Emergence of Acoustic Green's Functions from Time Averages of Ambient Noise

The emergence of deterministic Green's functions from cross-correlation of ambient noise is the physical basis for a number of passive remote sensing techniques. The data-accumulation time necessary for the Green's function emergence is of critical significance for the feasibility and implementation of the passive techniques. This paper re-examines calculation of the necessary data-accumulation times. Previously published estimates are extended to more general ambient noise fields and source-receiver geometries. The emergence time calculation is performed for arbitrary anisotropy of the noise field generated by random acoustic noise sources located on a surface or on a curve. The results apply to a general case of an inhomogeneous, moving or motionless medium with time-independent parameters. It is shown that in certain situations the emergence time estimates are influenced by the geometry (dimensionality) of the noise sources' layout, and not necessarily by the dimensionality of the propagation medium. A simpler technique using basic statistical principles is suggested for calculating the emergence time under rather general assumptions.