Incorporating the eruptive history in a stochastic model for volcanic eruptions

We show how a stochastic version of a general load-and-discharge model for volcanic eruptions can be implemented. The model tracks the history of the volcano through a quantity proportional to stored magma volume. Thus large eruptions can influence the activity rate for a considerable time following, rather than only the next repose as in the time-predictable model. The model can be fitted to data using point-process methods. Applied to flank eruptions of Mount Etna, it exhibits possible long-term quasi-cyclic behavior, and to Mauna Loa, a long-term decrease in activity. An extension to multiple interacting sources is outlined, which may be different eruption styles or locations, or different volcanoes. This can be used to identify an ‘average interaction’ between the sources. We find significant evidence that summit eruptions of Mount Etna are dependent on preceding flank eruptions, with both flank and summit eruptions being triggered by the other type. Fitted to Mauna Loa and Kilauea, the model had a marginally significant relationship between eruptions of Mauna Loa and Kilauea, consistent with the invasion of the latter's plumbing system by magma from the former.