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) = A0 exp(− πκf) for f > fE where f is frequency, fE is a low frequency limit and A0 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.

[1]  Luca Malagnini,et al.  Ground-Motion Scaling in the Western Alps , 2006 .

[2]  D. Giardini,et al.  Spectral Shear-Wave Ground-Motion Scaling in Switzerland , 2003 .

[3]  K. Campbell PREDICTION OF STRONG GROUND MOTION USING THE HYBRID EMPIRICAL METHOD AND ITS USE IN THE DEVELOPMENT OF GROUND-MOTION (ATTENUATION) RELATIONS IN EASTERN NORTH AMERICA , 2003 .

[4]  A. Papageorgiou,et al.  A specific barrier model for the quantitative description of inhomogeneous faulting and the prediction of strong ground motion. I. Description of the model , 1983 .

[5]  David M. Boore,et al.  Determination of Δσ and κ0 from response spectra of large earthquakes in Greece , 1998, Bulletin of the Seismological Society of America.

[6]  Philippe Guéguen,et al.  The French Accelerometric Network (RAP) and National Data Centre (RAP-NDC) , 2008 .

[7]  John G. Anderson,et al.  A MODEL FOR THE SHAPE OF THE FOURIER AMPLITUDE SPECTRUM OF ACCELERATION AT HIGH FREQUENCIES , 1984 .

[8]  Julian J. Bommer,et al.  Criteria for Selecting and Adjusting Ground-Motion Models for Specific Target Regions: Application to Central Europe and Rock Sites , 2006 .

[9]  J. Douglas,et al.  Making the most of available site information for empirical ground-motion prediction , 2009 .

[10]  T. Ohmachi,et al.  Ground Motion Characteristics Estimated from Spectral Ratio between Horizontal and Verticcl Components of Mietremors. , 1997 .

[11]  David M. Boore,et al.  SMSIM — Fortran Programs for Simulating Ground Motions from Earthquakes: Version 2.3 — A Revision of OFR 96–80–A , 2000 .

[12]  Michel Campillo,et al.  Frequency-dependent attenuation in the crust beneath Central France from Lg waves: Data analysis and numerical modeling , 1985 .

[13]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[14]  Stéphane Drouet,et al.  Simultaneous Inversion of Source Spectra, Attenuation Parameters, and Site Responses: Application to the Data of the French Accelerometric Network , 2008 .

[15]  Gail M. Atkinson,et al.  Earthquake Ground-Motion Prediction Equations for Eastern North America , 2006 .

[16]  Dino Bindi,et al.  Influence of Soil-Layer Properties on k Evaluation , 2004 .

[17]  Gail M. Atkinson,et al.  Ground-Motion Prediction Equations for Eastern North America from a Referenced Empirical Approach: Implications for Epistemic Uncertainty , 2008 .

[18]  N. Draper,et al.  Applied Regression Analysis: Draper/Applied Regression Analysis , 1998 .

[19]  M. Bouchon,et al.  Attenuation of crustal waves across the Alpine Range , 1993 .

[20]  D. Giardini,et al.  Predictive ground motion scaling in Switzerland: Best estimates and uncertainties , 2005 .

[21]  Frank Scherbaum,et al.  On the Discrepancy of Recent European Ground-Motion Observations and Predictions from Empirical Models: Analysis of KiK-net Accelerometric Data and Point-Sources Stochastic Simulations , 2008 .

[22]  R. Herrmann,et al.  Regional Ground-Motion Scaling in Central Europe , 2000 .

[23]  F. Cotton,et al.  Attenuation, Seismic Moments, and Site Effects for Weak-Motion Events: Application to the Pyrenees , 2005 .

[24]  Julian J. Bommer,et al.  The Influence of Magnitude Range on Empirical Ground-Motion Prediction , 2007 .

[25]  Chu-Chuan Peter Tsai,et al.  A Model for the High-Cut Process of Strong-Motion Accelerations in Terms of Distance, Magnitude, and Site Condition: An Example from the SMART 1 Array, Lotung, Taiwan , 2000 .

[26]  N. Draper,et al.  Applied Regression Analysis , 1967 .

[27]  John Douglas,et al.  GROUND-MOTION PREDICTION EQUATIONS FOR SOUTHERN SPAIN AND SOUTHERN NORWAY OBTAINED USING THE COMPOSITE MODEL PERSPECTIVE , 2006 .

[28]  L. M. Baker,et al.  Attenuation near Anza, California , 1988 .

[29]  Susan E. Hough,et al.  High-frequency spectra observed at Anza, California: Implications for Q structure , 1988 .