Foreshock probabiliites and the Båth law under the ETAS model

Abstract:

This study inverstigates at what degree the ETAS model, which is widely used in seismology for describing clustering features of the earthquake process, can explain the foreshock phenomenon and the båth law. Starting from the ETAS model with two exponential laws, the positive exponential laws for the expected number of earthquakes that an earthquake can trigger, and the well-known Gutenberg-Richter law (negative exponential distribution) for earthquake magnitude, this study shows that the magnitude distribution of the largest descendant from a given event determines the foreshock probabilities, which is close to the values in real seismicity. The båth law can alos be expressed as asymptotic forms of this magnitude distribution. These results are also verified by different analysis on real seismicity and synthetic catalogs that are simulated by the ETAS model.