Variation of singularity of earthquake-size distribution with respect to tectonic regime

Frequency–size relation of earthquakes in a region can be approximated by the Gutenberg-Richter law (GR). This power-law model involves two parameters: a-value measuring seismic activity or earthquake productivity, and b-value describing the relation between frequencies of small and large earthquakes. The spatial and temporal variations of these two parameters, especially the b-value, have been substantially investigated. For example, it has been shown that b-value depends inversely on differential stress. The b-value has also been utilized as earthquake precursor in large earthquake prediction. However, the physical meaning and properties of b-value including its value range still remain as an open fundamental question. We explore the property of b-value from frequency–size GR model in a new form which relates average energy release and probability of large earthquakes. Based on this new form of GR relation the b-value can be related to the singularity index (1–2/3b) of fractal energy – probability power-law model. This model as applied to the global database of earthquakes with size M ≥ 5 from 1964 to 2015 indicates a systematic increase of singularity from earthquakes occurring on mid-ocean ridges, to those in subduction zones and in collision zones.