Analyse et traitement de la matrice de covariance de données enregistrées sur des réseaux de stations sismiques

Green's function estimation from ambient seismic noise relies on the strong hypothesis that noise seismic sources are evenly distributed in the medium. Yet, observations of seismic data show that the noise sources do not provide such good conditions in real cases. Strongly coherent seismic sources or directional noise seismic sources may exist, and are harmful to the application of this in ambient seismic imaging. Several signal processing techniques are nowadays routinely applied to individual seismograms in frequency and temporal domain in order to improve the quality of reconstruction of the Green's function. The present work takes place in this context. Our approach is inspired by array-processing techniques, and is particularly focused on the covariance matrix of data recorded on seismic arrays. We show that the eigenstructure of this matrix provides crucial information about the seismic wavefield degree of coherence, as a function of time and frequency. This information is important because it allows to identify the time and frequency zones where the Green's function quality is ensured. An original array-processing technique is finally proposed, which consider the equalization of the covariance matrix eigenvalues, in order to attenuate the wavefield anisotropy such as earthquake-related signals or directive noise sources. We interpret this last method as an extension of the spectral whitening technique widely used in seismology to the spatial dimension encoded by the covariance matrix. We also invoke the analogy with the time-reversal technique that have recently led to a class of passive inverse filtering techniques.