A probabilistic approach for the classification of earthquakes as `triggered' or `not triggered'

Phenomena such as earthquakes or dike intrusions induce strain energy changes which can anticipate or delay the occurrence time of earthquakes on nearby faults. `Anticipated' earthquakes are generally called `triggered', however it is generally controversial to label a specific earthquake as triggered with 100% confidence. In this work we develop a methodology that leads to a quantitative probabilistic classification of earthquakes as triggered or not triggered. We illustrate this methodology by studying the M=6.2 Jan, 13th 1976 earthquake, which struck in the Grímsey Lineament, Tjörnes Fracture Zone, Northern Iceland. The general assumption is that this earthquake was triggered by a dike intrusion in the nearby Krafla rift system, the first dike of the 1975-1984 rifting episode. However, no quantitative studies are available demonstrating unambiguously that the event was triggered by the dike-induced stress change in the region. We use dislocation theory to calculate the Coulomb Failure Function induced by the dike, then derive the change in seismicity rate according to the rate and state theory. Next, we calculate the likelihood of the earthquake in a scenario which takes into account the tectonic stressing rate only, and in a scenario which includes the stress change caused by the dike. At this purpose, we produce spatial hazard maps for the whole Grimsey Lineament region, and convolve them with a location function which takes into account the location error and the fault rupture length for a M≥6 earthquake. Finally, by applying Bayes' theorem, we calculate the probability that the earthquake was indeed triggered by the dike as three orders of magnitude larger than the probability that the earthquake was due purely to accumulation of tectonic strain. This methodology allows to classify earthquakes as triggered or not triggered in an objective way.