LABIANCA/HARPER: A THEORETICAL APPROACH TO THE PREDICTION OF SIGNAL 



FLUCTUATIONS DUE TO ROUGH-SURFACE SCATTERING 



are for an acoustic frequency of 100 Hz and a surface-wave frequency 

 of 0.1 Hertz (surface wavelength A = 129 m) . Figure 10 shows the 

 total power in the acoustic signal as a function of range superimposed 

 on the corresponding smooth surface transmission-loss function. The 

 essential feature in this figure is the smoothing out of the power 

 curve because of the redistribution of energy. The receiver at 

 z = 1,000 m is located well below the source at z' = 50 m and the 

 radial direction, g = 0°, coincides with the direction in which the 

 surface wave is traveling. The computations were made for a surface 

 waveheight a = 2 m. Figure 11 displays the spectral decomposition 

 of the total power curve into the carrier and sideband curves. The 

 sideband curves are seen to be asymmetric with the down Doppler- 

 shifted sideband decreasing more rapidly with range. 



The azimuthal dependence of the sideband structure is illustrated 

 in the next two figures. In Figure 12, B = 45° and the sidebands 

 begin to spread apart further out in range. In Figure 13, g = 90° 

 and the sidebands are equal. The smoothing effect on the total power 

 in this plane of symmetry is greater than in any of the other direc- 

 tions by as much as 3 dB at the longer ranges. This is, of course, 

 because the equality of the sidebands doubles their contribution to 

 the total power. Finally, Figure 14 shows how the sidebands have 

 reversed in the 3 = 180° direction. 



There is another plane of symmetry across which the sideband 

 structure reverses and that is the plane where the receiver depth 

 equals the source depth. In this plane, regardless of the direction 

 specified by the angle g, the sidebands are always equal. Figure 15 

 shows the total power curves for a source and receiver depth of 50 m 

 at an angle g = 45°. The corresponding spectral breakdown is 

 illustrated in Figure 16 and the sidebands are seen to be equal. 



598 



