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Simultaneous Inversion of Source Spectra, Attenuation Parameters, and Site Responses: Application to the Data of the French Accelerometric Network

Laboratoire de Dynamique Terrestre et Planétaire, Observatoire Midi-Pyrénées, 14, Avenue Edouard Belin, 31400 Toulouse, France

Fabrice Cotton

Laboratoire de Géophysique Interne et Tectonophysique, Observatoire de Grenoble, Université Joseph Fourier, CNRS, BP 53X, 38041 Grenoble Cedex, France

Annie Souriau

Laboratoire de Dynamique Terrestre et Planétaire, Observatoire Midi-Pyrénées, 14, Avenue Edouard Belin, 31400 Toulouse, France

^* Present address: Institute of Engineering Seismology and Earthquake Engineering, 46 Georgikis Scholis Str., Thessaloniki, P.O. Box 53, GR-55102 Finikas, Thessaloniki, Greece.

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^-, being constant, and a frequency-dependent quality factor of the form Q=Q₀xf. 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 (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(f_c)=1.72-0.32xM_w. Stress drops range from 10⁵ to 10⁷ 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.

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