GNGTS 2013 - Atti del 32° Convegno Nazionale

phases. A signal like that is expected to have a low coherence. Seismic noise usually has the characteristics of a diffusive wavefield. The earthquake source radiates energy in a broad frequency range, therefore the wavelength of seismic waves involved in the scattering process cover a broad range of distance. Moreover, the scattering coefficient Qs has been observed dependent on the frequency in most of studied regions. For these reasons, a seismic wavefield may be diffusive at a given frequency but not at other frequencies. Higher frequency waves are expected to reach a diffusive regime before lower frequency waves. On the other hand, higher frequency signals attenuate faster than lower frequencies, therefore the late coda spectrum is dominated by low frequency energy. This means that diffusive wavefield of seismic waves may not be observed at any frequencies in the same time window along the late coda. Theoretical arguments about the multiple scattering imply the energy equipartition of a diffusive wavefield. In a diffusive regime the available energy is equally distributed, in fixed average amounts, among all the possible states (Sanchez-Sesma et al. , 2011). Another way to state the equipartition principle is that the phase space is uniformly populated (Weaver, 1982). Regarding seismic waves, the properties of conversion from P to S and from S to P are such that at the equilibrium (diffusive regime) the following energy relation holds (Papanicolaou et al. , 1996; Hennino et al. , 2001): (1) From this relation we expect S waves to be much more abundant than P waves along the earthquake coda. The few attempts to measure energy partition in the earthquake coda have given controversial results, mostly because separating P and S waves in a diffusive wavefield is impossible. The fact that most of seismic stations are installed at surface, or at most at few hundreds meters depth, and the strong heterogeneity that characterize the shallowest layers further contribute to the results uncertainty. In this paper we take advantage of a seismic array installed underground, at about 1.4 km depth, in the INFN Laboratory of Gran Sasso (Italy), from 2003 to 2010. The data from this array (named Underseis, hereafter UND) offer several advantages compared with typical surface single station recordings. First of all, the depth of 1.4 km makes negligible the contribution of surface waves for frequency greater than about 2 Hz. Second, the high number of stations in a small area permits to measure the spatial coherence of the wavefield. Third, the analysis by array methods gives an estimation of the propagation properties of the seismic wavefield. Fourth, site effects at the array stations are negligible because all stations are installed in the same geologic environment, constituted of hard rock limestone (Catalano et al. , 1984). Methods of analysis. The coherence of the seismic wavefield among the array stations is estimated by applying the equation: (2) (Foster and Guinzy, 1967), where i and j represent the stations, and c ij is the smoothed cross spectral matrix defined as: (3) 63 GNGTS 2013 S essione 1.1