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

Author

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  • Meng Zhang

    (China Earthquake Administration)

  • Hua Pan

    (China Earthquake Administration)

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.

Suggested Citation

  • Meng Zhang & Hua Pan, 2021. "Application of generalized Pareto distribution for modeling aleatory variability of ground motion," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 108(3), pages 2971-2989, September.
    • Handle: RePEc:spr:nathaz:v:108:y:2021:i:3:d:10.1007_s11069-021-04809-3
    DOI: 10.1007/s11069-021-04809-3
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    References listed on IDEAS

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    1. V. A. Pavlenko, 2017. "Estimation of the upper bound of seismic hazard curve by using the generalised extreme value distribution," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 89(1), pages 19-33, October.
    2. V. Pavlenko, 2015. "Effect of alternative distributions of ground motion variability on results of probabilistic seismic hazard analysis," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 78(3), pages 1917-1930, September.
    3. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
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