Temporal structure of the global sequence of volcanic eruptions: Order clustering and intermittent discharge rate

To study the temporal organization of global volcanic activity over time scales from years to centuries, the following three event sequences were studied: two subsets of the regular catalog of eruptions after Siebert and Simkin [Siebert, L., Simkin, T., 2002. Volcanoes of the World… http://www.volcano.si.edu/gvp/world/], and the “ice core volcanic index” (IVI) sequence, based on the volcanic eruption record as acid layers in big glaciers (Robock, A., Free, M.P., 1996. The volcanic record in ice cores for the past 2000 years. In: Jones, P.D., Bradley, R.S., Jouzel, J. (Eds.), Climatic Variations and Forcing Mechanisms of the Last 2000 Years. Springer-Verlag, New York, pp. 533–546). To perform the statistical analysis in a meaningful way, data subsets were extracted from the original data, with size thresholds and time intervals carefully selected to make these subsets nearly homogeneous. The analysis has revealed, generally, the tendency to clustering, manifested in the following three forms: (1) The event rate is not uniform in time: event dates form active episodes (“common” clusters). (2) In the time-ordered, sequential list of sizes of eruptions, larger events do not appear purely randomly; instead, they form tight groups (“order clusters”). (3) The volcanic products discharge rate is significantly non-uniform, and shows episodic (intermittent or bursty) behavior. It was also found that for the volcanic sequences analyzed, the two types of clustering behavior mentioned in (1) and (2) are positively correlated: larger events are concentrated at the periods of higher event rate. Such a relationship is best demonstrated by the fact that there is clear negative correlation between the following two time series: (1) of the exponent b of the power law size–frequency distribution (the analog of b-value of the Gutenberg–Richter law for earthquakes) and (2) of the current event rate. Power spectra of the analyzed sequences mostly follow power laws, with negative exponent β. Thus, these sequences can be qualified as pulse flicker noises. In other words, they are fractal sequences with correlation dimension Dc = β + 1 < 1, and both their clustering and episodicity are of self-similar character. The revealed peculiarities of the global volcanic sequence suggest that some global-scale mechanism exists that is responsible for their origin. They are also or primary importance for understanding the impact of volcanism on climate.