Tsunami variability from uncalibrated stochastic earthquake models: tests against deep ocean observations 2006-2016

This study tests three models for generating stochastic earthquake-tsunami scenarios on subduction zones by comparison with deep ocean observations from 18 tsunamis during the period 2006-2016. It focusses on the capacity of uncalibrated models to generate a realistic distribution of hypothetical tsunamis, assuming the earthquake location, magnitude and subduction interface geometry are approximately known, while details of the rupture area and slip distribution are unknown. Modelling problems like this arise in tsunami hazard assessment, and when using historical and palaeo-tsunami observations to study pre-instrumental earthquakes. Tsunamis show significant variability depending on their parent earthquake's properties, and it is important that this is realistically represented in stochastic tsunami scenarios. To clarify which aspects of earthquake variability should be represented, three scenario generation approaches with increasing complexity are tested: a simple fixed-area-uniform-slip (FAUS) model with earthquake area and slip deterministically related to moment magnitude; a variable-area-uniform-slip (VAUS) model which accounts for earthquake area variability; and a heterogeneous-slip (HS) model which accounts for both earthquake area variability and slip heterogeneity. The models are tested using deep-ocean tsunami time-series from 18 events 2006-2016) with moment magnitude M-w > 7.7. For each model and each observed event a 'corresponding family of model scenarios' is generated which includes stochastic scenarios with earthquake location and magnitude similar to the observation, with no additional calibration. For an ideal model (which perfectly characterizes the variability of tsunamis) the 18 observed events should appear like a random sample of size 18, created by taking one draw from each of the 18 'corresponding family of model scenarios'. This idea forms the basis of statistical techniques to test the models. First a goodness-of-fit criterion is developed to identify stochastic scenarios 'most similar' to the observed tsunamis, and assess the capacity of different models to produce good-fitting scenarios. Both the HS and VAUS models show similar capacity to generate tsunamis matching observations, while the FAUS model performs much more poorly in some cases. Secondly, the observed tsunami stage ranges are tested for consistency with the null hypothesis that they were randomly generated by the model. The null hypothesis cannot be rejected for the HS model, whereas both uniform-slip models exhibit a statistically significant tendency to produce small tsunamis too often. Finally, the statistical properties of slip for stochastic earthquake scenarios are compared against earthquake scenarios that best fit the observations. For the VAUS models the best-fitting model scenarios have higher slip on average than the stochastic scenarios, highlighting biases in this model. The techniques developed in this study can be applied to test stochastic tsunami scenario generation techniques, identify and partially correct their biases, and provide better justification for their use in applications.