Productivity within the epidemic-type seismicity model

SUMMARY The productivity of a magnitude m event can be characterized in term triggered events above − Δ: it is the number direct ‘descendants’ $\nu _\Delta$ and all $V_\Delta$. There evidence favour discrete exponential distribution for both $V_\Delta$ with dominant initial (the case aftershock cluster). We consider general Epidemic Type Aftershock Sequence model adapted to any _\Delta$. Our first result shows that models branching structure do not allow coincidence types (say, exponential, as scientific literature). second problem related tail behaviour distribution. show fundamental difference $V_\Delta$-distributions general-type clusters magnitude: heavy former light latter. real data demonstrate possibilities this kind. This provides theoretical practical constraints distributional analysis