Abstract
The occurrence time of earthquakes can be anticipated or delayed by external phenomena that induce strain energy changes on the faults. 'Anticipated' earthquakes are generally called 'triggered'; however, it can be controversial to label a specific earthquake as such, mostly because of the stochastic nature of earthquake occurrence and of the large uncertainties usually associated to stress modelling. Here we introduce a combined statistical and physical approach to quantify the probability that a given earthquake was triggered by a given stress-inducing phenomenon. As an example, we consider an earthquake that was likely triggered by a natural event: the M = 6.2 13 Jan 1976 Kpasker earthquake on the Grimsey lineament (Tjornes Fracture Zone, Iceland), which occurred about 3 weeks after a large dike injection in the nearby Krafla fissure swarm. By using Coulomb stress calculations and the rate-and-state earthquake nucleation theory, we calculate the likelihood of the earthquake in a scenario that contains only the tectonic background and excludes the dike and in a scenario that includes the dike but excludes the background. Applying the Bayes' theorem, we obtain that the probability that the earthquake was indeed triggered by the dike, rather than purely due to the accumulation of tectonic strain, is about 60 to 90 %. This methodology allows us to assign quantitative probabilities to different scenarios and can help in classifying earthquakes as triggered or not triggered by natural or human-induced changes of stress in the crust.