Stochastic Modeling of Explosive Eruptive Events at Galeras Volcano, Colombia

A statistical analysis of explosive eruptive events can give important clues on the behaviour of a volcano for both the time- and size-domains, producing crucial information for hazards assessment. In this paper, we analyse in these domains an up-to-date catalogue of eruptive events at Galeras volcano, collated by using data from the Colombian Geological Survey and from the Smithsonian Institution. The dataset appears to be complete, stationary and consisting of independent events since 1820, for events of magnitude $\geq$2.6. In the time-domain, Inter-Event Times (IETs) are fitted by various renewal models. On the basis of the Akaike Information Criterion (AIC), the preferred model is the Lognormal, with a characteristic time scale of $\sim$1.6 years. However, the coefficient of variation (=1.65) highlights a tendency for the events to cluster in time into "eruptive cycles". Therefore, we perform a cluster analysis, identifying three plausible partitions into 6, 8 and 11 clusters of events with magnitude $\geq2.6$. The 6-cluster partition is preferred based on the silhouette method. The IETs between cluster onsets (inter-cluster) and events belonging to the same cluster (intra-cluster) are also modelled by renewal models. For inter-cluster data, the preferred AIC is achieved by Brownian Passage Time, describing a periodical occurrence (mean return time $\sim$ 36 years) perturbed by a Gaussian noise. For the intra-cluster explosions, the preferred AIC is achieved by Lognormal model, with a characteristic time scale of $\sim$ 0.9 years. In the size-domain, we analyse only single events, due to the low number of clusters. Considering two independent parts of the catalogue, we cannot reject the null hypothesis of the erupted mass being described by a power law, implying no characteristic eruption size. Finally, looking for time- and size-predictability, we find a significant inverse linear relationship between the logarithm of the erupted mass during a cycle and the time to the subsequent one. These results suggest that, presently, Galeras is still in the eruption cycle started in 2007; a new eruptive cycle may be expected in a few decades, unless the present cluster resumes to activity with magnitude $\geq$2.6.