• Slight wind speed and frequency dependence

• Generally consistent with or slightly above perturbation theory

• Dependence on wind speed and frequency not well understood

• Transition region from air-water interface scattering to another mechanism

• Wind speed and frequency dependence similar to Chapman-Harris

• Another scattering mechanism needed (possibly bubble clouds)

Figure 8.3 Frequency-wind speed (f-U) domain for sea-surface scattering strengths (Ogden and Erskine, 1994a).

grazing angle. In the hatched area of the f-U domain of Figure 8.3, only the Chapman-Harris formula (Sch) should be used (i.e. a = 1). In the blank area of the f-U domain, only the perturbation theory formula (Spert) should be used (i.e. a = 0). In the stippled area corresponding to the transition region, the full equation (Stotal) should be used where a is evaluated at the input frequency (f) and input wind speed (U). Figure 8.3 can be used to determine the wind speeds at the perturbation theory (lower) boundary (Upert) and at the Chapman-Harris (upper) boundary (Uch). For convenience, Ogden and Erskine (1994a) put these boundaries into analytical form. The lower boundary was approximated by two line segments: from 240 to 1,000 Hz, the segment was defined by y = 7.22, while from 50 to 240 Hz the segment was given by y = 21.5 — 0.0595x. The upper boundary was approximated by the cubic equation:

y = 20.14 - 0.0340x + 3.64 x 10"V - 1.330 x 10"8x3

Ogden and Erskine (1994b) extended the range of environmental parameters (principally wind speed) used in modeling sea-surface backscattering strengths in the CST experiments. Related work (with minimal analysis) summarized bottom-backscattering strengths that had been measured during the CST program over the frequency range 70-1,500 Hz for grazing angles ranging from 25° to 50° (Ogden and Erskine, 1997). Nicholas et al. (1998) extended the analysis of surface-scattering strengths that were measured during the CST experiments over the approximate frequency range 60-1,000 Hz. Unexplained variations between measured and modeled scattering strengths were attributed to an incomplete parameterization of subsurface bubble clouds.

8.3.2 Under-ice reverberation

The detection, localization and classification of targets with active sonars under an ice canopy is limited by reverberation from the rough under-ice surface and by the false targets presented by large ice features such as ice keels. Sea ice is the dominant cause of reverberation in Arctic regions. For undeformed first-year ice, reverberation levels at frequencies above about 3 kHz are approximately equivalent to that expected from an ice-free sea surface with a 30-knot wind.

Because of the variation in the under-ice surface, scattering strength measurements as a function of grazing angle reveal different characteristics. When the under-ice surface is relatively smooth, the scattering strength increases with grazing angle as in the open ocean. When ridge keels are present, low-grazing-angle sound waves strike them at a near-normal incidence and substantial reflection occurs. Measurements of the scattering strength of the ice-covered sea for two Arctic locations at different times of the year have been summarized by Brown (1964) and by Milne (1964). Both sets of data show an increase of scattering strength with increasing frequency and grazing angle. Using highly directional sources and receivers to exploit optimum ray paths can minimize reverberation under the ice. Such paths could provide time discrimination between target echoes and reverberation for those targets spatially separated from the sea surface (Hodgkiss and Alexandrou, 1985).

8.3.3 Sea-floor reverberation

The sea floor, like the sea surface, is an effective reflector and scatterer of sound. Scattering can occur out-of-plane as well as within the vertical plane containing the source and receiver. A correlation of scattering strength with the size of the particles in a sedimentary bottom has consistently been observed (e.g. McKinney and Anderson, 1964). The sea floor can then be classified according to sediment composition (sand, clay, silt) and correlated with the scattering strength. For example, mud bottoms tend to be smooth and have a low impedance contrast to water, while coarse sand bottoms tend to be rough, with a high impedance contrast. There can be large spreads in the measured data for apparently the same bottom type. This may be due, in part, to the refraction and reflection of sound within the subbottom sediment layers.

A Lambert's law relationship (Urick, 1983: chapter 8) between scattering strength and grazing angle appears to provide a good approximation to the observed data for many deep-water bottoms at grazing angles below about 45°. Lambert's law refers to a type of angular variation that many rough surfaces appear to satisfy for both the scattering of sound and light. According to Lambert's law, the scattering strength varies as the square of the sine of the grazing angle. Mackenzie (1961) analyzed limited reverberation measurements at two frequencies (530 and 1,030 Hz) in deep water. The scattered sound responsible for reverberation was assumed to consist of nonspecular reflections obeying Lambert's law:

where SB is the bottom scattering strength (dB), f the bottom scattering constant and 0 the grazing angle (degrees). The term 10log10 f was found to be constant at -27 dB for both frequencies. This value has been largely substantiated by other measurements over a broad range of frequencies. The bottom-scattering strength (SB) has been graphed in Figure 8.4 according to Equation (8.6), using a value of — 27 dB for 10log10 f.

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