Is long-term PSHA time-dependent? Insights from SimplETAS model

Probabilistic seismic hazard analysis (PSHA) traditionally assumes time-invariant Poisson processes over mainshocks, while removing aftershocks through non-objective declustering procedures. This may underestimate seismic hazard, as recent sequences demonstrate significant ground-shaking contributions from aftershocks. Models for cluster correction (e.g., Marzocchi and Taroni, 2014; MT14) incorporate aftershock productivity but maintain temporally constant rates. While these models improve hazard estimates, the temporal persistence of conditioning effects in long-term forecasts remains poorly quantified.

This study investigates how long-term SimplETAS-based seismic hazard is affected by forecast initialization time, considering two scenarios: (i) an unconditional PSHA, i.e. not conditioned on a specific earthquake sequence, and (ii) a conditional PSHA initialized immediately after the 2009 L’Aquila earthquake sequence. We aim to assess whether 50-year PSHA remains consistent across different initialization times, which is typically assumed sufficient for the stationarity of the hazard process.

We employ the SimplETAS algorithm to generate two sets of 100,000 synthetic catalogs spanning 50 years: one set starting in 2024 (unconditional) and one starting immediately after the 2009 L’Aquila seismic sequence (conditional). For each earthquake in the synthetic catalogs, we assign a plausible seismogenic structure and compute fault-to-site distances for ground motion prediction using the GMPEs. Hazard curves are calculated empirically as the fraction of catalogs exceeding given PGA thresholds, without relying on the Poisson distribution. We analyze four Italian cities with varying seismicity levels: L’Aquila, Reggio Calabria, Firenze, and Milano. In the unconditional scenario, we compute 50-year hazard curves for all four cities. In the conditional scenario, we compute hazard curves for the same four cities to identify a conditioning effect only on the affected site of L’Aquila. Additionally, for that site, we quantify the temporal decay of conditioning by computing hazard curves over multiple time windows (1, 5, 10, and 50 years) and comparing them with the corresponding unconditional PSHA.

Unconditional PSHA shows good agreement with the reclustered version of the official Italian seismic hazard model (MPS19_cluster) across all four cities and different return periods, corroborating the use of SimplETAS-based approach for long-term PSHA, and the suitability of the MT14's PSHA correction across different return periods. The results of the conditional analysis reveal that L’Aquila exhibits differences of about 10-20% between conditional and unconditional PSHA even over the 50-year window, while Firenze, Milano, and Reggio Calabria remain essentially unchanged. The temporal decay analysis at L’Aquila shows how conditioning effects progressively decrease over longer periods, though the average effect remains detectable in a 50 years time window.