A principal goal of volcanology is to successfully forecast the start of volcanic eruptions. This paper introduces a general forecasting method, which relies on a stream of monitoring data and a statistical description of a given threshold criterion for an eruption to start. Specifically we investigate the timing of intrusive and eruptive events at inflating volcanoes. The gradual inflation of the ground surface is a well-known phenomenon at many volcanoes and is attributable to pressurized magma accumulating within a shallow chamber. Inflation usually culminates in a rapid deflation event caused by magma escaping from the chamber to produce a shallow intrusion and, in some cases, a volcanic eruption. We show that the ground elevation during 15 inflation periods at Krafla volcano, Iceland, increased with time towards a limiting value by following a decaying exponential with characteristic timescale τ. The available data for Krafla, Kilauea and Mauna Loa volcanoes show that the duration of inflation (t*) is approximately equal to τ. The distribution of t*/τ values follows a log-logistic distribution in which the central 60% of the data lie between 0.99 < t*/τ < 1.76. Therefore, if τ can be constrained during an on-going inflation period, then the cumulative distribution function of t*/τ values calibrated from other inflation periods allows the probability of a deflation event starting during a specified time interval to be estimated. The time window in which there is a specified probability of deflation starting can also be forecast, and forecasts can be updated after each new deformation measurement. The method provides stronger forecasts than one based on the distribution of repose times alone and is transferable to other types of monitoring data and/or other patterns of pre-eruptive unrest.
- eruption forecasting
- conditional probability