Sequence-based probabilistic seismic hazard analysis

Earthquakes are typically clustered both in space and time. Only main- shocks, the largest magnitude events within each cluster, are considered by classical seismic hazard, which is expressed in terms of rate of exceedance of a ground-motion intensity measure at a site of interest ( Cornell, 1968 ). This kind of probabilistic seis- mic hazard analysis ( PSHA ) is used for structural design or assessment in the long term. Recently, for short-term risk management purposes, a similar approach has been adopted to perform aftershock probabilistic seismic hazard analysis ( APSHA ), condi- tional to mainshock occurrence ( Yeo and Cornell, 2009 ). PSHA often refers to a homo- geneous Poisson process to describe event occurrence, whereas APSHA models aftershock occurrence via a conditional nonhomogeneous Poisson process, the rate of which depends on the magnitude of the mainshock that has triggered the sequence. On the other hand, the clusters, each of which is composed of the mainshock and the following aftershocks, may be seen as single events occurring at the same rate of the mainshocks. This may allow accounting for aftershocks in hazard analysis in a rel- atively simple manner, as first argued by Toro and Silva (2001) and further investi- gated by Boyd (2012) . In fact, this short note, focusing on the probabilistic aspects, shows the feasibility of analytically combining results of PSHA and APSHA to get a seismic hazard integral accounting for mainshock – aftershocks seismic sequences, which was still missing from the mentioned studies. The results of the application presented help to preliminarily assess the increase in seismic hazard in terms of rate of occurrence of events causing the exceedance of an acceleration threshold (e.g., that considered for structural design) also considering aftershocks. That is a relevant aspect from the earthquake engineering perspective.