A Probabilistic Model for Annual Maximum Peak Ground Motion Based on Shifted Lognormal Distribution

Abstract

Continuous seismic hazard curves can be used to flexibly determine earthquake intensity with an arbitrary annual exceedance probability for probabilistic structural seismic design. To obtain an explicit expression of the continuous curve based on several given earthquake intensities corresponding to different hazard levels from probabilistic seismic hazard analysis (PSHA), a model of the annual maximum peak ground motion based on the Fréchet distribution has been widely adopted over the past decades. However, recent studies showed that the mathematical limitations of statistic estimation and poor performance in the upper tail region of the Fréchet model are unfavorable for use in reliability-based studies, particularly for vital structures. In this study, a new probabilistic model for the annual maximum peak ground motion is proposed based on a shifted lognormal distribution. The performance of the proposed model was statistically validated by investigating the global fitting effect, accuracy of the upper tail region, and appropriateness of the estimated statistics based on a long-term Japanese earthquake catalogue. The application of the proposed model to generate continuous seismic hazard curves by fitting different types of the analytical PSHA data is illustrated using two numerical examples.