Application of generalized Pareto distribution for modeling aleatory variability of ground motion

Meng Zhang and Hua Pan ()
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Meng Zhang: China Earthquake Administration
Hua Pan: China Earthquake Administration

Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, 2021, vol. 108, issue 3, No 27, 2989 pages

Abstract: Abstract The lognormal distribution is commonly used to characterize the aleatory variability of ground-motion prediction equations (GMPEs) in probabilistic seismic hazard analysis (PSHA). However, this approach often leads to results without actual physical meaning at low exceedance probabilities. In this paper, we discuss how to calculate PSHA with a low exceedance probability. Peak ground acceleration records from the NGA-West2 database and 15,493 residuals calculated by Campbell-Bozorgnia using the NGA-West2 GMPE were applied to analyze the tail shape of the residuals. The results showed that the generalized Pareto distribution (GPD) captured the characteristics of residuals in the tail better than the lognormal distribution. Further study showed that the shapes of the tails of the distributions of residuals with different magnitudes varied significantly due to the heteroscedasticity of the magnitude; the distribution of residuals with larger magnitudes had a smaller upper limit on the right side. Moreover, the residuals of the three magnitude ranges given in this study were more consistent with the GPD of different parameters at the tail than the lognormal distribution and the GPD fitted by all the residuals, leading to a bounded PSHA hazard curve. Therefore, the lognormal distribution is more representative up to a determined threshold, and the GPD fitted to the residuals of three ranges of magnitude better characterizes the tail for PSHA calculation.

Keywords: Probabilistic seismic hazard analysis; Ground-motion prediction equation; Generalized Pareto distribution; Peak ground acceleration (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11069-021-04809-3

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