On acoustic transmission in ocean-surface waveguides

A sound speed profile which increases monotonically with depth below the ocean surface is upward-refractive, acting as a duct in which sound may be transmitted to long ranges with little attenuation. A well-known example is the mixed layer, in which the temperature is uniform and the sound speed approximately scales with the hydrostatic pressure, increasing linearly with depth. The depth of the mixed layer depends on surface conditions, but is of the order of 100 m. Deeper channels are found in ice-covered polar waters, where the temperature and sound speed profiles both show a minimum at the surface. A typical surface duct in the Arctic Ocean may extend to depths of 1000 m or more and is capable of supporting very-low-frequency (VLF) (1-50 Hz) acoustic transmissions with no bottom interactions. On a depth scale that is smaller by several orders of magnitude, wave-breaking events create a bubbly layer one or two metres thick below the sea surface, with the highest concentration of bubbles, and correspondingly the lowest sound speed, at the surface. The bubble layer acts as a waveguide for sound in the audio frequency range, above 2 kHz, although transmission may be severely attenuated due to absorption and scattering by the bubbles, as well as by the irregular geometry of the sea surface and the bubble clouds. Most ocean-surface waveguides can be accurately represented by an inverse-square sound speed profile, which may be monotonic increasing (upward refracting) or decreasing (downward refracting) with depth, and whose detailed shape is governed by just three parameters. An analysis of the sound field below the sea surface in the presence of such a profile shows that it consists of a near-field component, given by a branch-line integral, plus a sum of uncoupled normal modes representing the trapped radiation which propagates to longer ranges. The modal contribution is identically zero in the case of the downward refracting profiles. The properties of the modes emerge from a straightforward theoretical development involving first- and second-order asymptotics: each mode shows an oscillatory region immediately below the surface, terminating at the extinction depth, below which the mode decays exponentially to zero; the extinction depth increases rapidly with both mode number and the reciprocal of the acoustic frequency; a reciprocal relationship exists between the extinction depth and the mode strength; and there is no mode cutoff, nor are there any evanescent modes. On applying the inverse-square theory to VLF Arctic Ocean transmissions, the spectral density of the modal field is found to show a steep positive gradient between 5 and 50 Hz, the rising level occurring as more modes make a significant contribution to the field. This result is compared with observations of infra-sonic ambient noise that have been made in the marginal ice zone of the Greenland Sea, using surface suspended, flow-shielded hydrophones. The measured spectra show a deep minimum at about 5 Hz, in accord with the theoretical prediction. The inverse-square theory also has application to under-ice ocean-acoustic tomography, where the dispersive nature of the upward refractive channel governs the arrival times of the modes at the receivers. A simple expression for the group velocity of the modes gives the arrival times. More generally, the full modal structure of the field across the tomography array may be constructed from the theory. Acoustic signatures of wave-breaking events have recently been observed in the ocean-suiface bubble layer by farmer & Vagle (1989). The spectra show well-defined peaks (La Perouse) or a broader-band structure (FASINEX), both of which are fully explained, in terms of intermode interference, by the inverse-square theory. The differences between the two data-sets are attributed to the different sound speed profiles in the bubble layers at the two sites. The spectral banding in fasinex is a modulation phenomenon, showing a strong dependence on the source depth. A straightforward inverse calculation indicates that the bubble sources in fasinex are located at a depth of 1.5 m, corresponding roughly to the base of the bubble layer, this is a slightly unexpected conclusion, since acoustically active bubbles generated by spilling breakers under wind-free conditions in a laboratory tank are known to be located within a few millimetres of the surface. However, aeration is much more pronounced at the wind-driven surface of the ocean than in a tank, which may be a factor in accounting for the deeper sources. There are practical difficulties in measuring the source distribution using conventional techniques, but the inverse-square transmission theory in conjunction with near-surface measurements of wave-breaking signatures provides an effective means of making such a determination.