Regressions over a data set of broadband seismograms are performed to quantify the attenuation of the ground motion in the Apennines (Italy), in the 0.25–5.0 Hz frequency band. The data set used in this article consists of over 6000 horizontal-component seismograms from 446 events, with magnitude ranging from Mw ≃ 2 to Mw = 6.0. Waveforms were collected during recent field experiments along the Apennines. Data from two MedNet broadband stations, located in central and southern Apennines, were also used.

Seismograms are bandpass-filtered around a set of sampling frequencies, and the logarithms of their peak values are written as  
\[\mathrm{AMP}(f,{\ }r)=\mathrm{EXC}(f,{\ }r_{\mathrm{ref}})+\mathrm{SITE}(f)+D(r,{\ }r_{\mathrm{ref}},{\ }f).\]
EXC(f, rref) is the excitation term for the ground motion at the hypocentral distance rref. SITE(f) represents the distortion of the seismic spectra induced by the shallow geology at the recording site. D(r, rref, f) includes the effects of the geometrical spreading, g(r), and of a frequency-dependent crustal attenuation Q. It is determined as a piecewise linear function, allowing to consider complex behavior of the regional attenuation.
A first estimate of D(r, rref, f) is obtained using a coda normalization technique (Aki, 1980; Frankel et al., 1990) and used as a starting model in the inversion of the peak values. Then, by trial and error, the empirical D(r, rref, f) is fitted using a trilinear geometrical spreading, with crossover distances at 30 and 80 km, and the crustal parameter  
\[Q(f)=130\left(\frac{f}{f_{\mathrm{ref}}}\right)^{0.10};{\ }f_{\mathrm{ref}}=1.0{\ }\mathrm{Hz}\]
These results suggest a low-Q crust in the entire Apennines in the 0.25–5.0 Hz range, implying that the seismic hazard in the region may be dominated by the local seismicity.

The final section is devoted to highlight the limitations of the formula proposed by Console et al. (1988) to estimate duration magnitudes Md in Italy.

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