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Ground-motion prediction equations (GMPE) are essential in probabilisticseismic hazard studies for estimating the ground motions generated by theseismic sources. In low seismicity regions, only weak motions are available inthe lifetime of accelerometric networks, and the equations selected for theprobabilistic studies are usually models established from foreign data.Although most ground-motion prediction equations have been developed formagnitudes 5 and above, the minimum magnitude often used in probabilisticstudies in low seismicity regions is smaller. Desaggregations have shown that,at return periods of engineering interest, magnitudes lower than 5 can becontributing to the hazard. This paper presents the testing of several GMPEsselected in current international and national probabilistic projects againstweak motions recorded in France (191 recordings with source-site distances upto 300km, 3.8\leqMw\leq4.5). The method is based on the loglikelihood valueproposed by Scherbaum et al. (2009). The best fitting models (approximately2.5\leqLLH\leq3.5) over the whole frequency range are the Cauzzi and Faccioli(2008), Akkar and Bommer (2010) and Abrahamson and Silva (2008) models. Nosignificant regional variation of ground motions is highlighted, and themagnitude scaling could be predominant in the control of ground-motionamplitudes. Furthermore, we take advantage of a rich Japanese dataset to runtests on randomly selected low-magnitude subsets, and check that a dataset of~190 observations, same size as the French dataset, is large enough to obtainstable LLH estimates. Additionally we perform the tests against largermagnitudes (5-7) from the Japanese dataset. The ranking of models is partiallymodified, indicating a magnitude scaling effect for some of the models, andshowing that extrapolating testing results obtained from low magnitude rangesto higher magnitude ranges is not straightforward.

On the Testing of Ground--Motion Prediction Equations against Small--Magnitude Data