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Range

Figure 3.9 Illustration of image interference effects. The transmission anomaly (TA) represents the difference between the observed TL and losses due to the effects of spherical spreading (TA = 20log10(r) — TL), where the range (r) is measured in meters (adapted from Urick, 1979).

This phenomenon, also known as the Lloyd Mirror effect, diminishes with increasing surface roughness.

Assuming an acoustically smooth sea surface (R ^ 1) and a shallow source depth (d) in deep water, the ranges r1 and r2 in Figure 3.9 can be approximated as (Urick, 1982, 1983):

2VdH

where X is the acoustic wavelength and H the receiver depth.

The image effect can be used to estimate the depth of a submerged object at short ranges. In Figure 3.8, if the source is replaced by a submerged object that has been ensonified by a single, short pulse, then the depth (d) of the object is approximated by:

d rcAt ~2H

where c is the speed of sound and At the difference in time between receipt of the direct and the surface-reflected pulses (Albers, 1965: 50-1).

The concept of surface interference can also be used to solve relatively simple propagation problems. The approach is called the "method of images" and is valid for all frequencies. The solution is normally expressed as a sum of contributions from all images within a multilayered space. Although this method is usually cumbersome, it is commonly employed as a physical model against which to check the results of more elaborate mathematical models (to be discussed in Chapter 4). Kinsler et al. (1982: 427-30) provided a detailed

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