Abstract
We introduce a doubly stochastic method for performing material failure theory based forecasts of volcanic eruptions. The method enhances the well known Failure Forecast Method equation, introducing a new formulation similar to the Hull-White model in financial mathematics. In particular, we incorporate a stochastic noise term in the original equation, and systematically characterize the uncertainty. The model is a stochastic differential equation with mean reverting paths, where the traditional ordinary differential equation defines the mean solution. Our implementation allows the model to make excursions from the classical solutions, by including uncertainty in the estimation. The doubly stochastic formulation is particularly powerful, in that it provides a complete posterior probability distribution, allowing users to determine a worst case scenario with a specified level of confidence. We apply the new method on historical datasets of precursory signals, across a wide range of possible values of convexity in the solutions and amounts of scattering in the observations. The results show the increased forecasting skill of the doubly stochastic formulation of the equations if compared to statistical regression.
Highlights
The Failure Forecast Method (FFM) for volcanic eruptions is a classical tool applied in the interpretation of monitoring data as potential precursors, providing quantitative predictions of the eruption onset
The method was retrospectively applied to several volcanic systems, including dome growth episodes and explosive volcanic eruptions (Voight and Cornelius, 1991; Cornelius and Voight, 1994, 1996; Voight et al, 2000)
Laboratory experiments and theoretical models have demonstrated the FFM under constant stress and temperature, and this is a hypothesis difficult to verify for realistic scenarios
Summary
The Failure Forecast Method (FFM) for volcanic eruptions is a classical tool applied in the interpretation of monitoring data as potential precursors, providing quantitative predictions of the eruption onset. Laboratory experiments and theoretical models have demonstrated the FFM under constant stress and temperature, and this is a hypothesis difficult to verify for realistic scenarios Without this assumption, the FFM should be generalized to more fundamental relations between rock fracture and deformation, which imply time dependent changes in the power law expressing the precursor rate (Kilburn, 2012). We use a doubly stochastic model to develop a short-term eruption forecasting method based on precursory signals. We remark that these signals could be any time series related to material failure, e.g., seismic or deformational.
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