B‐Positive: A Robust Estimator of Aftershock Magnitude Distribution in Transiently Incomplete Catalogs

Abstract

Earthquake magnitudes are exponentially distributed. This means that for any magnitude M, the number of earthquakes N with magnitude larger than M can be written 10 log N bM   , in what is known as the Gutenberg-Richter (GR) distribution. The parameter b describes the slope of the distribution in log-linear space. In probabilistic terms, the b-value characterizes the relative likelihood of small versus large earthquakes within a population of earthquakes, and therefore has utility in earthquake forecasting. It has also been argued that b-value may carry diagnostic information about the state of stress on the faults generating the earthquakes (

Frequency‐Magnitude Statistics of Laboratory Foreshocks Vary With Shear Velocity, Fault Slip Rate, and Shear Stress

“…To conclude, all of our F/M curves may not follow a strict exponential relationship and this could lead one to question the validity of our b-value results (e.g., Herrmann & Marzocchi, 2021;van der Elst, 2021). However, the purpose of this work is to demonstrate that preseismic AEs (i.e., foreshocks) are modulated by shear velocity, shear stress, and fault slip rate.…”

Earthquakes Triggered by Fluid Diffusion and Boosted by Fault Reactivation in Weiyuan, China Due to Hydraulic Fracturing

“…We then calculate b ‐values of the Gutenberg‐Richter (G‐R) law (Gutenberg & Richter, 1944) for all earthquakes. The b ‐value characterizes the relative number of large earthquakes versus small ones, and has be used to infer differential stresses, asperity locations, pore fluid distributions (Schorlemmer & Wiemer, 2005; Tormann et al., 2014; van der Elst, 2021; Wiemer & Katsumata, 1999). It has been shown that 50 events are sufficient for establishing statistically significant difference in the b ‐values (Eaton & Maghsoudi, 2015), although the b ‐value tends to be more stable with larger number of events.…”

Tidal Triggering of Microseismicity at the Equatorial Mid‐Atlantic Ridge, Inferred From the PI‐LAB Experiment

“…Moreover, although the AD test cannot reject the exponentiality hypothesis in all the datasets we tested, with one exception (Figure S9), there is a strong dependence of b-value on magnitude cut-off selection. This means that, although unlikely, the GR law violation and/or the temporal catalogue incompleteness cannot be unequivocally ruled out (e.g., Hermann and Marzocchi, 2020;Leptokaropoulos et al, 2018;van der Elst, 2021). However, even without achieving a strong statistical significance, the derived results indicate some relative differences in the magnitude distribution of events during different stages of tidal cycles, suggesting further investigation of larger datasets with better determined magnitudes is warranted.…”

“…The network operated for 1 year and the data acquired were used, in combination with other geophysical measurements, in a variety of studies focused on sediment structure Saikia et al, 2020), infragravity wave sources (Bogiatzis et al, 2020), a multidisciplinary marine geophysical investigation of the active transform valley, the adjacent spreading segments and oceanic lithosphere (e.g. Harmon et al, 2018Harmon et al, , 2020Harmon et al, , 2021Wang et al, 2020;Rychert et al, 2020;2021;Saikia et al, 2021), deeper imaging of thinning of the mantle transition zone (Agius et al, 2021),and a high-resolution study of a MW=7.1 earthquake on the nearby Romanche TF (Hicks et al, 2020). Here, we use the data gathered within the duration of the PI-LAB experiment, in order to study the properties and triggering mechanisms of microseismicity that occurred in the equatorial segment of the MAR.…”