Resampling methods for evaluating the uncertainty of the nonparametric magnitude distribution estimation in the Probabilistic Seismic Hazard Analysis |
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| Authors: | Beata Orlecka-Sikora |
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| Institution: | aDepartment of Geophysics, Faculty of Geology, Geophysics and Environmental Protection, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland |
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| Abstract: | The cumulative distribution function (CDF) of magnitude of seismic events is one of the most important probabilistic characteristics in Probabilistic Seismic Hazard Analysis (PSHA). The magnitude distribution of mining induced seismicity is complex. Therefore, it is estimated using kernel nonparametric estimators. Because of its model-free character the nonparametric approach cannot, however, provide confidence interval estimates for CDF using the classical methods of mathematical statistics.To assess errors in the seismic events magnitude estimation, and thereby in the seismic hazard parameters evaluation in the nonparametric approach, we propose the use of the resampling methods. Resampling techniques applied to a one dataset provide many replicas of this sample, which preserve its probabilistic properties. In order to estimate the confidence intervals for the CDF of magnitude, we have developed an algorithm based on the bias corrected and accelerated method (BCa method). This procedure uses the smoothed bootstrap and second-order bootstrap samples. We refer to this algorithm as the iterated BCa method. The algorithm performance is illustrated through the analysis of Monte Carlo simulated seismic event catalogues and actual data from an underground copper mine in the Legnica–Głogów Copper District in Poland.The studies show that the iterated BCa technique provides satisfactory results regardless of the sample size and actual shape of the magnitude distribution. |
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| Keywords: | Magnitude cumulative distribution function Resampling methods Bootstrap Jackknife Seismic hazard |
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