RODERICK: FORWAPUD SCATTERED LOW-FREQUENCY SOUND FROM THE SEA SURFACE 



7 nautical miles. The scattering function, as shown in Figure 11, is 

 a three-dimensional description of the transmission in terms of the 

 intensity, frequency, and delayed time of arrival. For surface- 

 ref lected-bottom-ref lected arrivals, the Doppler spectrum has side- 

 band frequencies at surface-wave frequencies. The scattering func- 

 tion was measured during typical summer conditions with onshore winds 

 of 10 to 15 knots. Asymmetrical sidebands were observed in some of 

 the scattering functions. 



Asymmetrical sidebands can result when scattering occurs from 

 a multi-frequency surface (see Figure 12) . Consider the case of a 

 two-frequency surface: the magnitude of each frequency component 

 is proportional to the product of two Bessel functions and the side- 

 band frequencies represent all possible combinations of the carrier 

 and multiples of each surface frequency. If the surface frequencies 

 are commensurable, then each sideband frequency is made up of a 

 vector summation of the individual terms. In general, this will 

 result in asymmetrical sidebands. The spectrum shown for surface 

 frequencies of 4 and 6 Hertz has asymmetrical sidebands at a dif- 

 ference frequency of 2 Hertz from the carrier. 



The AFAR range has also been used (O'Brien, et al., 1974) to 

 measure the Doppler spectrum at different transmitted center fre- 

 quencies. At 600 Hertz (see Figure 13) , the received energy is 

 coherent and predominately in the carrier frequency. As the fre- 

 quency increases, the Doppler spectrum consists of more and more 

 incoherent scattered acoustic energy. The sea state was 0.45 meters 

 rms. 



In terms of the Doppler spectrum, we want to know what has been 

 done; where we are; and what needs to be done. I have tried to 

 illustrate the state of these affairs. We have made enough 



345 



