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

 FLUCTUATIONS DUE TO ROUGH-SURFACE SCATTERING 



The essential feature to notice about the pressure time series 

 is that it has basically the same form as in the single sinusoid 

 case, except that now there are contributions from all frequencies 

 in the spectrum. To second order in the perturbation there are still 

 four contributions to a field point: the direct field, the corrected 

 specular reflection, and the up and down Doppler-shif ted sidebands. 



Figure 19 displays the form of the power spectrum, the Fourier 

 transform of the autocorrelation function, for the pressure process. 



The sideband spectra are seen to be linear combinations of the average 



2 

 value of the square of the sideband amplitude functions Q . 



The weighting factors are the squared amplitudes of the surface 



2 



sinusoids. Thus, the quantities Q can be regarded as the 



squared magnitude of a sideband system function evaluated at the 

 mean values of ^j . 



The value of the carrier spectrum is not as simple to describe. 

 There is no simple linear relationship between it and the surface 

 spectrum. About all that can be said for it is that it is a compli- 

 cated function of the square of the amplitudes of the surface 

 sinusoids. 



We have been able to generate a large number of numerical 

 results for the random surface case and we will show a selected few 

 of them. All the following plots are computer generated for an 

 acoustic frequency of f (F on the plots) = 50 Hz, and an rms wave- 

 height a (A on the plots) = 2.48 m. The latter is computed from a 

 Pierson-Moskowitz spectrum which is illustrated below. Again note 

 the asymmetry of the sidebands and the plans of symmetry 3 = 90° 

 and z (Z on the plots) = z' {ZP on the plots). 



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