Estimation of the Mean Free Path using Cross-Correlations in the Seismic Coda

Abstract:

We present recent results concerning the extraction of Green’s functions from coda waves.

Campillo and Paul 2003 used earthquakes codas and found that the causal and anticausal parts of the cross-correlation are asymmetrical for some stations, depending on the earthquake source region.

The lapse time in the coda window is a key parameter to understand causal to anticausal amplitude ratio. We show that this ratio result from the competition between the source signature (non-symmetric cross-correlations when the distribution of sources is non-isotropic around the receivers) and the scattering processes which tend to restore the time symmetry of the correlations.

The theoretical analysis is derived from wave propagation theory for single scattering and multiple scattering as initiated by Roux 2005. We propose to use the temporal evolution of cross-correlation function amplitude in coda waves to estimate the value of the mean free path in the propagation medium.

The equipartition of the energy is clearly observed in the numerical simulations conducted in a two-dimensional acoustic medium. The cross-correlations between the distinct time windows in synthetic coda records at two points are measured for a set of events for which we obtain a good estimate of the medium mean free path.

We perform the same analysis on a set of icequakes recorded at Mount Erebus. The correlations averaged over sources and time exhibit a temporal evolution that obeys to convergence patterns similar to those observed in numerical studies.