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



FLUCTUATIONS DUE TO ROUGH-SURFACE SCATTERING 



violent fluctuations illustrated earlier. We will show subsequently 

 that nearly equal carrier and sideband energy occurs at the nulls in 

 the carrier due to surface-image interference in a nonrefracting 

 ocean. Mangano's (1959) results indicate that in regions of refrac- 

 tive interference at greater range, a similar reduction of the carrier 

 relative to the sideband energy occurs. Finally, Hirsch's third con- 

 clusion is that in the case of widely spaced arrays, high coherence 

 is achieved when the skewed Doppler arrivals are rejected by narrow 

 beams. 



The qualitative conclusions drawn by Hirsch are correct in their 

 gross features but the reasoning does not permit detailed prediction 

 of fluctuations on a regular basis. This is the reason why we have 

 developed our model. We will first describe the model and later 

 present numerical results. We will indicate some possible improve- 

 ments. 



PERTURBATION MODEL 



The perturbation method utilized in our model is ideally suited 

 to situations where the acoustic wavelength is the order of the ocean 

 surface wavelength. This is in contrast to cases where the acoustic 

 wavelength is small compared to the surface irregularities, in which 

 case the Kirchoff or physical-optics approximation becomes suitable 

 (see Holford) . Figure 4 outlines the procedure for setting up the 

 scattering formalism. Part A is a mathematical statement of the 

 boundary-value problem. The pressure P satisfies the wave equation 

 with a depth-dependent sound speed, a time-harmonic point-source 

 forcing function and the usual boundary conditions. The function i; 

 gives the spatial behavior of the surface (deterministic or random) 

 and a can be thought of as an rms surface waveheight. Part B shows 



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