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Green's functions (GFs) of surface wave propagation between two receivers can be estimated from the cross-correlation of ambient noise under the assumption of diffuse wavefields or energy equipartitioning. Interferometric GF reconstruction is generally incomplete, however, because the distribution of noise sources is neither isotropic nor stationary and the wavefields considered in the cross-correlation are generally non-diffuse. Furthermore, medium complexity can affect the empirical Green's function (EGF) from the cross-correlation if noise sources are all far away (i.e. approximately plane-wave sources), which makes the problem non-linear. We analyse the effect of uneven ambient noise distribution and medium heterogeneity and azimuthal anisotropy on phase velocities measured from EGFs with an asymptotic plane wave (far-field) approximation (which underlies most constructions of phase velocity maps). Phase velocity bias due to uneven noise distribution can be determined (and corrected) if the noise energy distribution and the velocity model are known. We estimate the (normalized) azimuthal distribution of ambient noise energy directly from the cross-correlation functions obtained through ambient noise interferometry. The (smaller, second order) bias due to non-linearity can be reduced iteratively, for instance by using the tomographic model that results from the inversion of uncorrected data. We illustrate our method for noise energy estimation, phase velocity bias suppression, and ambient noise tomography (including azimuthal anisotropy) with data from a seismic array (26 stations) in SE Tibet. We show that the phase velocity bias due to uneven noise energy distribution (and medium complexity) in SE Tibet has a small effect (<1 per cent) on the isotropic part phase velocities (for T = 10–30 s) and the azimuthal anisotropy obtained before and after bias correction shows very similar pattern and magnitude.
Yao et al. (Tue,) studied this question.