Improving ambient noise correlation functions with an SVD-based Wiener filter

This paper introduces a technique for improving seismic noise correlation functions (NCF) via a singular value decomposition (SVD) of a list of NCF and the Wiener filter. SVD is commonly used for denoising signals by keeping singular values associated with signal while rejecting others. However, singular vectors associated with signal may contain non-coherent information, so the reconstructed matrix generally still contains random perturbations. The Wiener filter is a different approach where signals statistics are used to remove incoherent signal parts. We suggest to combine both these approaches by applying the Wiener filter to the singular vectors, in order to maximize coherency directly in the signal subspace prior to reconstructing the NCF matrix. This denoising method significantly enhances signal-to-noise ratio in NCF. Benefits are demonstrated to be both in the convergence towards the Green's function for tomography purposes, and in the time-resolution improvement for monitoring applications.