Natural Hazards

, Volume 78, Issue 3, pp 1917–1930

# Effect of alternative distributions of ground motion variability on results of probabilistic seismic hazard analysis

Original Paper

## Abstract

Probabilistic seismic hazard analysis (PSHA) is a regularly applied practice that precedes the construction of important engineering structures. The Cornell–McGuire procedure is the most frequently applied method of PSHA. This paper examines the fundamental assumption of the Cornell–McGuire procedure for PSHA, namely the log-normal distribution of the residuals of the ground motion parameters. Although the assumption of log-normality is standard, it has not been rigorously tested. Moreover, the application of the unbounded log-normal distribution for the calculation of the hazard curves results in nonzero probabilities of the exceedance of physically unrealistic amplitudes of ground motion parameters. In this study, the distribution of the residuals of the logarithm of peak ground acceleration is investigated, using the database of the strong-motion seismograph networks of Japan and the ground motion prediction equation of Zhao and co-authors. The distribution of residuals is modelled by a number of probability distributions, and the one parametric law that approximates the distribution most precisely is chosen by the statistical criteria. The results of the analysis show that the most accurate approximation is achieved with the generalized extreme value distribution for a central part of a distribution and the generalized Pareto distribution for its upper tail. The effect of replacing a log-normal distribution in the main equation of the Cornell–McGuire method is demonstrated by the calculation of hazard curves for a simple hypothetical example. These hazard curves differ significantly from one another, especially at low annual exceedance probabilities.

## Keywords

Ground motion variability Probabilistic seismic hazard analysis Hazard curve Ground motion prediction equation Peak ground acceleration

## Notes

### Acknowledgments

I would like to express my appreciation to Professor Andrzej Kijko for formulating the problem, guidance during this study, the review of this paper, and the valuable comments that helped to significantly improve its quality. I would like to thank two anonymous reviewers for their valuable comments and suggestions that allowed to make this paper even better. I am grateful to the K-NET and KiK-net strong-motion seismograph networks of Japan for seismic ground motion records (available online at http://www.kyoshin.bosai.go.jp).

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