## Constraints on the size of the smallest triggering earthquake from the epidemic-type aftershock sequence model, Båth's law, and observed aftershock sequences

Didier Sornette, & Maximilian J. WernerPublished August 2005, SCEC Contribution #859

The physics of earthquake triggering together with simple assumptions of self-similarity imply the existence of a minimum magnitude m 0 below which earthquakes do not trigger other earthquakes. Noting that the magnitude m d of completeness of a seismic catalog is not, in general, the same as the magnitude m 0 of the smallest triggering earthquake, we compare observed aftershock sequence parameters with the predictions made by the epidemic-type aftershock sequence model to constrain the value of m 0. In particular, we use quantitative fits to observed aftershock sequences from three previous studies, as well as Båth's law, to obtain four estimates of m 0. We show that the branching ratio n (average number of triggered earthquakes per earthquake, also equal to the fraction of aftershocks in a seismic catalog) is the key parameter controlling the estimate of the minimum triggering magnitude m 0. Conversely, physical upper bounds for m 0 estimated from rate and state friction indicate that at the very least, 55% of all earthquakes are aftershocks.

**Citation**

Sornette, D., & Werner, M. J. (2005). Constraints on the size of the smallest triggering earthquake from the epidemic-type aftershock sequence model, Båth's law, and observed aftershock sequences. *Journal of Geophysical Research*, 110(B08304). doi: 10.1029/2004JB003535 .