Identifying volcanic regimes using Hidden Markov Models

Abstract

We examine the application of Hidden Markov Models (HMMs) to volcanic occurrences. The parameters in HMMs can be estimated from data by means of the Expectation—Maximization (EM) algorithm. Various formulations permit modelling the activity level of a volcano through onset counts, the intensity of a Markov Modulated Poisson Process (MMPP), or through the intervals between onsets. More elaborate models allow investigation of the relationship between durations and reposes. After fitting the model, the Viterbi algorithm can be used to identify the underlying (hidden) activity level of the volcano most consistent with the observations. The HMM readily provides forecasts of the next event, and is easily simulated. Data of flank eruptions 1600–2006 from Mount Etna are used to illustrate the methodology. We find that the volcano has longish periods of Poissonian behaviour, interspersed with less random periods, and that changes in regime may be more frequent than have previously been identified statistically. The flank eruptions of Mount Etna appear to have a complex time-predictable character, which is compatible with transitions between an open and closed conduit system. The relationship between reposes and durations appears to characterize the cyclic nature of the volcanoes activity.