Gareth Davies, Rikki Weber, Kaya Wilson, Phil Cummins

Offshore Probabilistic Tsunami Hazard Assessments (offshore PTHAs) provide large-scale analyses of earthquake-tsunami frequencies and uncertainties in the deep ocean, but do not provide high-resolution onshore tsunami hazard information as required for many risk-management applications. To understand the implications of an offshore PTHA for the onshore hazard at any site, in principle the tsunami inundation should be simulated locally for every earthquake scenario in the offshore PTHA. In practice this is rarely feasible due to the computational expense of inundation models, and the large number of scenarios in offshore PTHAs. Monte-Carlo methods offer a practical and rigorous alternative for approximating the onshore hazard, using a random subset of scenarios. The resulting Monte-Carlo errors can be quantified and controlled, enabling high-resolution onshore PTHAs to be implemented at a fraction of the computational cost. This study develops efficient Monte-Carlo approaches for offshore-to-onshore PTHA. Modelled offshore PTHA wave heights are used to preferentially sample scenarios that have large offshore waves near an onshore site of interest. By appropriately weighting the scenarios, the Monte-Carlo errors are reduced without introducing bias. The techniques are demonstrated in a high-resolution onshore PTHA for the island of Tongatapu in Tonga, using the 2018 Australian Probabilistic Tsunami Hazard Assessment as the offshore PTHA, while considering only thrust earthquake sources on the Kermadec-Tonga trench. The efficiency improvements are equivalent to using 4-18 times more random scenarios, as compared with stratified-sampling by magnitude, which is commonly used for onshore PTHA. The greatest efficiency improvements are for rare, large tsunamis, and for calculations that represent epistemic uncertainties in the tsunami hazard. To facilitate the control of Monte-Carlo errors in practical applications, this study also provides analytical techniques for estimating the errors both before and after inundation simulations are conducted. Before inundation simulation, this enables a proposed Monte-Carlo sampling scheme to be checked, and potentially improved, at minimal computational cost. After inundation simulation, it enables the remaining Monte-Carlo errors to be quantified at onshore sites, without additional inundation simulations. In combination these techniques enable offshore PTHAs to be rigorously transformed into onshore PTHAs, with quantification of epistemic uncertainties, while controlling Monte-Carlo errors.