Importance sampling of seismic tsunami sources with near-field emphasis for inundation PTHA: benchmarking with complete ensembles

SUMMARY Site-specific Probabilistic Tsunami Hazard Assessment (PTHA) is a powerful tool for coastal planning against tsunami risk. However, its typically high computational demands led to the introduction of a Monte Carlo Stratified Importance Sampling (SIS) approach, which selects a representative subset of scenarios for numerical inundation simulations. We here empirically validate this sampling approach, for the first time to our knowledge, using an existing extensive data set of numerical inundation simulations for two coastal sites in the Mediterranean Sea (Catania and Siracusa, both located in Sicily, Italy). Moreover, we propose a modified importance sampling function to prioritize seismic tsunami scenarios based on their arrival time at an offshore point near the target site, in addition to their wave amplitude and occurrence rate as leveraged in the previous work. This sampling function is applied separately in each earthquake magnitude bin, and allows denser sampling of near-field earthquakes to whose variations tsunamis are very sensitive. We compare the confidence intervals of the offshore PTHA estimates obtained with the new and the original importance sampling functions. Then, we benchmark our onshore PTHA estimates obtained with both functions against the inundation PTHA calculated using the full set of scenarios. We also test the assumption that onshore random errors follow a normal distribution, as found previously for the offshore case. As a result of the benchmarks, we find that the SIS approach works satisfactorily. Introducing the arrival time as an additional sampling factor enhances the precision of the estimates of both the mean and the percentiles for the two coastal sites considered. With this modification it is possible to deal efficiently with heterogeneous near-field earthquake sources involving coastal deformation at Catania and Siracusa, in addition to regional crustal and subduction sources. By comparing the sampling errors with the model (epistemic) uncertainty, an optimal trade-off between the number of simulations employed and the uncertainty of the PTHA model can be found, even for such a complex situation. A relatively small number of scenarios, on the order of a few thousand, is sufficient to perform site-specific PTHA for practical applications. These numbers correspond to 4–8 per cent of the already reduced ensembles used in previous assessments at the same sites.