CAUSES OF FLUCTUATION 



169 



Figure 9. Transmission run showing image interference effect. 



lished by UCDWR* and is reproduced in Figure 9. 

 The signal level was recorded by a sound-level re- 

 corder. It will be noted that the ranges are very 

 short, extending to not more than 90 ft. The recorder 

 trace shows clearly that the amphtude of the signal 

 fluctuation is greatest near the minima of the regular 

 interference pattern (drawn in as a theoretical curve) 

 where the magnitude of the resultant would be most 

 sensitive to phase shifts of the components. This rec- 

 ord was taken in shallow harbor water, and the sur- 

 face was undoubtedly quite smooth. Otherwise, the 

 interference pattern might not have been so notice- 

 able. 



Finally, attention is called to the experiments 

 carried out with a deep transducer, which were men- 

 tioned in Section 7.1.1. These experiments indicate 

 that the fluctuation is often reduced to a fraction of 

 its usual magnitude when both the sound source and 

 receiving hydrophone are so deep that the direct 

 signal can be separated from the surface-reflected 

 signal. It is true that some fluctuation remains, even 

 when interference with the surface-reflected sound 

 is eliminated; this small fluctuation may be the result 

 of imperfect equipment. In all cases, however, the 

 fluctuation of the direct signal is reduced drastically 

 when it can be separated from the surface-reflected 

 signal. The fluctuation of the surface-reflected signal 

 by itself is somewhat higher than the fluctuation of 

 the combined signal usually observed with a shallow 

 projector. 



Several Paths 



In shallow water, or even in fairly deep water with 

 a transmitter of low directivity, sound will reach the 

 receiving hydrophone not only over the direct path 

 and through one surface reflection, but also through 

 one bottom reflection, one bottom and one surface 



reflection, etc. The number of possible paths is, 

 strictly speaking, infinite, and small changes in 

 geometry may bring about random phase shifts be- 

 tween the different arrivals. Nevertheless, the distri- 

 bution cannot be expected to approach the Rayleigh 

 case, because the intensity for the paths drops rapidly 

 as the number of reflections is increased, both be- 

 cause there are recurring energy losses on reflection 

 and because the high-order paths are steep-angle 

 paths and therefore discriminated against by the 

 transducer. Only very few of the theoretically possi- 

 ble paths of transmission will, therefore, be effective 

 in contributing to the resultant signal. It has been 

 found that in the presence of bottom-reflected sound 

 the rapidity of fluctuation increases, as shown by the 

 oscillograph trace reproduced in Figure 10. Unfortu- 

 nately, no quantitative information is available con- 

 cerning the decrease in the self -correlation coefficient 

 due to the contribution of bottom-reflected sound. 



Many Paths 



Figure 2 shows a distribution function obtained at 

 UCDWR, and superimposed on the experimental 

 points is a curve representing the Rayleigh distribu- 

 tion. The fit is good. A model of sound transmission 

 was set up in an attempt to explain this observed 

 approximation to Rayleigh distribution. The model 

 is based on the thermal microstructure which has 

 been found to exist in the ocean' and which is de- 

 scribed in Chapter 5. On the basis of ray acoustics, it 

 was suggested tliat the irregular thermal structure of 

 the ocean may give rise, simultaneously, to more than 

 one ray path connecting the transmitter with the re- 

 ceiving hydrophone. It seems reasonable to assume 

 that these paths will have different travel times and 

 that the signals transmitted along them are, there- 

 fore, not in phase with each other. If the phase dif- 



