The Spatial Scale of Detected Seismicity

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.