B-positive: A robust estimator of aftershock magnitude distribution in transiently incomplete catalogs

The earthquake magnitude-frequency distribution is characterized by the b-value, which describes the relative frequency of large versus small earthquakes. It has been suggested that changes in b-value after an earthquake can be used to discriminate whether that earthquake is part of a foreshock sequence or a more typical mainshock-aftershock sequence, with a decrease in b-value heralding a larger earthquake to come. However, the measurement of b-value during an active aftershock sequence is strongly biased by short-term incompleteness of the earthquake catalog and by data-windowing, and these biases have the same direction as the proposed signal. Here I develop a new estimator of the b-value that is insensitive to transient changes in catalog completeness and that does not require data windowing. The new estimator “b-positive” is based on the positive-only subset of the differences in magnitude between successive earthquakes, which are described by a double-exponential (Laplace) distribution with the same b-value as the magnitude distribution itself. The b-positive estimator greatly improves the robustness of continuous b-value measurements during active earthquake sequences, as well as in historical catalogs with unknown or variable completeness. The new estimator confirms some of the observations of Gulia and Wiemer (2019), although at a reduced level, showing a decrease and recovery of the b-value during several recent foreshock sequences that cannot be attributed simply to measurement bias. However, the unbiased b-value changes may be too subtle to use in a real-time earthquake alarm system.