As a complement to experimental efforts in seismics and acoustics to infer geo-acoustic properties of the propagation environment from the second order statistics of ambient noise measurements, a set of exact, explicit, closed form expressions for the cross-spectral density and spatial coherence of diffuse random wave fields is presented. Taken together, the expressions are well suited for modeling broadband, diffuse wave coherence in realistic scenarios involving directive, ambient noise from local (i.e., volume) and distant (i.e., plane wave) source features in an open, dispersive, attenuating medium.
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