Modelling peak accelerations from earthquakes

Dupuis, Debbie J.; Flemming, Joanna Mills

doi:10.1002/eqe.565

Cited by 6 publications

(9 citation statements)

References 12 publications

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“…The results of the analysis indicate that the best approximation for the distribution of residuals was obtained with the GEVD. This result is consistent with the conclusions of Dupuis and Flemming (2006) and Raschke (2013). The "peaks Hazard curves calculated using different parametric distributions over threshold" method was applied in an attempt to model an upper tail of the distribution of residuals more precisely.…”

Section: Resultssupporting

confidence: 93%

“…It is important to note that a similar conclusion was reached in Dupuis and Flemming (2006) from theoretical considerations. In Dupuis and Flemming (2006) the regression analysis was performed using both the GEVD and the normal distribution as a model for the distribution of residuals, it was demonstrated that a better fit to the data and in turn more accurate acceleration estimates are obtained with the use of the GEVD. A similar conclusion in regards of the distribution of the ground motion residuals was also reached in Raschke (2013).…”

Section: Resultssupporting

confidence: 75%

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

Pavlenko

2015

Nat Hazards

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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.

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Section: Resultssupporting

confidence: 93%

Section: Resultssupporting

confidence: 75%

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

Pavlenko

2015

Nat Hazards

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“…Besides, Dupuis and Flemming (2006) have estimated a GMR with GED for the residuals of PGA with extreme value index γ≈0, which also indicates the Gumbel domain.…”

Section: The Distribution Of the Maximum Of A Random Sequencementioning

confidence: 99%

“…If the KS test is applied to estimated parameters, then the test does not work (Raschke 2009). If there is not an applicable goodness-of-fit test for the distribution type used, then a quantile plot (q-q plot) can be used for a visual, qualitative test as done by Dupuis and Flemming (2006) for residuals with a mixed, non-normal distribution. However, there is no objective criterion for rejecting the distribution hypothesis in this case.…”

Section: The Test Of the Distribution Assumptionmentioning

confidence: 99%

Statistical modeling of ground motion relations for seismic hazard analysis

Raschke¹

2013

J Seismol

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We introduce a new approach for ground motion relations (GMR) in the probabilistic seismic hazard analysis (PSHA), being influenced by the extreme value theory of mathematical statistics. Therein, we understand a GMR as a random function. We derive mathematically the principle of area-equivalence; wherein two alternative GMRs have an equivalent influence on the hazard if these GMRs have equivalent area functions. This includes local biases. An interpretation of the difference between these GMRs (an actual and a modeled one) as a random component leads to a general overestimation of residual variance and hazard. Beside this, we discuss important aspects of classical approaches and discover discrepancies with the state of the art of stochastics and statistics (model selection and significance, test of distribution assumptions, extreme value statistics). We criticize especially the assumption of logarithmic normally distributed residuals of maxima like the peak ground acceleration (PGA). The natural distribution of its individual random component (equivalent to exp(ε 0 ) of Joyner and Boore 1993) is the generalized extreme value. We show by numerical researches that the actual distribution can be hidden and a wrong distribution assumption can influence the PSHA negatively as the negligence of area equivalence does. Finally, we suggest an estimation concept for GMRs of PSHA with a regression-free variance estimation of the individual random component. We demonstrate the advantages of event-specific GMRs by analyzing data sets from the PEER strong motion database and estimate event-specific GMRs. Therein, the majority of the best models base on an anisotropic point source approach. The residual variance of logarithmized PGA is significantly smaller than in previous models. We validate the estimations for the event with the largest sample by empirical area functions, which indicate the appropriate modeling of the GMR by an anisotropic point source model. The constructed distances like the Joyner-Boore distance do not work well for event-specific GMRs. We discover also a strong relation between magnitude and the squared expectation of the PGAs being integrated in the geo-space for the event-specific GMRs. One of our secondary contributions is the simple modeling of anisotropy for a point source model. ground motion relation, probabilistic seismic hazard analysis, area-equivalence, regression analysis, extreme value statistics, model selection, statistical test, random function * *

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“…Accordingly, Lavallée and Archuleta (2005) have investigated the distribution of the absolute values of PGA obtained from the strong motion records of the 1999 Chi-Chi earthquake and have suggested to model it by the Lévy distribution. Dupuis and Flemming (2006) have indicated that the distribution of residuals of PGA should theoretically correspond to the generalised extreme value distribution (GEVD). Dupuis and Flemming (2006) have performed regression analysis under assumption of the log-normal distribution of residuals, as well as under assumption of the residuals being distributed according to the GEVD.…”

Section: Introductionmentioning

confidence: 99%

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

Pavlenko

2017

Nat Hazards

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The problem considered in this study is that of unrealistic ground motion estimates, which arise in the Cornell-McGuire method when the seismic hazard curve is calculated for extremely low annual probabilities of exceedance. This problem stems from using the normal distribution in the modelling of the variability of the logarithm of ground motion parameters. In this study, the database of the strong-motion seismograph networks of Japan was used to examine the distribution of the logarithm of peak ground acceleration (PGA). The normal distribution and the generalised extreme value distribution (GEVD) models were considered in the analysis, with the preferred model being selected based on statistical criteria. The results of the analysis demonstrated the superiority of the GEVD in the vast majority of considered examples. The estimates of the shape parameter of the GEVD were negative in every considered example, indicating the presence of a finite upper bound of PGA. Therefore, the GEVD provides a model that is more realistic for the scatter of the logarithm of PGA, and the application of this model leads to a bounded seismic hazard curve.

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Modelling peak accelerations from earthquakes

Cited by 6 publications

References 12 publications

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

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

Statistical modeling of ground motion relations for seismic hazard analysis

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

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