Theoretical demonstrations of the Green’s function reconstruction from cross-correlations of the ambient noise rely on a strong hypothesis about the spatial homogeneity of the noise sources distribution. However, real seismic noise within the Earth is not homogeneously distributed. In particular, strongly coherent signals from earthquakes or localized noise sources might be harmful to the application of this method. Most of signal pre-processing techniques used to compensate for the wavefield inhomogeneity are based on temporal or spectral normalization of individual seismograms.
This thesis considers an approach based on simultaneous analysis of records from multiple sensors of a seismic array. We perform time-frequency analyses of the eigenvalue spectrum of the covariance matrix. In a case of a wavefield dominated by a single noise source, the rank of the array covariance matrix is very low. Consequently, its eigenvalue spectrum contains a single dominant value. In a case of a well distribution of uncorrelated noise sources, the matrix rank increases and the eigenvalue spectrum is much broader. Therefore, we use the width of the eigenvalue spectrum as a measure of the level of the wavefield spatial coherence. The results are interpreted within the random matrix theory.
With this approach, we can make distinctions between the signals generated by isolated deterministic sources and the "random" ambient noise. We design an algorithm that uses the distribution of the array covariance matrix eigenvalues to detect signals corresponding to coherent seismic events. We investigate the detection capacity of our methods at different scales and in different frequency ranges by applying it to the records of real networks, such as the seismic monitoring network operating on the Piton de la Fournaise volcano at La Réunion island composed of 21 receivers and with an aperture of ∼15 km, and the transportable component of the USArray composed of ∼100 receivers with ∼70 km inter-station spacing.
We also use this method to evaluate the effect of the energy normalization usually applied to single data prior to cross-correlation computation, that aims to improve the noise sources distribution. We show that many coherent events resist to this normalization, and are still harmful to ambient noise tomography. We finally propose a new way to improve the energy normalization of data. We modify the eigenvalue spectrum of the covariance matrix to mitigate the effect of strong events. We show that cross-correlation symmetry is improved with this new technique, that may allow to use noise cross-correlations in zones where the seismic activity usually prevents the use of ambient seismic noise in the analysis of the Earth’s crust.