ETAS-positive: Extracting unbiased epidemic-type aftershock models from incomplete earthquake catalogs

Earthquake catalogs are inherently incomplete, and short-term fluctuations in catalog completeness can strongly bias estimates of seismicity parameters. Here, we extend the positive statistics framework recently introduced for estimating Gutenberg–Richter a and b values to the Epidemic-Type Aftershock Sequence (ETAS) model. The approach focuses on complete magnitude–time intervals defined by pairs of earthquakes in which the second event is larger than the first. Comprehensive synthetic tests demonstrate that the proposed ETAS⁺ method retrieves nearly unbiased parameter estimates even from highly incomplete catalogs, whereas parameters obtained using classical estimation approaches are strongly biased. Application to Southern California reveals a similar trend, with the productivity scaling parameter α approaching the b value, consistent with self-similar earthquake triggering within estimation uncertainties. Owing to its robustness against catalog incompleteness and computational efficiency, the ETAS⁺ method provides a powerful new tool for seismicity analysis and earthquake forecasting.