Theory of the directionality and spatial coherence of wind-driven ambient noise in a deep ocean with attenuation

Acoustic attenuation in seawater usually has little effect on the spatial statistics of ambient noise in the ocean. This expectation does not hold, however, at higher frequencies, above 10 kHz, and extreme depths, in excess of 6 km, an operating regime that is within the capabilities of the most recently developed acoustic instrument platforms. To quantify the effects of attenuation, theoretical models for the vertical directionality and the spatial coherence of wind-generated ambient noise are developed in this paper, based on a uniform distribution of surface sources above a semi-infinite, homogeneous ocean. Since there are no bottom reflections, all the noise is downward traveling; and the angular width of the directional density function becomes progressively narrower with increasing frequency because sound from the more distant sources experiences greater attenuation than acoustic arrivals from overhead. This narrowing of the noise lobe modifies the spatial coherence, shifting the zeros in the horizontal (vertical) coherence function to higher (lower) frequencies. In addition, the attenuation modifies the amplitudes of the higher-order oscillations in the horizontal and vertical coherence functions, tending to suppress the former and enhance the latter. These effects are large enough to be detectable with the latest deep-diving sensor technology.