Simultaneous Inversion of Source Spectra , Attenuation Parameters , and Site Responses 199

Displacement spectra of earthquakes recorded by the French accelerometric network at regional scale are modeled as the product of source, propagation (including geometric and anelastic attenuation), and site effects. We use an iterative Gauss–Newton inversion to solve the nonlinear problem and retrieve these different terms. This method is easy to implement because the partial derivatives of the amplitude spectrum with respect to the different parameters have simple analytic forms. After convergence, we linearize the problem around the solution to compute the correlation matrix, which allows us to identify the parameters which are poorly resolved. We analyze data from two tectonically active regions: the Alps and the Pyrenees. Eighty-three earthquakes with local magnitudes between 3.0 and 5.3 are analyzed, with epicentral distances in the range 15–200 km. S-wave displacement spectra are computed using a fast Fourier transform and integration in the 0.5–15-Hz frequency domain. We assume a Brune-type source, with a geometric attenuation of the form R γ , γ being constant, and a frequency-dependent quality factor of the form Q Q0 × fα. The results reveal that the attenuation parameters are correlated to each other and to the seismic moments. The two regions have different attenuation patterns. The geometrical spreading factor is equal to 1 for the Alps and 1.2 for the Pyrenees. The anelastic attenuation exhibits low Q0 values (322 and 376 for the Alps and the Pyrenees, respectively) with regional variations for α (0.21 in the Alps and 0.46 in the Pyrenees). Computed moment magnitudes are generally 0.5 unit smaller than local magnitudes, and the logarithms of the corner frequencies decrease linearly with magnitude according to log10 fc 1:72 0:32 ×Mw. Stress drops range from 10 to 10 Pa (i.e., 1–100 bars), with a slight dependence to magnitude (large stress drops for large magnitudes). Finally, robust site responses relative to an average rock-site response are derived, allowing us to identify good reference rock sites. Introduction In regions of low to moderate seismicity, as is the case in France, strong motion prediction is generally based upon extrapolation of weak-motion modeling, with extrapolations implying nonlinear processes (Bay et al., 2005). Attenuation and site responses are crucial parameters to perform such a prediction. Another important parameter that requires careful determination is the seismic moment. For historical and practical reasons, several magnitude scales are used to characterize small events, based on either record duration, S-wave amplitude, or on the coda decay. Moment magnitudes are now widely used for large events, but their determination for small events still leads to variable results. In a previous study (Drouet et al., 2005), we used a twostep linear inversion adapted from Scherbaum and Wyss (1990) to retrieve the source, propagation, and site terms. This method was applied to accelerometric data collected by the Réseau Accélérométrique Permanent (i.e., French Accelerometric Network, RAP) in the French Pyrenees. However, the linearization process required several simplifications in the formalization of the problem, in particular an anelastic attenuation that is not frequency dependent. In addition, this method did not resolve some parameters that are strongly correlated, such as attenuation parameters and corner frequencies, or attenuation parameters and seismic moments. Present address: Institute of Engineering Seismology and Earthquake Engineering, 46 Georgikis Scholis Str. , Thessaloniki, P.O. Box 53, GR-55102 Finikas, Thessaloniki, Greece. 198 Bulletin of the Seismological Society of America, Vol. 98, No. 1, pp. 198–219, February 2008, doi: 10.1785/0120060215