Evaluation of PSHA logic trees considering the Pólya distribution to model the spatial correlation between observation sites
摘要
Probabilistic Seismic Hazard Analysis (PSHA) is the standard methodology for estimating the likelihood of exceeding ground-motion intensity thresholds at a given site, accounting for both aleatory and epistemic uncertainties, yet remains subject to criticism due to the high uncertainty and the limited observational data for validation. This study proposes a novel framework for the direct evaluation and Bayesian updating of PSHA logic-tree weights using observed ground-motion records, explicitly addressing spatial correlation among multiple observation sites. The methodology combines event-based simulations of branch-consistent ground-motion fields, site-effect corrections, and operational-period modeling to ensure comparability with empirical data. Correlated exceedance counts are modeled using the Pólya (negative binomial) distribution, which preserves the expected total number of exceedances of the classical Poisson reference while capturing the variance inflation induced by spatial dependence. At the same time, joint multi-IML updating employs a Bernstein copula to represent dependence across intensity measure levels. The framework is applied to a PSHA model for metropolitan France using a reference database spanning 1977–2020 and comprising EDF industrial sites and EPOS-France stations. Results confirm the adequacy of the Pólya distribution for correlated exceedance modeling, with spatial correlation observed consistently at monthly resolution. EDF sites provide nearly the same effective observation time as the full network due to their wide spatial distribution, while EPOS-France stations contribute limited additional statistical power due to site clustering. Bayesian updating of logic-tree branch weights improves model consistency, particularly when applied jointly across multiple IMLs. Results highlight systematic overestimation at low thresholds, and sensitivity analyses reveal that station operability uncertainties, while influential, cannot fully account for the discrepancy between predicted and observed exceedances. A fundamental contributing factor is that observations reflect a non-ergodic, site- and path-specific reality, whereas simulated fields are at best site-specific approximations—a mismatch inherent to current PSHA practice that sets an irreducible limit on model-data agreement. This correlation-aware, multi-IML evaluation framework enhances the statistical robustness of PSHA validation and provides a principled approach for data-informed logic-tree weighting, offering clear pathways for methodological refinement and regulatory application.