| While the physics determining how individual earthquakes trigger each other may be impossibly complex, the overall statistics of seismicity are fairly simple, and may be used to learn about the rules of earthquake triggering. I first use statistics to generate synthetic aftershock catalogs with a Monte Carlo algorithm based on the following: (1) All earthquakes may trigger aftershocks, at a rate proportional to 10bM where M is earthquake magnitude and b is from the Gutenberg-Richter relationship. (2) The timing of direct aftershocks is governed by the modified Omori Law with parameters that remain constant with time, and (3) The magnitude of each aftershock is chosen randomly from the Gutenberg-Richter distribution. In agreement with previous authors I find that this statistical model produces realistic aftershock sequences. I use this model to demonstrate that many aftershocks in large sequences are actually secondary aftershocks, e.g. most directly triggered by previous (small and large) aftershocks. This finding presents a challenge to the popular method of predicting aftershock locations based on stress changes induced solely by large mainshocks, and suggests that simply using the locations and times of previous aftershocks may be more effective. For four large aftershock sequences in California I find that using previous aftershocks does produce better predictions of aftershock locations than using main shock-induced Coulomb static stress changes.; One of the more controversial assumptions of my Monte Carlo model is that the magnitudes of aftershocks are chosen randomly, independent of the magnitude of their mainshocks. Others have argued that foreshocks are observed because they are triggered by the nucleation phase of the following large earthquake, not because they are simply small mainshocks, and that special circumstances are involved when several large earthquakes cluster together (multiplets). I make use of global and California earthquake catalog statistics to demonstrate that the rates and magnitude distributions of aftershocks, multiplets, and foreshocks are in fact in agreement with the hypothesis that aftershock magnitudes are chosen randomly, and that there is only a single earthquake triggering process. I additionally demonstrate that there is no correlation between mainshock magnitude and foreshock magnitude, number, or spatial extent. This makes it highly unlikely that foreshocks could be triggered by the mainshock nucleation phase. |
