The Geophysical Journal International published an article by Doctor of Physical and Mathematical Sciences G. Molchan and his Italian colleagues, devoted to the theoretical analysis of the productivity of seismic events. The productivity of a magnitude m event can be characterized in term of triggered events of magnitude above m – Δ: it is the number of direct ‘descendants’ νΔ and the number of all ‘descendants’ VΔ. There is evidence in favour of the discrete exponential distribution for both νΔ and VΔ with a dominant initial magnitude m (the case of aftershock cluster). We consider the general Epidemic Type Aftershock Sequence model adapted to any distribution of νΔ. Our first result shows that models with branching aftershock structure do not allow for the coincidence of distribution types of νΔ and VΔ (say, the discrete exponential, as in the scientific literature). The second problem is related to the tail behaviour of the VΔ distribution. We show the fundamental difference in tail behaviour of the VΔ – distributions for general-type clusters and clusters with a dominant initial magnitude: the tail is heavy in the former case and light in the latter. The real data demonstrate the possibilities of this kind.
Source: G. Molchan, E. Varini, A. Peresan Productivity within the epidemic-type seismicity model Geophysical Journal International, Volume 231, Issue 3, December 2022, Pages 1545–1557,DOI: 10.1093/gji/ggac269, Published: 22 July 2022