Stochastic models for earthquake triggering of volcanic eruptions

Abstract

[1] Many accounts, anecdotal and statistical, have noted a causal effect on volcanic eruptions from large, not too distant, earthquakes. Physical mechanisms have been proposed that explain how small static stress changes, or larger transient dynamic stress changes, can have observable effects on a volcano. While only ∼0.4% of eruptions appear to be directly triggered within a few days of an earthquake, these physical mechanisms also imply the possibility of delayed triggering. In the few regional studies conducted, data issues (selection bias and scarcity, inhomogeneity, and cleaning of data) have tended to obscure any clear signal. Using a perturbation technique, we first show that the Indonesian volcanic region possesses no statistically significant coupling for the region as a whole. We then augment a number of point process models for eruption onsets by a time-, distance-, and earthquake magnitude-dependent triggering term and apply this to the individual volcanoes. This method weighs both positive and negative (i.e., absence of eruptions following an earthquake) evidence of triggering. Of 35 volcanoes with at least three eruptions in the study region, seven (Marapi, Talang, Krakatau, Slamet, Ebulobo, Lewotobi, and Ruang) show statistical evidence of triggering over varying temporal and spatial scales, but only after the internal state of the volcano is accounted for. This confirms that triggering is fundamentally a property of the internal magma plumbing of the volcano in question and that any earthquake can potentially "advance the clock" toward a future eruption. This is further supported by the absence of any dependence on triggering of the eruption size.

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“…The volume history model has an intensity that increases monotonically between eruptions. Both cases are supported by records of many volcanoes (Bebbington & Marzocchi, 2011).…”

“…Because both the repose and volume distributions are highly skewed, the logarithmic transformation is also advisable to reduce the high leverage of the tail points. Bebbington & Marzocchi (2011) fitted a variety of proportional hazard models, using elapsed time, distance and magnitude of earthquakes as covariates, in the Poisson process, Weibull renewal and volume history models. Applied to earthquake and eruption data from Indonesia 1900-2010, only after the entire volume history of the volcano was accounted for using the volume history model (13) was a significant triggering effect observed.…”

Bayesian Modelling of Marked Point Processes with Incomplete Records: Volcanic Eruptions

“…Even the regions with the best records, e.g. Iceland (Guttorp and Thompson, ), Indonesia (Bebbington and Marzocchi, ) and Japan (Kiyosugi et al ., ) have identifiable departures from Poisson behaviour. We tried to perform regional analyses separately for each region.…”

“…(), Connor et al . (), Bebbington (), Bebbington and Marzocchi () and Wadge and Burt ()). The activity of individual volcanoes may show variation on the timescale of decades to centuries, reflecting, for example, the supply of magma to the shallow crust (e.g.…”

Analysis of stochastic model for nonlinear volcanic dynamics

“…Many uncertainties in physical parameters of volcanic dynamics (Woo, 2000) lead to a conclusion that like the climate systems (see, among others, Saltzman, 2002;Alexandrov et al, 2014), volcanoes, representing stochastic and chaotic systems, need to be described in terms of probabilities (Sparks, 2003;Bebbington and Marzocchi, 2011). Stochastic approaches and mathematical formalisms can be found in Gardiner (2009).…”