A κ Model for Mainland France


An important parameter for the characterization of strong ground motion at high-frequencies (>1 Hz) is kappa, κ, which models a linear decay of the acceleration spectrum, a(f), in log-linear space (i.e. a(f) = A 0 exp(− π κ f) for f > f E where f is frequency, f E is a low frequency limit and A 0 controls the amplitude of the spectrum). κ is a key input parameter in the stochastic method for the simulation of strong ground motion, which is particularly useful for areas with insufficient strong-motion data to enable the derivation of robust empirical ground motion prediction equations, such as mainland France. Numerous studies using strong-motion data from western North America (WNA) (an active tectonic region where surface rock is predominantly soft) and eastern North America (ENA) (a stable continental region where surface rock is predominantly very hard) have demonstrated that κ varies with region and surface geology, with WNA rock sites having a κ of about 0.04 s and ENA rock sites having a κ of about 0.006 s. Lower κs are one reason why high-frequency strong ground motions in stable regions are generally higher than in active regions for the same magnitude and distance. Few, if any, estimates of κs for French sites have been published. Therefore, the purpose of this study is to estimate κ using data recorded by the French national strong-motion network (RAP) for various sites in different regions of mainland France. For each record, a value of κ is estimated by following the procedure developed by Anderson and Hough (Bull Seismol Soc Am 74:1969–1993, 1984): this method is based on the analysis of the S-wave spectrum, which has to be performed manually, thus leading to some uncertainties. For the three French regions where most records are available (the Pyrenees, the Alps and the Côtes-d’Azur), a regional κ model is developed using weighted regression on the local geology (soil or rock) and source-to-site distance. It is found that the studied regions have a mean κ between the values found for WNA and ENA. For example, for the Alps region a κ value of 0.0254 s is found for rock sites, an estimate reasonably consistent with previous studies.

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This study was funded by BRGM research and public service projects and a grant from the Réseau Accélérometrique Permanent (RAP) of France. The strong-motion networks in France are operated by various organizations (see the RAP website), under the aegis of the RAP. The RAP data centre is based at Laboratoire de Géophysique Interne et de Tectonophysique, Grenoble. We are very grateful to the personnel of these organizations for operating the stations and providing us with the data, without which this study would have been impossible. Finally, we thank Stéphane Drouet, Glenn Biasi and David Boore for careful and detailed reviews of earlier versions of this article and Stéphane Drouet for his GMT script to draw maps of epicentral and station locations and travel paths.

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Correspondence to John Douglas.

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John Douglas is currently on teaching leave at Earthquake Engineering Research Centre, University of Iceland, Austurvegur 2A, 800 Selfoss, Iceland.

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Douglas, J., Gehl, P., Bonilla, L.F. et al. A κ Model for Mainland France. Pure Appl. Geophys. 167, 1303–1315 (2010). https://doi.org/10.1007/s00024-010-0146-5

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  • Strong-motion data
  • kappa
  • high-frequency decay
  • France
  • RAP
  • near-surface attenuation