Båth's law derived from the Gutenberg‐Richter law and from aftershock properties

By Agnes Helmstetter, Didier Sornette. 2003

154 citations recorded by the source corpus.

The empirical Båth's law states that the average difference in magnitude between a mainshock and its largest aftershock is 1.2, regardless of the mainshock magnitude. Following Vere‐Jones' [1969] and Console et al. [2003] , we show that the origin of Båth's law is to be found in the selection procedure used to define mainshocks and aftershocks rather than in any difference in the mechanisms controlling the magnitude of the mainshock and of the aftershocks. We use the ETAS model of seismicity, which provides a more realistic model of aftershocks, based on (i) a universal Gutenberg‐Richter (GR) law for all earthquakes, and on (ii) the increase of the number of aftershocks with the mainshock magnitude. Using numerical simulations of the ETAS model, we show that this model is in good agreement with Båth's law in a certain range of the model parameters.

Subfields: Geophysics

View Paper: https://www.semanticscholar.org/paper/812148ffc2bc0e5684a5670711c8f64b4d9fdaa9

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In Geophysics

Citations in the corpus

Earthquake clusters in southern California I: Identification and stability (2013, background): “To the best of our knowledge, the existing statistical explanations of the Bath law [e.g., Helmstetter and Sornette, 2003; Saichev and Sornette, 2005; Vere-Jones, 2008] do not refer to this particular form of the magnitude difference distribution.”
A generalized Omori's law for earthquake aftershock decay (2004, background): “A number of studies of the statistical variability of Dm have been carried out [Vere-Jones, 1969; Kisslinger and Jones, 1991; Tsapanos, 1990; Felzer et al., 2002; Console et al., 2003; Helmstetter and Sornette, 2003].”
Earthquake scaling relations for mid‐ocean ridge transform faults (2004, background): “RTF earthquakes are driven by tectonic loading and subseismic slip, rather than triggered by other seismic events [Helmstetter and Sornette, 2003b].”
Dragon-kings: Mechanisms, statistical methods and empirical evidence (2012, unknown): “ower law distribution. This is called Bäth’s law in seismology. Using the self-excited Hawkes conditional Poisson model (known as the ETAS model in seismology, for epidemic-type aftershock sequence), Helmstetter and Sornette (2003) have shown that the magnitude gap of about 1.2 between a main shock ”