Tsunami hazard assessments with consideration of uncertain earthquake slip distribution and location

This paper proposes a stochastic approach to model the earthquake uncertainties in terms of the rupture location and the slip distribution for a future event, with an expected earthquake magnitude. Once the statistical properties of earthquake uncertainties are described, they are then propagated into the tsunami response and the inundation at assessed coastal areas. The slip distribution is modeled as a random field within a non-rectangular rupture area. The Karhunen-Loeve (K-L) expansion method is used to generate samples of the random slip, and a translation model is employed to obtain target probability properties. A strategy is developed to specify the accuracy of the random samples in terms of numbers of sub-faults of the rupture area and the truncation of the K-L expansion. The propagation of uncertainty into the tsunami response is performed by means of a Stochastic Reduced Order Model. To illustrate the methodology, we investigated a study case in north Chile. We first demonstrate that the stochastic approach generates consistent earthquake samples with respect to the target probability properties. We also show that the results obtained from SROM are more accurate than those obtained with classic Monte Carlo simulations. To validate the methodology, we compared the simulated tsunamis and the tsunami records for the 2014 Chilean earthquake. Results show that leading wave measurements fall within the tsunami sample space. At later times, however, there are mismatches between measured data and the simulated results, suggesting that other sources of uncertainties are as relevant as the uncertainty of earthquakes.