Spatial coherence and cross correlation of three-dimensional ambient noise fields in the ocean

Ambient acoustic noise fields in the ocean are generally three dimensional in that they exhibit vertical and horizontal directivity. A model of spatially homogeneous noise is introduced in which the directionality is treated as separable, that is, the overall directionality of the field is the product of the individual directivities in the horizontal and vertical. A uni-modal von Mises circular distribution from directional statistics is taken to represent the noise in the horizontal, whilst the vertical component is consistent with a surface distribution of vertical dipoles. An analysis of the coherence and cross correlation of the noise at two horizontally aligned sensors is developed. The coherence function involves a single integral over finite limits, whilst the cross-correlation function, derived on the assumption that the noise has been pre-whitened, is given by an integral with limits that depend on the correlation delay time. Although the cross-correlation function does not exhibit delta functions that could be identified with the Green's function for propagation between the two sensors in the field, it does drop abruptly to zero at numerical time delays equal to the travel time between the sensors. Hence the noise could be used to recover the sound speed in the medium.