Abstract
An experimental method for the spatial resolution analysis of the earthquake frequency-magnitude distribution is introduced in order to identify the intrinsic spatial scale of the detected seismicity phenomenon. We consider the unbounded magnitude range m ∈ (−∞, +∞), which includes incomplete data below the completeness magnitude m c. By analyzing a relocated earthquake catalog of Taiwan, we find that the detected seismicity phenomenon is scale-variant for m ∈ (−∞, +∞) with its spatial grain a function of the configuration of the seismic network, while seismicity is known to be scale invariant for m ∈ [m c, +∞). Correction for data incompleteness for m < m c based on the knowledge of the spatial scale of the process allows extending the analysis of the Gutenberg–Richter law and of the fractal dimension to lower magnitudes. This shall allow verifying the continuity of universality of these parameters over a wider magnitude range. Our results also suggest that the commonly accepted Gaussian model of earthquake detection might be an artifact of observation.
Highlights
Earthquakes represent a complicated geographical phenomenon, which is shown to be self-similar in a wide range of scales (BAK et al 2002)
We investigate the shape of the earthquake frequency-magnitude distribution over the range m [ (-?, ??) to determine the fundamental spatial unit of the geographical phenomenon that is detected seismicity (Sect. 2; PEREIRA 2001)
We show that the spatial scale of detected seismicity can be inferred from the analysis of the shape of the earthquake frequency-magnitude distribution (FMD)
Summary
Earthquakes represent a complicated geographical phenomenon, which is shown to be self-similar in a wide range of scales (BAK et al 2002). It has been shown that this parameter is ambiguous with the m_ c estimate depending at a same location on the computation method and on the spatial scale considered (MIGNAN and CHOULIARAS 2014). The behavior of seismicity at m \ mc is ambiguous due to the fact that the intrinsic spatial scale of the detected seismicity phenomenon has not been considered so far. There is an implicit assumption that the detection process is self-similar, which has recently been shown to be incorrect (i.e., the frequency-magnitude distribution does not display the same statistical properties or same shape at different scales; see Fig. 16 in MIGNAN 2012)
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