Two b’s or Not Two b’s

Abstract The b -value, a crucial parameter in the Gutenberg–Richter magnitude distribution, plays a pivotal role in understanding seismic activity. Its significance stems primarily from its inverse correlation with stress levels in the Earth’s crust, offering valuable insights into the underlying forces that drive earthquake occurrences. It is often observed that the Gutenberg–Richter histogram presents two different slopes, with higher magnitudes featuring the smaller slopes; the two slopes may be caused by a data sample containing events from two different populations having different b -values. In this case, the higher-magnitude slope tends asymptotically to the smaller of the two b -values and, if data are enough to measure this slope, the parameters of the two populations can be approximately recovered. Numerical examples are used to justify the proposed recovery method, and applications to real data are shown.