Observations Favor BASS, the Self-Similar Limit of ETAS

What is the ETAS model? It is a stochastic model for the generation of aftershock sequences. It is based on the concept of parent and daughter earthquakes. The number of daughter earthquakes that a parent earthquake generates is determined randomly from a productivity relation. The magnitude and time of occurrence of each daughter earthquake is determined randomly from the Gutenberg-Richter and Omori laws. Each first generation daughter earthquake becomes a parent for second generation daughters, and so forth until the sequence dies out. What is the BASS model? The BASS model is the self-similar limit of the ETAS model. Instead of the productivity relation, the modified form of Bath's law is used. The two arbitrary parameters in the productivity relation are replaced by the b-value in the GR law and the magnitude difference Delta m* between the parent earthquake and the largest expected daughter earthquake. Why is the BASS model preferred to the ETAS model? Because the BASS model is in better agreement with observations than the ETAS model. Specifically: (1) The BASS model generates Bath's law statistics since they are an input; (2) The BASS model generates inverse GR statistics for foreshock generation. The distribution of magnitudes of foreshocks is independent of the mainshock magnitude. The ETAS model has an exponential dependence of foreshock magnitude on the mainshock magnitude which is not in agreement with observations. Why do ETAS model proponents reject the BASS model? Because the BASS model is inherently unstable generating infinite numbers of aftershocks. However, this instability is easily removed by making the physically reasonable hypothesis that the excess magnitudes of daughter earthquakes over the parent earthquake cannot exceed a specified difference.