A forward test for interaction between remote earthquakes and volcanic eruptions: the case of Sumatra (June 2000) and Denali (November 2002) earthquakes

We propose a formal procedure to validate the hypothesis of a causal relationship between great tectonic earthquakes and volcanic eruptions through a forward statistical test. This approach allows such a hypothesis to be evaluated in an objective way, ruling out any possible unconscious overfitting of the past data. The procedure consists of two steps: (a) the computation of the stress perturbation in a volcanic area due to some selected seismic event, by means of a spherical, layered, viscoelastic and self-gravitating earth model; and (b) the application of a statistical test to check the differences in the spatio-temporal distribution of eruptions before and after the earthquake, weighting each eruption with the stress perturbation induced at the volcano at the time of the eruption. Finally, for the sake of example, we apply the method to the case of the recent Engano earthquake in Sumatra (June 2000) and the Denali earthquake in Alaska (November 2002).