STICKLER: NORMAL MODES IN OCEAN ACOUSTICS 



the leaky -wave modes still depends on the range and depth coordinate. 

 When there is refraction in the model, the situation becomes more 

 complicated. A discussion of the Stonely wave will not be given 

 here (see Ewing, Jardetsky, and Press, 1957). 



A hybrid representation is, of course, possible. For example, 

 the diagram at the bottom center of Figure 7 might be chosen to model 

 a sedimentary layer (i.e., the longitudinal sound speed higher than 

 the water speed but with the shear speed slower than the water speed.) 

 As remarked above, for this geometry there are no trapped modes; hence, 

 one representation would consist of two EJP branch integrals. However, 

 if one chose an EJP branch for the longitudinal speed and a Pekeris 

 branch for the shear speed, then the representation would consist of 

 an infinity of leaky shear modes plus a Pekeris-type branch and an 

 EJP- type branch. Some care must be exercised in this approach be- 

 cause, while it may be possible to neglect the contribution of the 

 Pekeris branch, we can expect the EJP branch to yield a contribution 

 comparable to the sum of leaky shear modes. 



BRIEF DESCRIPTION OF EXISTING NORMAL-MODE PROGRAMS 



In this section, several working normal-mode programs are 

 described. 



The first group includes programs constructed by Cybulski, by 

 Kanabis, by Blatstein and Uberall, as reported by Spofford (1973), 

 and by Newman and Ingenito (1972) . These programs all involve a 

 numerical integration of Equation 2 beginning at the ocean-bottom 

 interface and using the pressure-release condition at the ocean sur- 

 face to determine the characteristic wavenumbers k and the wave 



n 



functions P(z,z ,1 ). The proper modes are summed, 

 on 



144 



