Source characterisation by mixing long-running tsunami wave numerical simulations and historical observations within a metamodel-aided ABC setting

摘要

Uncertainty related to the source parameters of earthquake can largely impact the tsunami-induced wave characteristics, especially in the case of near-field tsunami source. The combination of numerical simulations and historical eyewitness accounts can be used to better constrain those uncertainties. In the present study, we propose a Bayesian procedure to infer (i.e. learn) the probability distribution of the source parameters of the earthquake. The strategy is based on the combination of: (1) kriging-based metamodelling techniques to overcome the high computation time cost of the numerical simulator; and (2) Approximate Bayesian Computation (ABC) procedure to perform the Bayesian inference. The procedure is applied to the Ligurian (North West of Italy) 1887 tsunami case, for which tsunami-induced sea surface elevations at the coast have been reported at four locations, namely Marseille, Imperia, Diano-Marina and Genoa. The kriging metamodels are trained using only 300 long-running numerical simulations that were performed using the FUNWAVE-TVD code. Contrary to recent inversion exercises that can benefit from current modern observation networks (like tide gauges, sea bottom pressure gauges, GPS-mounted buoys), the case of historical tsunami like Liguria is complicated by the imprecision and scarcity of the observations: this is accounted for by conducting the combined ABC-kriging procedure a large number of times (i.e. 1000); each time a new set of observations being randomly generated to account for this observational error. The combined analysis of the inference results and of the observation uncertainty reveals that: (1) the coseismic slip is the most important source parameter with a very peaky density distribution around low values ranging from 0.3 to 0.6 m; (2) The fault width has a peaky density distribution around low values ranging from 10 to 12 km; (3) The rake and azimuth distribution only slightly deviate from the uniform prior, hence indicating a low influence of those parameters; (4) The bi-modal distribution of the dip is also evidenced.