a‐Positive: A Robust Estimator of the Earthquake Rate in Incomplete or Saturated Catalogs.

Detection thresholds in earthquake catalogs frequently change in time due to station coverage improvements and network saturation effects during active periods such as mainshock‐aftershock cascades. This presents a challenge to seismicity‐rate estimation; there is a tradeoff between using as low a minimum magnitude as possible to maximize data while not undercounting the rate due to catalog incompleteness. Here we present a simple method, "a‐positive," which makes use of differential statistics to robustly estimate the seismicity rate in catalogs with time‐varying detection thresholds. We demonstrate the effectiveness of this method for a centuries‐long, hybrid earthquake catalog with both historical and instrumentally‐detected earthquakes in the Central and Eastern U.S., as well as for the 2019 Ridgecrest aftershock sequence in California, which has rapid changes in completeness due to network saturation. We find that the a‐positive method leads to more precise and less biased estimates of seismicity rate than traditional methods. In addition, with our improved estimate of earthquake rate early in the aftershock cascade, we find no evidence of rate‐saturation at short times from the mainshock; that is, the Omori c‐value is not distinguishable from zero. Plain Language Summary: The seismicity rate is a fundamental aspect of statistical seismology, and it is used to create long‐ term models that inform building codes and seismic hazard assessments. However, earthquake catalogs are imperfect records of earthquakes, due to both changing network coverage and short‐ term aftershock incompleteness, where large earthquakes obscure smaller ones in times of high activity. We here present a new method "a‐positive" to estimate the seismicity rate in catalogs with time‐varying detection thresholds. This method uses differential statistics to estimate the seismicity rate from interevent times, where interevent times are measured to the next larger earthquake, with no reference to a completeness magnitude. The "a‐positive" method provides more precise and less biased estimates of seismicity rate than traditional methods. The method has been tested on a centuries‐long, hybrid earthquake catalog with both historical and instrumentally‐detected earthquakes in the Central and Eastern U.S. and on the 2019 Ridgecrest aftershock sequence in California, which has rapid changes in completeness due to short‐term aftershock incompleteness. The results show that the "a‐positive" method is minimally sensitive to catalog incompleteness and provides an unbiased estimate of the earthquake rate even in the first moments of an aftershock sequence. Key Points: Earthquake catalogs are imperfect records of the earthquake rate, suffering from both network sparseness and short‐term rate saturation"a‐positive" estimates seismicity rate based on the time to the next larger earthquake, with no reference to completeness magnitudeUnbiased measurement of the aftershock rate shows no evidence for rate saturation at early times [ABSTRACT FROM AUTHOR]