We derive attenuation models, site response functions, and source parameters from small-magnitude events recorded at a regional scale. Our data set consists of 45 Pyrenean events with magnitude 2.7 to 5.4, recorded at distances from 15 to 200 km, for which about 600 displacement spectra could be computed.

We assume that the far-field displacement spectrum is the product of source, propagation, and site effects. S-wave displacement spectra are computed for accelerometric and velocimetric records using fast Fourier transforms by integration in the frequency domain for 0.5–15 Hz. Owing to the velocimeter response, the spectra may be unreliable below 1 Hz. A Brune-type source is assumed. Attenuation is decomposed into a frequency-dependent term (anelastic attenuation) and a non-frequency-dependent term (geometric attenuation). Adapting a process proposed by Scherbaum and Wyss (1990), we invert the data with a two-step regression. The first step recovers the geometric attenuation, the seismic moment, and a frequency-independent scaling factor. The second step gives the corner frequency, the anelastic attenuation, and a frequency-dependent site effect.

Our results show that the propagation term includes a slightly superspheric geometric attenuation that varies as 1/r1.2 and an anelastic attenuation that cannot be safely resolved with a linear approach. Computed moment magnitudes are generally 0.5 to 1 unit smaller than local magnitudes. Corner frequencies decrease linearly with magnitude, and the stress drops obtained appear to be nearly constant whatever the magnitude. Finally, robust site responses are computed that are compatible with those derived with other methods.

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