Omori law for eruption foreshocks and aftershocks

Abstract

Using the 1973–2009 worldwide catalogs for M ≥ 4.8 seismicity and VEI ≥ 0 volcano eruptions, we compare the properties of seismic damage patterns contemporary with eruption with the properties of foreshocks and aftershocks of classic tectonic earthquakes. Using superposed epoch analysis, we demonstrated that the seismicity rate after eruption decreases as a power law similar to the Omori law of earthquake aftershocks. We further show that a complete mapping of Omori law of earthquake aftershocks onto eruption aftershocks does exist as Rerup(t) = (K0.10β(VEI))/[(t+c)p], volcanic explosivity index (VEI), being an empirical measure that exponentially scales with eruption size. β close to 0.4 is the value reported for M = 5–6.5 earthquakes from the same catalog. The p values are in the 0.7 range, i.e., robustly smaller than the 0.9–1.0 range for earthquake aftershocks we estimated in the volcanic area. K value for eruptions is 2–10 times smaller than for earthquakes, and it scales with VEI values. All those parameters characterize a slower damage relaxation after eruptions than after earthquakes. When earthquakes' foreshock rates are proposed to be independent of the main shock magnitude, we resolved a strong increase in foreshock rates including an increase of the p′ value of the inverse Omori law prior eruptions with eruption size. These patterns, all emerging from mean field analysis, are evidence of the volcanic eruptions being contemporary with a stochastic brittle damage in the Earth crust. These results suggest a generic damage relaxation within the Earth crust as power law distributed after or before events. The loading and relaxation exponents and the damage rate emerge as being controlled by the loading rate, as reported during lab‐scale experiments. The more impulsive the loading, i.e., km/s for the slip velocity during earthquakes against km/h for dyke propagation, the faster the relaxation (0.9–1.0 p values for earthquakes' aftershocks against 0.7 for eruptions' aftershocks). Before eruptions, the larger the impending events, the higher the p values. All the observations converge toward the amplitude and frequency of the stress step to drive the Omori law parameters as qualitatively reproduced by the rate and state friction law response of brittle crust faults to loading.