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Authors: Garcia-Aristizabal, A.* 
Marzocchi, W.* 
Fujita, E.* 
Title: A Brownian Model for Recurrent Volcanic Eruptions: an Application to Miyakejima Volcano (Japan)
Issue Date: Mar-2012
Series/Report no.: /74 (2012)
DOI: 10.1007/s00445-011-0542-4
Keywords: Probabilistic models; Brownian passage-time distribution;
Hazard function; Miyakejima volcano
Subject Classification04. Solid Earth::04.08. Volcanology::04.08.08. Volcanic risk 
05. General::05.01. Computational geophysics::05.01.04. Statistical analysis 
05. General::05.08. Risk::05.08.01. Environmental risk 
Abstract: 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 com- pletely deterministic description of the processes preceding eruptions is practically impos- sible. 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 load- ing 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 os- cillator and Brownian passage-time distribution connect together physical notions of unob- servable 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 his- tory 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.
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