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.