TAPPERT: SELECTED APPLICATIONS OF THE PARABOLIC-EQUATION METHOD IN 

 UNDERWATER ACOUSTICS 



is converted to SRBR and RBR leading to the so-called megaphone 

 effect. Figures 19 and 20 illustrate the impact of a high-loss sea- 

 mount on energy from an axial source and a near-surface source, 

 respectively. In the first case, the source couples well to the 

 near-axial modes which suffer little attenuation in passing the sea- 

 mount. Hence, beyond the seamount, the high-angle modes are stripped 

 away leaving the very distinct focal regions. For the shallow source 

 which does not couple well with the axial modes, the seamount strips 

 nearly all of the energy away. Figure 21 is for the shallow source 

 where now the bottom is highly reflecting. Paths which before were 

 annihilated by the seamount now steepen to SRBR going up the sea- 

 mount and convert back to RSR and RR on the downslope. 



RANDOM OCEANS 



The final example of the use of the parabolic-equation method 

 addresses the random ocean problem (Garrett and Munk, 1972; Munk, 

 1974) . The main advantage of the parabolic-equation method is that 

 it can take into account rapid range variations in the ocean environ- 

 ment. We now know that there are important random components in the 

 acoustic sound speed due to internal-wave fluctuations and micro- 

 fluctuations in the ocean temperature structure. 



The following work was begun this summer with Stan Flatte and 

 Walter Munk. This discussion is merely an introduction to the work 

 which is covered in detail in subsequent papers (reproduced in these 

 'Proceedings) . 



The technique is summarized in Figure 22. By adding a time 

 dependence to the sound speed (23) , it can be expressed as a mean 

 function of depth and range, and a fluctuating function of depth, 

 range, and time. The refractive index (24) is then a sum of a 

 deterministic part and a random part. 



183 



