Spectral models for ground motion prediction in the L'Aquila region (central Italy): evidence for stress-drop dependence on magnitude and depth

In this study we derive a spectral model describing the source, propagation and site characteristics of S waves recorded in central Italy. To this end, we compile and analyse a high-quality data set composed of more than 9000 acceleration and velocity waveforms in the local magnitude (M l ) range 3.0-5.8 recorded at epicentral distances smaller than 120 km. The data set spans the time period from 2008 January 1 to 2013 May 31, and includes also the 2009 L'Aquila (moment magnitude M w 6.1, M l = 5.8) sequence. This data set is suitable for the application of data-driven approaches to derive the empirical functions for source, attenuation and site terms. Therefore, we apply a non-parametric inversion scheme to the acceleration Fourier spectra of the S waves of 261 earthquakes recorded at 129 stations. In a second step, with the aim of defining spectral models suitable for the implementation in numerical simulation codes, we represent the obtained non-parametric source and propagation terms by fitting standard parametric models. The frequency-dependent attenuation with distance r shows a complex trend that we parametrize in terms of geometrical spreading, anelastic attenuation and highfrequency decay parameter k. The geometrical spreading term is described by a piecewise linear model with crossover distances at 10 and 70 km: in the first segment, the spectral ordinates decay as r -1.01 while in the second as r -1.68 . Beyond 70 km, the attenuation decreases and the spectral amplitude attenuate as r -0.64 . The quality factor Q(f ) and the high-frequency attenuation parameter k, are Q( f ) = 290 f 0.16 and k = 0.012 s, respectively, the latter being applied only for frequencies higher than 10 Hz. The source spectra are well described by 2 models, from which seismic moment and stress drops of 231 earthquakes are estimated. We calibrate a new regional relationship between seismic moment and local magnitude that improves the existing ones and extends the validity range to 3.0-5.8. We find a significant stress drop increase with seismic moment for events with M w larger than 3.75, with so-called scaling parameter close to 1.5. We also observe that the overall offset of the stress-drop scaling is controlled by earthquake depth. We evaluate the performance of the proposed parametric models through the residual analysis of the Fourier spectra in the frequency range 0.5-25 Hz. The results show that the considered stress-drop scaling with magnitude and depth reduces, on average, the standard deviation by 18 per cent with respect to a constant stress-drop model. The overall quality of fit (standard deviation between 0.20 and 0.27, in the frequency range 1-20 Hz) indicates that the spectral model calibrated in this study can be used to predict ground motion in the L'Aquila region.