MELLEN: SOUND PROPAGATION IN A RANDOM MEDIUM 



The resulting attenuation shown in Figure 5 is a three-component 

 model consisting of: 



• The fresh water viscous component 



• The MgSO relaxation component 



• The anomaly which has recently been identified as a 

 second relaxation involving the boron content in sea- 

 water (Yaeger et al., 1973). 



Thus, we may now say that all three components are absorptive and do 

 not involve scattering or other anomalies. 



Several of the experiments do not follow the three-component 

 absorption model very well at all and Hudson Bay (Browning, 1971) is 

 one of those cases (see Figure 6) . Since we have no reason to suspect 

 either the experiment or the absorption model, it is plausible that 

 the excess arises from some other mechanism. If we subtract the 

 theoretical from the experimental, we find that the excess attenu- 

 ation coefficient is a constant 0. 04 dB/kyd over the frequency range. 

 This might suggest another relaxation below 100 Hz; however, this 

 hypothesis must be rejected for other reasons. A more likely cause 

 is forward scatter from inhomogeneities within the water columns. 



As a first attempt to test this forward scattering hypothesis, 

 we have investigated the turbulent cell model of Chernov (1962) . In 

 Figure 7 we see a plane wave progressing through a perturbed medium 

 where the refractive -index inhomogeneities are random, roughly 

 spherical, and have a scale size a . The wavefront becomes corrugated 

 and the ray angles become randomly distributed. Energy is conserved. 



In a sound channel, energy is normally trapped for all angles 

 less than some critical angle, , and leaks out for larger angles 

 (see Figure 8) . Because of the diffusion by the inhomogeneities. 



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