Use of arrays for acoustic transmission in a noisy ocean

Abstract

The ocean can be regarded as a horizontally stratified waveguide for the transmission of acoustical signals. The use of transducer arrays in the ocean presents special problems that are not present in an infinite homogeneous medium. For example, the signal at the receiver is the sum of many arrivals and each arrival is dispersive. In the normal mode formalism, the solution for a single frequency source can be expressed as the product of spectrum functions. Each spectral component is the horizontal component of wave number κ. The responses of waveguide transmission function, transmitting arrays, and receiving array can be expressed as functions of κ. Because of the horizontal stratification, horizontal and vertical arrays have quite different properties and are considered separately. The horizontal array is much less critical in design and operates more as it would in homogeneous space. The vertical array operates as a mode filter and is extremely sensitive to the depth and phase adjustment of the transducers. The signal output of the receiving array filter is the product of source, transmission, and receiver functions of κ. The maximum signal‐to‐noise ratio is obtained when the receiver array amplitude and phase response are the complex conjugate of the signal field at the receiver divided by the noise power. The condition is analogous to the matched filter condition of electrical circuit theory. The effect of fluctuations of the stratification of the ocean on sound transmission is included in an approximate treatment. The radiation in a mode is assumed to be trapped, and the radiation scattered by inhomogeneities can be ignored. The average signal transmission was found to depend on the correlation functions and distribution functions of the irregularities. The maximum signal‐to‐noise ratio is obtained when all modes or arrivals can be added coherently; i.e., no phase fluctuations exist. The performance of the arrays decreases as the phase fluctuation increases. Upper and lower limits of the signal‐to‐noise ratio are given for small and large phase fluctuations. The degree of coherence of the modes has been related to the reproducibility of the signal transmission between a single source and a single receiver.