . We apply this model to analyze the eruptive history of Miyakejima volcano, Japan, finding a value of 44.2(±6.5 years) for the μ parameter and 0.51(±0.01) for the (dimensionless) α parameter. The comparison with other models often used in volcanological literature shows that this pysically-motivated model may be a good descriptor of volcanic systems that produce eruptions with a characteristic size. BPT is clearly superior to the exponential distribution and the fit to the data is comparable to other two-parameters models. Nonetheless, being a physically-motivated model, it provides an insight into the macro-mechanical processes driving the system. A. Garcia-Aristizabal Istituto Nazionale di Geofisica e Vulcanologia, via Donato Creti 12, 40128 Bologna, Italy Tel.: +39.051.5141465, Fax: +39.051.4151499 E-mail: [email protected] W. Marzocchi Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, 00143 Roma, Italy E. Fujita National Research Institute for Earth Science and Disaster Prevention, Tennodai 3-1, Tsukuba, Ibaraki, 3050006, Japan