Stochastic Modeling of Explosive Eruptive Events at Galeras Volcano, Colombia

Abstract

A statistical analysis of explosive eruptive events can give important clues on the behavior of a volcano for both the time- and size-domains, producing crucial information for hazards assessment. In this paper, we analyze in these domains an up-to-date catalog of eruptive events at Galeras volcano, collating 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 ≥2.6. In the time-domain, Inter-Event Times are fitted by various renewal models to describe the observed repose times. On the basis of the Akaike Information Criterion, the preferred model is the Lognormal, with a characteristic time scale of ∼1.6 years. However, a tendency for the events to cluster in time into “eruptive cycles” is observed. Therefore, we perform a cluster analysis, to objectively identify clusters of events: we find three plausible partitions into 6, 8 and 11 clusters of events with magnitude ≥2.6 the 6-cluster partition being the preferred. The Inter-Event Times between cluster onsets (inter-cluster) and between events belonging to the same cluster (intra-cluster) are also modeled by renewal models. For inter-cluster data, the preferred model is the Brownian Passage Time, describing a periodical occurrence (mean return time ∼36 years) perturbed by a Gaussian noise. For the intra-cluster explosions, the preferred model is the Lognormal, with a characteristic time scale of ∼0.9 years. In the size-domain, we analyze only single events, due to the low number of clusters. Considering two independent parts of the catalog, 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 ≥2.6.

A simple two-state model interprets temporal modulations in eruptive activity and enhances multivolcano hazard quantification

“…This feature is very appealing, as it is sufficient to interpret the eruptive history of three very different and well-studied volcanoes. Of course, specific adjustments and sophistications may be required to universally apply this model to other volcanic systems, such as the consideration of multiple states ( 15 ), or, for each state, the integration of temporal behaviors more complex than a homogeneous Poisson process ( 12 ). However, our application to the Neapolitan volcanoes highlights the need of homogeneous model definitions for an effective comparison among volcanoes and for producing coherent multivolcano long-term hazard and risk quantifications.…”

“…Conditions for magma rising and eruption are determined by the complex interaction of magma overpressure and local stress conditions [e.g., ( 3 , 22 , 23 )]. The eruptions themselves may induce structural weakening of the volcanic system and, on the other side, may potentially trigger further magma rise from depth by increasing the pressure gradient [e.g., ( 12 , 24 )]. The occurrence of one eruption is always a rupture of equilibrium between magmatic pressures and confining forces, which usually takes time to restore.…”

“…These complex temporal behaviors have been modeled using different statistical approaches [for a review, see (7)] that range from constant-rate homogeneous Poisson models to different flavors of renewal processes [e.g., Brownian passage-time, Weibull, and Gamma distributions], including size/time predictable and non-homogeneous Poisson models [e.g., (6,(8)(9)(10)(11)(12)]. Given that several volcanoes show the existence of episodes characterized by a series of events followed by long repose times, several authors suggested a specific class of models that assumes that volcanoes randomly oscillate through time between discrete regimes, each characterized by a specific stochastic behavior with random duration [e.g., (4,7,(12)(13)(14)(15)(16)(17)(18)].…”

“…For long-term hazard quantification purposes, with inference time windows of tens of years to centuries or more (31), the difficulty in defining a consistent temporal behavior for eruptions in many cases has pushed research toward the quantification of the hazard conditional upon the occurrence of one eruption (32)(33)(34)(35)(36). Very different techniques have been developed to quantify the probability of eruption in a given time window, ranging from counts of months without unrest (37,38) to the application of different statistical distributions [e.g., (9,12,18,39)], to the development of more complex self-exciting nonhomogeneous processes (40,41). Often, such methods concentrate on the next eruption, neglecting the possibility of multiple eruptions or of changes in the eruptive regime.…”

Forecasting explosions at Sinabung Volcano, Indonesia, based on SO2 emission rates

“…One class of techniques relies solely on stochastic analysis of the volcanic event time series itself (i.e., explosions, collapses). For example, Sandri et al (2021) apply stochastic modelling of explosions at Galeras Volcano (Colombia) to analyze parameters such as the typical interevent time and the tendency for events to temporally cluster into "eruptive cycles". Derived from the past observational record, the statistical properties of the time series of explosive events can then be used to assign probabilities for future events (see Wickman (1976) for a general overview).…”