Reconstructing Green's function by correlation of the coda of the correlation (C3) of ambient seismic noise

Abstract

Analysis of long‐range correlation of the microseisms has been shown to provide reliable measurements of surface wave speeds that can be used for seismic imaging and monitoring. In the case of an even distribution of noise sources, it has been theoretically demonstrated that the correlation is the exact Green's function, including all types of waves. This method is limited in its application by the actual source distribution. In practice, the azimuthal distribution of energy flux of the noise is dominated by some particular directions resulting in a clear azimuthal dependence of the quality of the reconstruction of Rayleigh waves, with a poor reconstruction in some azimuths. To solve this problem, we use noise correlations measured on the entire network. We consider two stations, A and B, for which the Rayleigh waves could not be discerned in the in the correlation of continuous records of ambient noise. We computed all correlations between the station A (respectively B) and all the 150 other stations located at regional distances. Theoretically, these virtual seismograms contain direct waves and coda, although they are clearly contaminated by the influence of the imperfect ambient noise field and most are inadequate for direct analysis. We used these correlation functions as equivalents to seismograms produced by sources acting at the 150 stations locations and recorded in A (respectively B). We select time windows in those virtual seismograms that correspond to coda and compute correlations between them. This metacorrelation is found to exhibit the surface wave part of the Green's function that was not visible in the raw correlation of ambient noise. We illustrate the legitimacy of the reconstruction by comparison with raw noise correlations. This procedure can be used to assess seismic velocity between stations, even in presence of a directive and poorly oriented ambient noise. The result shows that in spite of the small signal‐to‐noise ratios often seen in correlations of ambient noise, especially at large lag time corresponding to coda, their codas are better equipartitioned than was the ambient noise upon which they were based. They are therefore presumably multiply scattered and contain information on both direct surface waves and also on more complex travel paths.