Identifying different regimes in eruptive activity: An application to Etna volcano

Abstract

The objective identification of different regimes in the eruptive time-history of a volcano is crucial to the understanding of its physics. While a problem well-known in statistical literature under the name of change-point or scan-point problem, no method of general applicability exists for the identification of different regimes in a time-series. In particular, the available techniques seem unsuitable to the volcanological case. We developed an original procedure based on two-sample Kolmogorov-Smirnov statistics which offers satisfactory accuracy in a broad range of conditions with a minimum of assumptions and is expressly tailored to the study of geophysical phenomena. Our procedure requires neither the a priori knowledge of the number of regimes nor of the statistical distributions governing the whole process, which can be of different type. The parent distribution of each regime is inferred through a goodness-of-fit test, and this in turn allows the confidence intervals for each of the change-points identified to be estimated by numerical simulation. This procedure is applied to the eruptive history of Mount Etna volcano. Available data allow the analysis of flank eruptions in the period 1600–1980, while the total output (summit and flank activity) can be studied only in the period 1971–1981. Information on eruptive history can be therefore obtained at two different timescales. Since no univocally accepted catalog exists except for the last few decades, we use two different sets of data, which practically exhaust all the available information. The results are interpreted by a stability analysis, and only stable results are retained. Our analysis yields that: • - The inter-event times of flank eruptions in the period 1600–1980 follow two regimes before and after year 1865, while the eruptive activity in the period 1971–1981 follows four different regimes. In each regime eruptions occur according to a Poisson process and Etna behaves as a random nonstationary volcano both at long (few centuries) and short (few years) time-scales. The eruptions appear therefore to be triggered by several combining effects with a balance showing fluctuations at both time-scales. • - The volume output of flank eruptions in the period 1600–1980 follows three different regimes, with change-points at 1670 and 1750. The volume output in the period 1971–1981 follows a single regime. Least squares regression and the related confidence bounds, calculated for each regime, suggest that, even accounting for summit activity, the output rate in the period 1971–1981 is not anomalously high. Provided that no further change in regime takes place, the confidence bounds can be used to cast estimates on the expected future activity. • - The series of the mean effusion rates (erupted volume/duration of the eruption) applied to flank eruptions in the period 1600–1980 follows two different regimes, with a change-point around year 1950. There is a net decrease in the mean effusion rate from over 24 m 3 s −1 to about 7 m 3 s −1, which suggests a change in the eruptive style to lower mean effusion rates. The total output (flank + summit) data of the period 1971–1981 confirms this issue, with averaged mean effusion rates lower than 12 m 3 s −1. • - The points of change in regime in the time-series of the inter-eruption times and volume outputs do not coincide, thus implying that eruptions are governed by other factors than the input of magma. At the same time, the analysis of seismic activity does not suggest the stress field as a most important factor. The eruptive activity does not appear to be controlled by a single factor, but by the balance of several contributing factors, further corroborating the conclusion that Etna behaves as a random nonstationary volcano. • - The relatively small fluctuations in each of the periods identified in the flank output series suggest a constant input within each output regime, although the unavailability of both a reliable model and accurate estimates on historical summit eruptions recommends prudence in accepting this conclusion. • - There appears to be no significant correlation between the volume of a “large” flank eruption and the subsequent inter-event time. This, with the above proviso, suggests the absence of any high-level magma reservoir.