Modeling Extreme Ground-Motion Intensities Using Extreme Value Theory
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Pure and Applied Geophysics
Modeling Extreme Ground-Motion Intensities Using Extreme Value Theory SHAHIN BORZOO,1 MORTEZA BASTAMI,1 Abstract—The current study attempted to determine the appropriate distribution of large ground-motion intensities using extreme value theory (EVT). In this regard, normal, lognormal and generalized extreme value (GEV) distributions were examined. The ground motions were extracted from the PEER NGA-West2 database and analyses were done on the three different categories of data. These categories were selected based on the block maxima method (BMM) and the following criteria: annual maxima, nearsource and far-source classification and ten selected earthquakes having the greatest number of records in the database. The loglikelihood, Akaike information criteria (AIC) and Bayesian information criteria (BIC) were used for all categories to investigate the results. The results revealed that the appropriate distribution of the annual maxima of PGA, PGV, PSA (T = 0.3 s) and PSA (T = 1 s) was the GEV distribution. In both the near-source and far-source data, the appropriate distribution of PGA and PSA in low periods was the GEV distribution. In the last category, the GEV distribution showed appropriate goodness of fit. In addition to the mentioned criteria, a ground motion model (GMM) was developed to evaluate the mentioned distributions. Accordingly, normal, lognormal and GEV distributions were used to develop three GMMs. The GMM coefficients were obtained using the maximum likelihood (ML) method, then the GMMs were evaluated using residual analysis. On average, the standard deviation and the root mean square error (RMSE) of residuals decreased 18% and 19%, respectively, in GMMs using the GEV distribution. Keywords: Extreme value theory (EVT), generalized extreme value (GEV) distribution, ground-motion model (GMM), block maxima method (BMM).
1. Introduction Developing an appropriate ground-motion model (GMM) for estimation of ground-motion intensity measures, peak ground acceleration (PGA), peak
1 International Institute of Earthquake Engineering and Seismology, Tehran, Iran. E-mail: [email protected]; [email protected] 2 Department of Statistics, Imam Khomeini International University, Qazvin, Iran. E-mail: [email protected]
and AFSHIN FALLAH2
ground velocity (PGV) and 5% damped pseudospectral acceleration (PSA) is essential for seismic hazard assessment. Large ground-motion intensities describe the tail behavior of their distributions. Since the probability of occurrence of large ground-motion intensities is low, a family of statistical distributions based on extreme value theory (EVT) can be applied (De Haan and Ferreira 2007). EVT is applicable for prediction of the return level and return period of extreme accelerations. Moreover, the statistical distributions of EVT families can be used instead of lognormal distributions to develop the GMM of extreme accelerations. This leads to changes in the functional form of GMMs. The low probability of occurrence and long return peri
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