An Explicit Formulation for the Logic-Tree Representation of Epistemic Uncertainties in PSHA

Abstract In the recent probabilistic seismic hazard analysis (PSHA), the logic tree approach has been commonly adopted to represent epistemic uncertainties the PSHA inputs. While several studies have explored fundamental principles behind constructing logic trees, none have explicitly detailed the calculation of the weight and hazard at each end branch, particularly when multiple sources are combined to contribute to the hazard at a site. This study addresses this gap by introducing a clear and explicit expression for calculating branch weights and the corresponding seismic hazard at a given site.