Stephane Drouet, Sebastien Chevrot, Fabrice Cotton, and Annie Souriau
Simultaneous inversion of source spectra, attenuation parameters, and site responses; application to the data of the French accelerometric network
Bulletin of the Seismological Society of America (February 2008), 98(1):198-219

Abstract:
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 (super -gamma ) , gamma being constant, and a frequency-dependent quality factor of the form Q = Q ₀ Xf (super alpha ) . 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 Q ₀ values (322 and 376 for the Alps and the Pyrenees, respectively) with regional variations for alpha (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 log ₁₀ (f _c ) = 1.72-0.32XM _w . Stress drops range from 10 ⁵ to 10 ⁷ 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.