Probabilistic Seismic Hazard Analysis based on Probability Density Evolution Method

Probabilistic seismic hazard analysis (PSHA) is a widely used framework to assess the seismic hazard of an interested site. This framework contains uncertainties which can be categorized into the aleatory uncertainty and the epistemic uncertainty. Generally, the aleatory uncertainty is measured by the total probability theorem, and the epistemic uncertainty is quantified by the logic tree. Despite its wide usage, the framework, especially the uncertainty representation by the logic tree faces two controversies. The first controversy is how to determine the assigned weights of the logic tree objectively, and the second controversy is how to interpret the logic-tree output reasonably. To address the two controversies, a probability density evolution method (PDEM)-based PSHA method was proposed in this study from the prospective of uncertainty quantification and propagation. Different from the traditional PSHA procedure, this method quantifies the probability density functions (PDFs) of basic random variables from source rupture to site condition first, and then adopts the generalized F-Discrepancy method to divide the probability space of basic random variables as the representation point set. After that, each representation point produces a seismic hazard curve following the classical PSHA formula. Finally, the generalized density evolution equation (GDEE) was introduced to obtain the PDFs of seismic hazard curves. To illustrate the advantage of the proposed method, a hypothetic site in Shanghai was chosen as a demonstrative example to evaluate the PDFs of peak ground acceleration (PGA) under varying annual exceedance rate of seismic hazards. The investigation indicates that the proposed method can resolve the aforementioned controversies effectively, where the assigned weights of the logic tree can be well determined by the generalized F-Discrepancy method, and the GDEE can obtain the PDFs of seismic hazard curves without much difficulties.