IV -39 



For the high frequency case, this yields the condition (IV- 15) which has been 

 used earlier without justification. To obtain order of magnitude estimates of the 

 quantities involved, we may assume a typical value for < u^ > in the ocean to be 

 of the order of 5 x 10" . A typical value of the patch radius a is of the order of 

 1 to 10 meters, depending on the depth of the measurement. The results of 

 Table IV-3 were obtained for the first time by Mintzer in 1953 for the case of a 

 spherically spreading wave in a medium with a Gaussian correlation function. 

 Mintzer compared the behavior of the scattered power as linearly depending on 

 the range with experimental data obtained by Sheehy. (See Figure IV- 12.) The 

 coefficient of variance (the square root of the mean square power) is seen to 

 behave very much more as the square root of the range than as the three-halves 

 power of the range which would have been predicted by ray acoustics. The above 

 arguments do not give us the near field, which is important at high frequencies 

 when the focusing range can be quite large. Also, the measurements under actual 

 ocean conditions are usually not measurements of the scattered pressure by itself 

 but rather of the total pressure, i.e., of the sum of scattered and incident pres- 

 sures, which are not normally in phase. The measurements usually recorded by 

 instruments are either proportional to the square of the amplitude of the local 

 pressure or else measurements of the phase of the pressure. Let us first consider, 

 therefore, the type of results required to estimate the mean square fluctuations 

 of the amplitude and the phase of the total acoustic pressure at a point in the medium. 

 It is appropriate to perform the analysis on the basis of the "smooth" method of 

 approximation rather than the method of "small" perturbations, since the fluctuations 

 can be large. We recall from (IV- 16a), (IV-19) and(IV-36) that the incident pressure, 

 the total pressure, and the correction to the complex phase may be expressed as 

 follows: 



p (x)-A (x)e^V-^ (IV- 16a) 



o — o — 



p (x) - p^ (x) e "*" (IV-19) 



1^ = i£^ d ? u(5)-Vt = Si - iBi (IV-36) 



4n I - r - p (x) 



V 



In the above version of (IV-36), we have defined the quantities Si and Bi as the real 

 and the negative imaginary parts of ijfi, respectively. We note here that their 

 physical meaning, according to (IV- 22a) and (IV- 22b), is that of the fluctuation of 

 the phase and of the logarithmic amplitude, respectively. The phase angle of the 

 total pressure is therefore given by: 



S (x) = Arg (p (x) ) = S^ (x) + Si (x) = S^ (x) + Re i|;i (x) (IV- 82) 



arthur B.ILittlc.3nt. 



S-7001-0307 



