A point whose distance from V is large compared with the linear dimensions 

 of V will be in the radiation field of all the scattering elements, and at such a point 



A f 



4lTX Jy 



A f 



4tt:c 7v 



= e«**-* f >r(fc) 



4xx 



where r is the Fourier transform of the function Q that describes the distribution of 

 the relevant property of the medium, and k = k — kI (where I = x/x) is the so-called 

 scattering vector that bisects the direction of the incident wave and that of x reversed 

 (see figure). The scattered wave at a considerable distance from V thus consists of a 

 spherical wave of frequency M propagating radially outwards with an amplitude propor- 

 tional to that of the incident wave and to the function T(k). The appearance of T(k) 

 in the analysis is to be expected from considerations of the mutual interference of the 

 scattered waves from the different volume elements. The Fourier component of Q(y) 

 with vector wave-number k = k — kI is the only one for which the phases of the scat- 

 tered waves from the various volume elements combine in such a way as to produce a 

 sinusoidal variation of fa along a line drawn from V in the direction I; all other Fourier 

 components of the distribution of the relevant property of the medium produce scattered 

 waves which annul each other at distance points in the direction I. 



Now the properties of the medium vary randomly as a result of the action of 

 turbulence, and the function T(k), and consequently fa(x, t), take different values 

 from one realization to another. Only the statistical properties of Y(k) and ip x (x, t) 



-» 



INCIDENT WAVE 



\ 

 \ 

 \ \ 



\ \ 



\ V>^ SCATTERED 



\ .* *\ WAVE 



^ \ \ 



» \ 



\ I 



I 



M - K- K-i 



Figure 1 



413 



