respectively J may be represented as a D.C. term and a 

 superimposed sinusoidal modulation at the difference fre- 

 quency and wavenumber ( co,k ) = ((_^j_(^]^ _]^ ), 



m ~i" 1 2 ~ 1 ~ 2 



(It Is assumed here that the power Is averaged over a period 



large compared with w" ^ but small compared with w"^ .) 



1 ''^ in 



On account of its finite frequency w^ , the modulation 

 term can be readily filtered from the mean power. Thus 

 separated, the value of the fluctuating beam as a wave probe 

 follows primarily from its sinusoidal spatial variation. 

 Assuming that the Bragg scattering surface waves were essen- 

 tially homogeneous over scales large compared with the 



modulation wavelength X = 27r/l k -k I , the modulated 



m -1-2 



backscattered return. Integrated over an illuminated area 

 of dimension large compared with ^j^ , would average to 

 effectively zero. However, if the Bragg-scattering surface 

 waves are themselves modulated by long wind-sea components, 

 the product of the modulated incident power and the modu- 

 lated backscatter cross-section yields a non-vanishing 

 contribution on integration over the illuminated area. If 

 the modulation of the Bragg scattering waves is linear with 

 respect to the wind sea, which appears a reasonable first 

 approximation, the modulated microwave acts as a filter 

 extracting the modulating wind-sea component at the wave- 

 number k . Since the effect is linear in the (statis- 

 tlcal) surface wave amplitudes, the ensemble average of 



25-41 



