Figure 3.4 Hypothetical relationship between (a) TL curve and (b) the corresponding propagation paths and detection zones (cross-hatched areas near the sea surface) associated with a FOM of 85 dB. A plausible sound-speed profile is shown at the left side of panel (b). Both the source (target) and receiver (ship's sonar) are positioned near the surface.

In basic ray tracing, Snell's law is used in one form or another. This law describes the refraction of sound rays in a medium in which sound speed varies as a function of depth, but is constant within discrete horizontal layers of the water column. Consider Figure 3.6 where a ray (which is normal to the acoustic wavefronts) is traveling from medium 1 (with sound speed ci) into medium 2 (with sound speed c2), where c1 = c2. Let X1 be the distance between successive wavefronts (i.e. the wavelength) in medium 1 and k2 the corresponding value in medium 2. Then, as defined in Figure 3.6:

x Source o Receiver

Figure 3.5 Six basic propagation paths in the sea: (a) direct path (DP); (b) surface duct (SD); (c) bottom bounce (BB); (d) convergence zone (CZ); (e) deep-sound channel (DSC); and (f) reliable acoustic path (RAP).

Figure 3.6 Geometry for Snell's law.

Figure 3.6 Geometry for Snell's law.

where At is an increment of time. Rearranging terms, we obtain the familiar relationship:

sin 0i sin 02 ci c2

or, equivalently from Figure 3.6:

cos 01 cos 02

ci c2


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