Abstract
—The magnitude of completeness {{M}_{c}} of the earthquakes above which 100% of events are thought to be reliably detected is a vital parameter characterizing the completeness of seismic data. A known fact is that to obtain correct estimates of the parameters of seismicity, it is compulsory to take into account {{M}_{c}} variations in space and time. In this work, we compare six modern methods for estimating {{M}_{c}}. To compare the methods, we use event samples from real instrumental earthquake catalogs and synthetic catalogs generated based on the three models of magnitude distribution. We analyze the dependences of the two first moments of the distributions of {{M}_{c}} estimates on the shape of magnitude distributions and the sample size. We use three models corresponding to sample distributions that occur in the analysis of instrumental earthquake catalogs. Based on the obtained results, we formulate recommendations on selecting the suitable method for estimating the magnitude of completeness {{M}_{c}}.
Highlights
One of the key characteristics of a seismic process is the frequency of occurrence of earthquakes of different magnitudes
Where N is the number of earthquakes with magnitude m ≥ M ; a is the parameter of seismic activity, and parameter b is the slope of the GR frequency–magnitude distribution
The results for the samples from the Earthquake Catalog of Switzerland (ECOS), Northern California Seismic Network (NCSN), and NIED catalogs are closely consistent with the results presented in (Woessner and Wiemer, 2005; Amorèse, 2007)
Summary
One of the key characteristics of a seismic process is the frequency of occurrence of earthquakes of different magnitudes. The relationship between the frequency of occurrence and the magnitude is referred to as the recurrence law of earthquakes. Where N is the number of earthquakes with magnitude m ≥ M ; a is the parameter of seismic activity, and parameter b (referred to as the b-value) is the slope of the GR frequency–magnitude distribution. Temporary decrease in b-value has been repeatedly observed before strong earthquakes (Gibowicz, 1973; Zavyalov, 1984; 2006; Nuannin et al, 2005). Temporary decays and buildups of seismic activity known as seismic quiescences and foreshock activations are considered as probable precursors of the strong earthquakes (Wyss et al, 1999; Zöller et al, 2002)
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