Improve the estimate of the b-value in regional catalogs by means of the the b-more positive method

Abstract: The b-value, which controls the slope of the frequency-magnitude distribution of earthquakes, is a critical parameter in seismic forecasting. However, accurately measuring the true b-value is challenging due to the temporal and spatial variations in the completeness of instrumental seismic catalogs. In this study, we systematically compare traditional methods for estimating the b-value with newer approaches, specifically focusing on the b-more-positive estimator based on positive magnitude difference statistics. We conduct this comparison using both synthetic ETAS catalogs, with artificially introduced incompleteness, and instrumental catalogs from five regions: Japan, Italy, Southern California, Northern California, and New Zealand. Our results from synthetic ETAS catalogs reveal that traditional estimators tend to underestimate the b-value, while the b-more-positive estimator provides a more accurate measurement. Similar patterns are observed in instrumental catalogs, suggesting that traditional methods may also underestimate the true b-value in real datasets.