Generalized Earthquake Counting Processes for Sequence‐Based Hazard

Sequence‐based probabilistic seismic hazard analysis (SPSHA) allows us to account for the effect of aftershocks in the assessment of seismic structural‐design actions (Iervolino et al., 2014, 2018). In fact, it generalizes classical probabilistic seismic hazard analysis (PSHA; Cornell, 1968), combining it with aftershock‐PSHA (Yeo and Cornell, 2009). SPSHA associates in time aftershocks to mainshocks and, therefore, retains a desirable property of classical PSHA; that is, events (earthquakes in PSHA and mainshock–aftershock sequences in SPSHA) occur according to homogeneous Poisson processes (HPPs). Nevertheless, the number of earthquakes in SPSHA is not Poisson‐distributed. This is addressed herein, in which the probability distribution is formulated and discussed for the following random variables: (1) the count of all earthquakes pertaining to sequences originating in any time interval; (2) the count of all earthquakes occurring in any time interval; (3) the count of all earthquakes that cause exceedance of an arbitrary ground‐motion intensity threshold at the site of interest, generated by sequences originating in any time interval. An application referring to central Italy is also developed to help the discussion. The three main findings are that: (1) the formulated SPSHA counting processes further generalize PSHA; that is, they degenerate in the corresponding mainshock HPPs, if aftershocks are neglected; (2) to associate the aftershocks to the corresponding mainshocks in time is fit for hazard assessment purposes; and (3) the variance‐to‐mean ratio of the counting distributions is significantly larger than one; consequently, the occurrence processes cannot be approximated by Poisson processes. These results, which complete the SPSHA framework, can be a reference for model calibration exercises when SPSHA is computed via simulation and in those cases in which the probability of an exact number of exceedances is of interest, rather than that of observing at least one exceedance (e.g., for seismic damage accumulation studies).