Bayesian hierarchical modeling for probabilistic estimation of tsunami amplitude from far-field earthquake sources

Evaluation of tsunami disaster risk for a coastal region requires reliable estimation of tsunami hazard, for example, wave amplitude close to the shore. Observed tsunami data are scarce and have poor spatial coverage, and for this reason probabilistic tsunami hazard analysis (PTHA) traditionally relies on numerical simulation of “synthetic” tsunami generation and propagation toward the coast. Such an approach has been extensively studied in the past and it is widely recognized as an important disaster-risk mitigation tool. PTHA can not only provide less uncertain and spatially coherent hazard estimates in comparison with classical empirical data analysis which is restricted at the tide gauge stations, but also local inundation information. In this paper, we explore a purely statistical alternative to traditional PTHA for evaluation of tsunami amplitude hazard. Here, we use tide gauge measurements of tsunami amplitude along the western United States, specifically California and Oregon, and develop a spatial Bayesian hierarchical model (BHM) to assess tsunami hazard from far-field earthquake sources at various recurrence intervals. The configuration of our model incorporates latent Gaussian fields that utilize information on the distance between tide gauges as well as on the continental shelf width, that is, a covariate linked to potential dissipative effects on wave energy as the tsunami travels over shallow water. Through our BHM, we produce spatially continuous probabilistic maps of far-field tsunami hazard which can aid comprehensive tsunami disaster risk reduction and management.