Bilinearity in the Gutenberg‐Richter Relation Based on M_L for Magnitudes Above and Below 2, From Systematic Magnitude Assessments in Parkfield (California)

Abstract

Several studies have shown that local magnitude, ML, and moment magnitude, M, scale differently for small earthquakes (M < ~2) than for moderate to large earthquakes. Consequently, frequency‐magnitude relations based on one or the other magnitude type cannot obey a power law with a single exponent over the entire magnitude range. Since this has serious consequences for seismic hazard assessments, it is important to establish for which magnitude type the assumption of a constant exponent is valid and for which it is not. Based on independently determined M, ML and duration magnitude, Md, estimates for 5,304 events near Parkfield, we confirm the theoretically expected difference in scaling between the magnitude types, and we show that the frequency‐magnitude distribution based on M and Md follows a Gutenberg‐Richter relation with a constant slope, whereas for ML it is bilinear. Thus, seismic hazard estimates based on ML of small earthquakes are likely to overestimate the occurrence probability of large earthquakes.

The 2018 national seismic hazard assessment of Australia: Quantifying hazard changes and model uncertainties

“…This is in excellent agreement with other theoretical and empirical studies of M L - M relationships for small events, both in Australia and in abroad (e.g. Allen et al, 2011; Deichmann, 2017; Dost et al, 2018; Edwards et al, 2010, 2015; Munafò et al, 2016; Staudenmaier et al, 2018). Together, the M L corrections and the subsequent conversions to M approximately reduce the number of earthquakes exceeding magnitude 4.5 and 5.0, respectively, by 50% or more (Figure 6).…”

Fast MW estimation of microearthquakes recorded around the underground gas storage in the Montello-Collalto area (Southeastern Alps, Italy)

“…For example, it is known that the b value is a crucial parameter for seismic hazard assessment (Cornell 1968;Weichert 1980); it represents the relative number of large and small earthquakes in a specific area, and together with the a value, it is useful to provide an estimate of the maximum expected magnitude. However, it has been found that seismic hazard assessments based on M L of small earthquakes likely overestimate the occurrence probability of large earthquakes (Staudenmaier et al 2018). Another application is the discrimination between induced and natural seismicity, where b value deviations from its theoretical value may be symptomatic of induced seismicity (e.g., Stabile et al 2014;Goebel et al 2016).…”

“…At the same time, M W is preferred to M L in the probabilistic seismic hazard assessments, both for natural and induced earthquakes. Indeed, unlike M L , M W is not affected by saturation, anelastic attenuation, or scattering problems, and therefore, the fault to rupture provides more reliable estimations of the Gutenberg-Richter parameters (a and b values) (Edwards 2015;Staudenmaier et al 2018).…”

Inconsistencies and Lurking Pitfalls in the Magnitude–Frequency Distribution of High-Resolution Earthquake Catalogs

“…S14b). An additional explanation for the apparent under-representation of low magnitudes (which does not preclude the previous ones) is the scaling break of the (amplitude-based) local magnitude L , which, as shown by several studies [e. g., Bakun 1984;Hanks and Boore 1984;Ben-Zion and Zhu 2002;Edwards et al 2010;Zollo et al 2014;Staudenmaier et al 2018;Lanzoni et al 2019], scales differently with w below 2−4 (with L ∝ 1.5 w ) due to the attenuation of the higher frequency content in the medium (i. e., their corner frequencies remain constant) [Bethmann et al 2011;Munafò et al 2016;Deichmann 2017]. Anti-aliasing in the digital sampling process (an additional low-pass filter) can contribute to the scaling break [Uchide and Imanishi 2018].…”