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-1) 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-1 = 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 high-frequency 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 omega(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 epsilon 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.