The main purpose of this paper is to introduce a Bayesian event tree model for eruption forecasting (BET_EF). The model represents a flexible tool to provide probabilities of any specific event which we are interested in, by merging all the relevant available information such as theoretical models, a priori beliefs, monitoring measures, and any kind of past data. BET_EF is based on a Bayesian procedure and it relies on the fuzzy approach to manage monitoring data. The method deals with short-and long-term forecasting; therefore, it can be useful in many practical aspects such as land use planning and volcanic emergencies. Finally, we provide the description of a free software package that provides a graphically supported computation of short-to long-term eruption forecasting, and a tutorial application for the recent MESIMEX exercise at Vesuvius.

[1] We describe an event tree scheme to quantitatively estimate both long-and short-term volcanic hazard. The procedure is based on a Bayesian approach that produces a probability estimation of any possible event in which we are interested and can make use of all available information including theoretical models, historical and geological data, and monitoring observations. The main steps in the procedure are (1) to estimate an a priori probability distribution based upon theoretical knowledge, (2) to modify that using past data, and (3) to modify it further using current monitoring data. The scheme allows epistemic and aleatoric uncertainties to be dealt with in a formal way, through estimation of probability distributions at each node of the event tree. We then describe an application of the method to the case of Mount Vesuvius. Although the primary intent of the example is to illustrate the methodology, one result of this application merits special mention. The present emergency response plan for Mount Vesuvius is referenced to a maximum expected event (MEE), the largest out of all the possible eruptions within the next few decades. Our calculation suggest that there is a nonnegligible (1-20%) chance that the next eruption could be larger than that stipulated in the present MEE. The methodology allows all assumptions and thresholds to be clearly identified and provides a rational means for their revision if new data or information are obtained.

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Abstract. During the past 1000 years, eruptions of Vesuvius have often been accompanied by large earthquakes in the Apennines 50-60 km to the northeast. Statistical investigations had shown that earthquakes often preceded eruptions, typically by less than a decade, but did not provide a physical explanation for the correlation. Here, we explore elastic stress interaction between earthquakes and eruptions under the hypothesis that small stress changes can promote events when the Apennine normal faults and the Vesuvius magma body are close to failure.We show that earthquakes can promote eruptions by compressing the magma body at depth and opening suitably oriented near-surface conduits. Voiding the magma body in turns brings these same normal faults closer to Coulomb failure, promoting earthquakes. Such a coupling is strongest if the magma reservoir is a dike oriented normal to the regional extension axis, parallel to the Apennines, and the near-surface conduits and fissures are oriented normal to the Apennines. This preferred orientation suggests that the eruptions issuing from such fissures should be most closely linked in time to Apennine earthquakes. Large Apennine earthquakes since 1400 are calculated to have transferred more stress to Vesuvius than all but the largest eruptions have transferred to Apennine faults, which may explain why earthquakes more commonly lead than follow eruptions. A two-way coupling may thus link earthquakes and Vesuvius eruptions along a 100-km-long set of faults. We test the statistical significance of the earthquake-eruption correlation in the two-way coupling zone, and find a correlation significant at the 95% confidence level.

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In this paper, we illustrate a Bayesian Event Tree to estimate Volcanic Hazard (BET_VH). The procedure enables us to calculate the probability of any kind of long-term hazardous event for which we are interested, accounting for the intrinsic stochastic nature of volcanic eruptions and our limited knowledge regarding related processes. For the input, the code incorporates results from numerical models simulating the impact of hazardous volcanic phenomena on an area and data from the eruptive history. For the output, the code provides a wide and exhaustive set of spatiotemporal probabilities of different events; these probabilities are estimated by means of a Bayesian approach that allows all uncertainties to be properly accounted for. The code is able to deal with many eruptive settings simultaneously, weighting each with its own probability of occurrence. In a companion paper, we give a detailed example of application of this tool to the Campi Flegrei caldera, in order to estimate the hazard from tephra fall.

The Campi Flegrei caldera is a restless structure affected by general subsidence and ongoing resurgence of its central part. The persistent activity of the system and the explosive character of the volcanism lead to a very high volcanic hazard that, combined with intense urbanization, corresponds to a very high volcanic risk. One of the largest sources of uncertainty in volcanic hazard/risk assessment for Campi Flegrei is the spatial location of the future volcanic activity. This paper presents and discusses a longterm probability hazard map for vent opening in case of renewal of volcanism at the Campi Flegrei caldera, which shows the spatial conditional probability for the next vent opening, given that an eruption occurs. The map has been constructed by building a Bayesian inference scheme merging prior information and past data. The method allows both aleatory and epistemic uncertainties to be evaluated. The probability map of vent opening shows that two areas of relatively high probability are present within the active portion of the caldera, with a probability approximately doubled with respect to the rest of the caldera. The map has an immediate use in evaluating the areas of the caldera prone to the highest volcanic hazard. Furthermore, it represents an important ingredient in addressing the more general problem of quantitative volcanic hazards assessment at the Campi Flegrei caldera.

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