Explaining Foreshock and the Båth Law Using a Generic Earthquake Clustering Model

Abstract

Earthquake clustering is a well-known phenomenon and is associated with foreshocks, aftershock sequences and earthquake swarms. The rigorous mathematical formulation of Epidemic Type Aftershock Sequence (ETAS) model makes it possible to theoretically evaluate the degree to which the ETAS model can explain foreshock observations and the Båth law. This chapter summarizes theoretic probability distribution in terms of the magnitude difference between the initiating event and the largest triggered event in an earthquake cluster; it and clarifies how this distribution can be used to explain foreshock probabilities and the Båth law. It comments on results regarding the testing of the significance of foreshock activity against the ETAS model. The chapter provides the validation of the Båth law. The distinction between generic clustering models and the ETAS model is made specifically because the ETAS model still needs improvements.