Application of Generalized Pareto Distribution to Constrain Uncertainty in Peak Ground Accelerations

Abstract

Abstract Probabilistic seismic hazard analysis (PSHA) has become standard practice to characterize earthquake ground-motion hazard and to develop ground-motion inputs for seismic design and performance analyses. One emerging issue is the application of PSHA at low annual exceedance probabilities, particularly the characterization of scatter (aleatory variability) in the recorded ground-motion parameters, including peak ground acceleration (PGA). Lognormal distributions are commonly used to model ground-motion variability. However, a lognormal distribution, when unbounded, can yield a nonzero probability for unrealistically high ground-motion values. In this article, we evaluate the appropriateness of the lognormal assumption for low-probability ground motions by examining the tail behavior of the PGA recordings from the Pacific Earthquake Engineering Research–Next Generation Attenuation of Ground Motions (PEER NGA) database and the PGA residuals using Abrahamson–Silva NGA ground-motion relations. Our analyses show that the tail portion of the PGA and the residual data do not always follow a lognormal distribution and are instead often better characterized by the generalized Pareto distribution (GPD). We propose using a composite distribution model (CDM) that consists of a lognormal distribution (up to a threshold value of ground-motion residual) combined with GPD for the tail region. We demonstrate implications of the CDM in PSHA using a simple example and GPD parameters derived from the residual fit. Our results show that, at low annual exceedance probabilities, the CDM yields considerably lower PGA values than the unbounded lognormal distribution. It also produces smoother hazard curves than truncated lognormal distributions because the PGA increases asymptotically with a decreasing probability level. The presented approach is readily adapted to spectral accelerations and other ground-motion parameters.