Abstract
Two-point correlation functions of sufficiently diffuse wave fields generated by uncorrelated random sources are known to approximate deterministic Green's functions between the two points. This property is utilized increasingly for passive imaging and remote sensing of the environment. Here we show that the relation between the Green's functions and the noise cross-correlation function holds under much less restrictive conditions than previously thought. It can even hold when ambient noise sources have correlation ranges large compared to the wavelength. Admissible correlation ranges are limited from above by the size of the Fresnel zone at wave propagation between the points where noise cross correlation is evaluated.
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