The Gutenberg-Richter law based on rupture dynamics

2020 ◽  
Author(s):  
Zhenguo Zhang ◽  
Wenqiang Zhang ◽  
Jiankuan Xu ◽  
Xiaofei Chen
Keyword(s):  
Power Law Distribution ◽  
Magnitude Distribution ◽  
Rupture Dynamics ◽  
Earthquake Sources ◽  
Rupture Area ◽  
Earthquake Frequency ◽  
Frequency Magnitude Distribution ◽  
First Time ◽  
The Relationship ◽  
Frequency Magnitude

<p>Earthquakes recorded by instruments obey the Gutenberg-Richter law, which expresses the dependence of earthquake frequency on magnitude. The Gutenberg-Richter law reveals the physics of earthquake sources and is important for analyzing the seismicity of active fault systems and vulnerable areas. Based on rupture dynamics, for the first time, we obtain a power-law distribution for the relationship between earthquake frequency and magnitude. The weight of an earthquake relies on its rupture area and recurrence interval. Our derived frequency-magnitude distribution agrees with the Gutenberg-Richter law, which is summarized from global and regional earthquake catalogs. This work provides a new way to understand the Gutenberg-Richter law and the physics of earthquake sources.</p>

scholarly journals Generalized earthquake frequency–magnitude distribution described by asymmetric Laplace mixture modelling

2019 ◽  
Vol 219 (2) ◽  
pp. 1348-1364 ◽  
Author(s):  
A Mignan
Keyword(s):  
Homogeneous Space ◽  
Mixture Model ◽  
Space Time ◽  
Seismic Network ◽  
Earthquake Catalogues ◽  
Magnitude Distribution ◽  
Mixture Modelling ◽  
Earthquake Frequency ◽  
Frequency Magnitude Distribution ◽  
Frequency Magnitude

SUMMARY The complete part of the earthquake frequency–magnitude distribution, above the completeness magnitude mc, is well described by the Gutenberg–Richter law. On the other hand, incomplete data does not follow any specific law, since the shape of the frequency–magnitude distribution below max(mc) is function of mc heterogeneities that depend on the seismic network spatiotemporal configuration. This paper attempts to solve this problem by presenting an asymmetric Laplace mixture model, defined as the weighted sum of Laplace (or double exponential) distribution components of constant mc, where the inverse scale parameter of the exponential function is the detection parameter κ below mc, and the Gutenberg–Richter β-value above mc. Using a variant of the Expectation-Maximization algorithm, the mixture model confirms the ontology proposed by Mignan [2012, https://doi.org/10.1029/2012JB009347], which states that the shape of the earthquake frequency–magnitude distribution shifts from angular (in log-linear space) in a homogeneous space–time volume of constant mc to rounded in a heterogeneous volume corresponding to the union of smaller homogeneous volumes. The performance of the proposed mixture model is analysed, with encouraging results obtained in simulations and in eight real earthquake catalogues that represent different seismic network spatial configurations. We find that k = κ/ln(10) ≈ 3 in most earthquake catalogues (compared to b = β/ln(10) ≈ 1), suggesting a common detection capability of different seismic networks. Although simpler algorithms may be preferred on pragmatic grounds to estimate mc and the b-value, other methods so far fail to model the angular distributions observed in homogeneous space-time volumes. Mixture modelling is a promising strategy to model the full earthquake magnitude range, hence potentially increasing seismicity data availability tenfold, since ca. 90 per cent of earthquake catalogue events are below max(mc).

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