Figure 3.24 Cutoff frequency calculated according to Equation (3.10) assuming a sound speed of 1,500 ms-1.

Absorption loss


Scattering loss


Absorption loss

Scattering loss


Figure 3.25 Loss to a fixed range in a surface duct. The optimum frequency is that at which the total loss is a minimum (Urick, 1979).

3.8 Deep-sound channel

The deep-sound channel, sometimes referred to as the sound fixing and ranging (SOFAR) channel, is a consequence of the sound-speed profile characteristic of the deep ocean (see Section 2.3). This profile has a soundspeed minimum at a depth that varies from about 1,000 m at mid-latitudes to near the surface in polar regions. This sound-speed minimum causes the ocean to act like a lens: above and below the minimum, the sound-speed gradient continually refracts the sound rays back toward the depth of minimum sound speed. This depth is termed the axis of the sound channel (refer back to Figure 2.7). A portion of the acoustic energy originating in the deep-sound channel thus remains within the channel and encounters no losses by reflection from the sea surface or the sea floor. Sound in this channel will be diminished by the effects of absorption. The properties of the deep-sound channel were first investigated by Ewing and Worzel (1948). The exceptional ducting characteristics of this channel have been used to advantage by oceanographers in the design and conduct of acoustic tomography experiments (see Section 5.6.9).

In terms of the sound-speed profile, the upper and lower limits of the channel are defined by the two (conjugate) depths of equal maximum sound speed in the profile between which a minimum exists. In Figure 3.26, these limits of the deep-sound channel are the depths A and A'; the depth A' is

Sound-speed (a) Ray diagram profile

Figure 3.26 Ray paths for a source in the deep-sound channel. In (a), the channel extends between the sea surface and the sea floor. It is cut off by the sea surface in (b) and by the sea floor in (c). The depth A! is referred to as the critical depth. (Urick, 1983; Principles of Underwater Sound, 3rd edn; reproduced with permission of McGraw-Hill Publishing Company.)

referred to as the critical (or conjugate) depth. Different ray paths from a source in the channel exist depending on whether or not the channel extends to the sea surface or to the sea floor. In Figure 3.26(a), the sound speeds at the sea surface and sea floor are the same. All depths in the water column then lie within the channel, and sound is propagated via paths that are either refracted (path 1) or reflected (path 2). In Figure 3.26(b), the upper limit of the deep-sound channel lies at the sea surface (which may happen at high latitudes). Here, in addition to paths 1 and 2, refracted-surface-reflected (RSR) paths occur (path 3) involving losses at levels intermediate to those suffered by paths 1 and 2. In Figure 3.26(c), the channel is cut off by the sea floor and refracted-bottom-reflected (RBR) paths exist (path 4). The entirely refracted paths and the low TLs associated with these paths do not exist when the source or the receiver is outside the depth limits A and A' of the channel.

3.9 Convergence zones

Urick (1983: 163-8) described the formation of convergence zones in the ocean (Figure 3.26). Specifically, there must exist a refracted ray that leaves the source horizontally. If this ray is reflected at either the sea surface or the sea floor (ray types 2 or 4 in Figure 3.26), then the required caustic pattern is destroyed and no convergence is possible. Another requirement for convergence is that the water depth must be greater than the critical depth (depth A' in Figure 3.26) in order to allow the rays traveling downward to refract without striking the bottom and to later converge downrange (ray type 3). There must also be a depth excess (i.e. a vertical separation between the critical depth and the bottom) on the order of a few hundred meters. For water depths less than critical (Figure 3.26(a) and (c)), the rays that would converge if the water were deeper are cut off by the bottom and become bottom-reflected without convergence.

Because the deep waters of the ocean are of a fairly uniform low temperature (near 1°C), the speed of sound at great depths is largely a function of pressure only. Near the surface, however, the speed of sound is determined largely by the water temperature. Thus, water temperature near the sea surface and the water depth in any particular area will largely determine whether sufficient depth excess exists and therefore whether or not a CZ will occur. Charts of surface temperature and water depth can then be used as basic prediction tools for ascertaining the existence of CZs. A convergence-zone-range slide rule (TACAID 6-10) was developed in 1973 by the Naval Underwater Systems Center based on an analysis of oceano-graphic data performed by E.M. Podeszwa. This slide rule could be used in the North Atlantic and North Pacific oceans, and the Mediterranean, Norwegian and Caribbean seas to determine CZ ranges.

In the North Atlantic Ocean, CZs are seen to appear at intervals of approximately 35 nm (65 km), with zone widths of about 2nm (4 km). TL

is significantly lower than spherical spreading within the zones, but significantly higher than spherical spreading between zones. Successive CZs get wider with increasing range until, at a range beyond a few hundred nautical miles, they coalesce. Beyond this range, TL increases smoothly with range and is characterized by cylindrical spreading plus attenuation.

3.10 Reliable acoustic path

When a source is located at the critical depth (depth A in Figure 3.26), and provided sufficient depth excess exists, propagation to moderate ranges can take place via the so-called reliable acoustic path (RAP), as illustrated in Figure 3.5(f). Such paths are termed "reliable" because they are sensitive neither to near-surface effects nor to bottom interaction.

3.11 Shallow-water ducts

There are two definitions of shallow water: hypsometric and acoustic. The hypsometric definition is based on the fact that most continents have continental shelves bordered by the 200 m bathymetric contour, beyond which the bottom generally falls off rapidly into deep water. Therefore, shallow water is often taken to mean continental shelf waters shallower than 200 m. Using this definition, shallow water represents about 7.5 percent of the total ocean area.

Acoustically, shallow-water conditions exist whenever the propagation is characterized by numerous encounters with both the sea surface and the sea floor. By this definition, some hypsometrically shallow-water areas are acoustically deep. Alternatively, the deep ocean may be considered shallow when low-frequency, long-range propagation conditions are achieved through repeated interactions with the sea surface and the sea floor.

Shallow-water regions are distinguished from deep-water regions by the relatively greater role played in shallow water by the reflecting and scattering boundaries. Also, differences from one shallow-water region to another are primarily driven by differences in the structure and composition of the sea floor. Thus, aside from water depth, the sea floor is perhaps the most important part of the marine environment that distinguishes shallow-water propagation from deep-water propagation.

The most common shallow-water bottom sediments are sand, silt and mud (see Chapter 2), with compressional sound speeds greater than that of the overlying water. Sediments are also characterized by shear waves, which are not present in the water column. Acoustic energy that strikes the sea floor at sufficiently small grazing angles is nearly totally reflected back into the water column. This results in a slightly lossy duct with TL approximately characterized by cylindrical spreading within the frequency range 100-1,500 Hz. At low frequencies, the acoustic field can extend into

Range (km)

Figure 3.27 Example of TL data in shallow water illustrating the cylindrical spreading associated with energy trapping by the waveguide. Data are for the one-third-octave band centered at 200 Hz (Eller, 1984b).

Range (km)

Figure 3.27 Example of TL data in shallow water illustrating the cylindrical spreading associated with energy trapping by the waveguide. Data are for the one-third-octave band centered at 200 Hz (Eller, 1984b).

the bottom with sound being returned to the water by subbottom reflection or refraction (Eller, 1984b).

The tendency toward cylindrical spreading is illustrated in Figure 3.27, which shows one-third-octave-band TL data at a center frequency of 200 Hz as a function of range. An omnidirectional hydrophone was located at a depth of 91 m in water approximately 210 m deep. The sources were set at a depth of 91 m on a track along which the water depth increased gradually from about 220 to about 300 m. The sound-speed profile was nearly constant along the track, and the bottom sediments were reported to be silty-sand near the beginning range and sand-silt-clay at greater ranges. Figure 3.27 also presents reference curves depicting spherical and cylindrical spreading (beyond 1 km). The acoustic energy is effectively trapped in the shallow-water duct at ranges less than about 40 km, beyond which the TL drops below the reference curve for cylindrical spreading.

3.12 Arctic half-channel

The acoustic waveguide in the Arctic is determined by the geometry of the ocean (type of ice cover and water depth) and by a positive-gradient sound-speed profile (sound speed increases with increasing depth). This waveguide forms a half-channel, that is, the lower half of the deep-sound channel, with the axis of the sound channel located at the sea surface.

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