The Sea Surface as a Random Filter for Underwater Sound Waves

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Abstract
When underwater sound waves propagate from a transmitter to a receiver, part of the energy reaches the receiver after reflection and scattering from the sea surface. This boundary effect can be called the impulse response of the sea surface if the incident sound field is caused by a delta pulse. In this paper the Helmholtz diffraction integral is used together with a perturbation technique for the derivation of a formula for the corresponding transfer function. The result is a random function that depends on the frequency of the incident wave, on time, and on the source-receiver configuration. Its validity is limited by three assumptions: (1) the medium is ideal (constant velocity, no subsurface layer), (2) source and receiver depth are many times larger than the surface elevation, and (3) the bottom is infinitely far away. For very high frequencies the formula indicates specular reflection from each surface “highlight.” In the Fraunhofer domain, the transfer function reduces to specular reflection with phase fluctuations. Some results of a statistical analysis are included for that frequency domain.

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