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



FLUCTUATIONS DUE TO ROUGH-SURFACE SCATTERING 



One example of the application of the model is the current 

 interest in the stability of the relative phase between two receiver 

 points. A number of researchers, see Grube (1974), Gerlach (1973), 

 and Mangano (1969) , have reported apparently conflicting empirical 

 results, sometimes from the same experiment. For example, my Figure 1 

 shows the violent relative phase fluctuations observed by Mangano 

 (1969) for two hydrophones spaced only 22 feet apart. Figure 2 

 shows the more coherent behavior observed during a different period 

 of the same experiment for the same hydrophones.* On the other hand, 

 good long-term relative phase coherence has been observed between 

 arrays spaced many miles apart [Grube (1974), and Gerlach (1974)]. 



Various attempts [for example. Brock (1973)] have been made at 

 explaining such fluctuations. Hirsch (1974) has given a particularly 

 satisfying phenomenological explanation which is in agreement with 

 the predictions our model can make on a regular basis. Basically, 

 Hirsch comes to three main conclusions. First, for the closely 

 spaced elements, coherence is high when the energy is high and the 

 carrier dominates the Doppler shifted energy. Second, also for 

 closely spaced elements, when the carrier fades the Doppler shifted 

 energy is no longer negligible and the coherence decreases. Figure 3 

 shows the power spectrum associated with the violent fluctuation 

 illustrated in Figure 1. The spectrum within half of a Hertz of the 

 carrier (here labeled DC value) is typical of the type of acoustic 

 spectrum arising from rough-surface interaction. When the sideband 

 energy is comparable to the carrier energy, as it turns out to be in 

 this case, the relative phase coherence decreases giving rise to the 



* Both of these phase plots were recorded for a 115-Hz source drifting 

 at approximately 1 knot at broadside to the elements. 



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