Effect of Mainshock Selection, Earthquake Catalog and Definition on Foreshock Rate Estimates in Southern California

Estimates of the percentage of moderate to large crustal earthquakes (mainshocks) that have foreshocks (the foreshock rate) vary widely: Recent estimates in Southern California using an enhanced catalog range between 19% and 72%. Enhanced catalogs seem to reveal more foreshocks, possibly providing new constraints on nucleation mechanisms, but precise, commonly accepted foreshock definitions are lacking. To investigate the observed range we quantify the sensitivity of foreshock rates to mainshock selection method, catalog (standard and enhanced), foreshock definition, geographical restriction and magnitude cut-offs. We compare two foreshock definitions: Type A—any earthquakes above a magnitude threshold in a space-time window; and type B—an earthquake count in a space-time window that exceeds the 99th percentile of a statistical representation of past seismicity rates (using three distributions: Poisson, Gamma and Empirical). Foreshock rate estimates are increased by (in order of influence): Defining foreshocks using Poisson distributed background rates, using a type A foreshock definition, and removing aftershocks using fixed space-time windows. Rates are lowered by: Removing aftershocks using magnitude-dependent methods, and defining foreshocks using Gamma distributed inter-event times and Empirical distributions of seismicity. A large increase in foreshock rate between the standard and enhanced catalog is only observed when using Poisson distributed background rates for type B foreshocks. A lower magnitude of completeness may thus not lead to significantly more mainshocks with detected foreshocks. Our preferred method, using a more robust mainshock selection and quality-controlled data, estimates ∼25% of M ≥ 4 “mainshocks” in Southern California have foreshocks.