Frequency dependent Qα, and Qβ in the Umbria-Marche (Italy) region using a quadratic approximation of the coda-normalization method

The coda normalization method is one of the most used methods in the inference of attenuation parameters Q(alpha) and Q(beta) Since, in this method, the geometrical spreading exponent gamma is an unknown model parameter, the most part of studies assumes a fixed gamma, generally equal to 1. However gamma and Q could be also jointly inferred from the non-linear inversion of coda-normalized logarithms of amplitudes, but the trade-off between gamma and Q could give rise to unreasonable values of these parameters. To minimize the trade-off between gamma and Q, an inversion method based on a parabolic expression of the coda-normalization equation has been developed. The method has been applied to the waveforms recorded during the 1997 Umbria-Marche seismic crisis. The Akaike criterion has been used to compare results of the parabolic model with those of the linear model, corresponding to gamma = 1. A small deviation from the spherical geometrical spreading has been inferred, but this is accompanied by a significant variation of Q(alpha) and Q(beta) values. For almost all the considered stations, Q(alpha) smaller than Q(beta) has been inferred, confirming that seismic attenuation, in the Umbria-Marche region, is controlled by crustal pore fluids.