Probabilistic Enhancement of the Failure Forecast Method Using a Stochastic Differential Equation and Application to Volcanic Eruption Forecasts

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.

Radial interpolation of GPS and leveling data of ground deformation in a resurgent caldera: application to Campi Flegrei (Italy)

“…Since 2005, after 20 years long phase of subsidence with a total vertical displacement of ca. − 1 m, the Campi Flegrei caldera has been raising again with a slower rate than in the previously occurred main phases of uplift, but slowly accelerating (Chiodini et al 2017;Bevilacqua et al 2018Bevilacqua et al , 2019Patra et al 2019); http://www.ov.ingv.it/ov/it/campi -flegr ei/ monit oragg io.html), with a total maximum vertical displacement in the central area of ca. 63 cm (November 2019).…”

Major explosions and paroxysms at Stromboli (Italy): a new historical catalog and temporal models of occurrence with uncertainty quantification

“…Our methodology is transferable to other volcanoes and, doubtless, can be extended in its analytical scope. For instance, our approach provides a basis for setting up base rate hazard priors that can be easily updated with real-time monitoring data 45,68,69,111,112,114 . Ignoring the base rate is a well-known fallacy that compromises forecasting and diagnostic reliability in many areas of science and medicine 78 .…”

Thematic vent opening probability maps and hazard assessment of small-scale pyroclastic density currents in the San Salvador Volcanic Complex (El Salvador) and Nejapa-Chiltepe Volcanic Complex (Nicaragua)

“…It is remarkable, for example, the inclusion of structured expert judgment procedures to constrain the input parameters of the models adopted to construct these maps (Chapman et al, 2012;Bevilacqua et al, 2015;Tadini et al, 2017a;Bebbington et al, 2018), and their coupling with models aimed at describing the dispersal of volcanic products (e.g., Gallant et al, 2018;Hyman et al, 2019;Rutarindwa et al, 2019). A growing effort is aimed at the production of short-term vent opening maps which can modify the long-term estimates after plugin-in the monitoring information that progressively evolves during volcanic unrest (e.g., Bevilacqua et al, 2019c;Patra et al, 2019;Bevilacqua et al, 2020b;Sandri et al, 2020).…”