Bayesian Estimation of the Maximum Magnitude m max Based on the Extreme Value Distribution for Probabilistic Seismic Haz
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Pure and Applied Geophysics
Bayesian Estimation of the Maximum Magnitude mmax Based on the Extreme Value Distribution for Probabilistic Seismic Hazard Analyses IRMELA ZENTNER,1
GABRIELE AMERI,2 and EMMANUEL VIALLET3
Abstract—This work proposes a new approach, based on Bayesian updating and extreme value statistics to determine the maximum magnitudes for truncated magnitude-frequency distributions such as the Gutenberg Richter model in the framework of Probabilistic Seismic Hazard Analyses. Only the maximum observed magnitude and the associated completeness period are required so that the approach is easy to implement and there is no need to determine and use the completeness periods for smaller events. The choice of maximum magnitudes can have a major impact on hazard curves when long return periods as required for safety analysis of nuclear power plants are considered. Here, not only a singular value but a probability distribution accounting for prior information, data and uncertainty is provided. Moreover, uncertainties related to magnitude frequency distributions, including the uncertainty related to the maximum observed magnitude are discussed and accounted for. The accuracy of the approach is validated based on simulated catalogues with various parameter values. Then the approach is applied to French data for a specific region characterized by high-seismic activity in order to determine the maximum magnitude distribution and to compare the results to other approaches. Keywords: Maximum magnitude, extreme value, bayesian updating, simulation, earthquake catalogue, uncertainty.
1. Introduction Probabilistic Seismic Hazard Assessment (PSHA) has the goal to evaluate annual frequencies of exceeding a given ground motion intensity measure. For this purpose, it is necessary to describe occurrence rates of earthquakes and the distribution of their magnitudes. In the classical PSHA (Cornell 1968), the hazard integral is evaluated for magnitudes in the
1
EDF R&D Lab Paris Saclay, Palaiseau, France. E-mail: [email protected] 2 SEISTER, Aubagne, France. 3 EDF DIPNN Technical Direction, Lyon, France.
range mmin andmmax , where mmax is the maximum magnitude that can be expected for a given area and mmin is the minimum magnitude of relevance for engineering structures (Bommer and Crowley 2017). The most popular distribution of magnitudes frequencies is the Gutenberg-Richter (Gutenberg and Richter 1944) truncated exponential distribution. Numerous studies and applications showed that the GR distribution is a good choice to model the distribution of magnitudes over a wide magnitudes range. The maximum magnitude mmax is then the upper value used to truncate the GR model. The justification of the choice of mmax only from physics or simple statistics is not straightforward. The largest observed earthquake in a specified area provides an unarguable lower bound on mmax in the area. However it is difficult to estimate the upper bound of the mmax because the physical reasons why earthquake rupture stops are still poorly un
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