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

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 non-zero 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.

Estimation of the upper bound of seismic hazard curve by using the generalised extreme value distribution

“…Although there is no obvious trend, all the estimates of ξ were negative, which confirms the convergence of data to the bounded Weibull extreme value distribution. Similar results were obtained by Huyse et al (2010) and Pavlenko (2015).…”

“…Huyse et al (2010) applied the peaks over threshold method to analyse both the raw PGA data and the logarithmic residuals of PGA, and concluded that the generalised Pareto distribution (GPD), with the negative shape parameter, provided a model that was more accurate for the tail fractions of both the studied datasets. Similar results were obtained by Pavlenko (2015), who found that the GEVD was a more appropriate model for logarithmic residuals of PGA.…”

Ranking and Selection of Earthquake Ground-Motion Models Using the Stochastic Area Metric

“…Some tests, such as the LLH test, rely on this assumption. However, the assumption of lognormally distributed residuals has become a de-facto standard and, as a result, usually is not tested routinely for new datasets, but is accepted as a given (Pavlenko, 2015;Raschke, 2013).…”

A novel model and estimation method for the individual random component of earthquake ground-motion relations

“…The variance of the random component is equal to the residual variance of the regression analysis. However, arguments have been presented against the assumption of the log-normal distribution for the individual random component ε a (Dupuis and Flemming, 2006;Raschke, 2013a;Pavlenko, 2015). Furthermore, the residual variance is not an appropriate estimator for V(ε) because of the principal of area equivalence, as was revealed by Raschke (2013a).…”