Figure 7.1 Simple model for the vertical directionality of ambient-noise: (a) geometry with straight-line propagation paths and (b) directional patterns for surface distribution of monopoles and dipoles. The dashed segments near the horizontal show the effect of attenuation and refraction near the sea floor (A) and near the deep-sound channel axis (B). (Urick, 1983; Principles of Underwater Sound, 3rd edn; reproduced with permission of McGraw-Hill Publishing Company.)
But r = h tan 0, so that dr = h sec2 0 d0. Also, l = h sec 0. On substituting and rearranging terms, Equation (7.1) reduces to:
If ty is a solid angle, then dty = 2n sin 0 d0, so that the noise intensity per unit solid angle, N(0), becomes
When I(0) = Io, which represents a nondirectional source, Equation (7.3) yields
which is the ambient noise intensity per unit solid angle for a surface distribution of monopole sources. Using a distribution of dipole sources for which the intensity radiated at an angle 0 is I(0) = Io cos2 0, the beam pattern of the noise received at a depth below the surface is:
Equations (7.4a) and (7.4b) are plotted in polar coordinates in Figure 7.1(b). At angles near the horizontal (where 0 = 90o), the effects of attenuation, refraction and boundary multipaths prevent the curves from
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