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Global time-size distribution ov volcanic eruptions on Earth

Fig. 3
Figure 3. Relative frequencies of the different VEI class eruptions computed through MC simulation. For each VEI class (reported as a number above each distribution), the black circle represents the median of the MC distribution, and the smaller black circles represent the 50% and 90% confidence intervals; the x symbols represent the mean value after 5 million runs; the orange circles are frequencies directly obtained by the rate parameters λ in Table 2 (see Methods); and the blue circles are the cumulative of the mean values. The horizontal bars extend to cover the range of erupted volumes corresponding to each VEI class (Table 1). (a) Linear frequency axis. (b) Logarithmic frequency axis highlighting a power law (straight line) distribution of explosive eruption frequencies equal to or larger than VEI 3 (blue dashed line). The computed power law exponent is 1.95, with p-value = 0.65 providing statistical robustness to the power law hypothesis (see Methods).

Papale P. (2018).
Nature, Scientific Reports 8, Article number 6838, doi: 10.1038/s41598-018-25286-y.


Volcanic eruptions differ enormously in their size and impacts, ranging from quiet lava flow effusions along the volcano flanks to colossal events with the potential to affect our entire civilization. Knowledge of the time and size distribution of volcanic eruptions is of obvious relevance for understanding the dynamics and behavior of the Earth system, as well as for defining global volcanic risk. From the analysis of recent global databases of volcanic eruptions extending back to more than 2 million years, I show here that the return times of eruptions with similar magnitude follow an exponential distribution. The associated relative frequency of eruptions with different magnitude displays a power law, scale-invariant distribution over at least six orders of magnitude. These results suggest that similar mechanisms subtend to explosive eruptions from small to colossal, raising concerns on the theoretical possibility to predict the magnitude and impact of impending volcanic eruptions.