Stable estimation of the Gutenberg–Richter b-values by the b-positive method: a case study of aftershock zones for magnitude-7 class earthquakes

The traditional approach for estimating the b-value of the Gutenberg–Richter law, which is posited to inversely correlate with differential stress, has historically relied on the maximum likelihood technique, utilizing data from earthquakes exceeding a magnitude cutoff, Mc. This traditional approach is significantly influenced by the value of Mc, leading to extensive research focused on methods for determining Mc with greater accuracy. However, a recent study introduced a novel method based on the frequency distribution of magnitude difference, termed the b-positive method. This innovative method could enable more robust b-value estimations, even in scenarios where Mc may vary spatially and temporally. Our study concentrated on analyzing aftershocks, related to 25 magnitude-7 class earthquakes surrounding the Japanese archipelago. We estimated the b-values using both the goodness-of-fit test for Mc, a traditional approach, and the b-positive method. The aftershock data were examined over two distinct time frames: the initial 10 days following each mainshock and an extended period of 1000 days. Our findings indicated that the estimates produced by the b-positive method showed negligible variation between the 10-day and 1000-day aftershock periods (correlation coefficient of 0.95), whereas the traditional approach tended to yield lower b-values for the 10-day aftershocks compared to those from the 1000-day period. Variations in b-values, when analyzed using the traditional approach, could be inaccurately ascribed to temporal fluctuations in differential stress that may not actually be present. The b-positive method offers a vital solution to prevent these erroneous interpretations, serving as an essential alternative. Graphical abstract