STICKLER: NORMAL MODES IN OCEAN ACOUSTICS 



The residue contributions from the poles give rise to two types 

 of modes: proper and improper. These will be described more 

 completely below, after the role of the branch points has been 

 discussed. 



Physically, the outward going wave condition in the high speed 

 sound layer gives rise to one pair of branch points. The other pair 

 is due to the outward-going wave condition in the isovelocity shear 

 layer. Each pair of branch points gives rise to a single branch-line- 

 integral contribution to the field. Furthermore, the choice of the 

 branch cut influences which modes or pole singularities contribute 

 to the acoustic field. This point is now discussed. 



To describe the differences arising from the choice of branch 

 cut, it is convenient to examine the Pekeris model and to determine 

 the differences in the representations that result from the two most 

 common choices for the branch lines. The statements that will be 

 made about this model apply, with little change, to the more general 

 profile. 



The Pekeris model, shown in Figure 4, consists of an isovelocity 

 layer over a high-speed isovelocity half space. There is no shear in 

 this model. The two common choices for the branch cuts are shown in 

 the two lower figures. The EJP branch on the left is the branch cut 

 chosen by Brekhovskikh; on the right is the branch cut chosen by 

 Pekeris. First, I will discuss the representation arising from the 

 EJP (Ewing, Jardetsky, Press) branch. The EJP branch is chosen such 



y; 2 ,2 



that on this sheet Im V k - k > 0. The negative root occurs on 

 the second sheet. This means the residue contribution from any pole 

 on this sheet will eventually decay exponentially with depth and will 

 represent a mode with finite energy. For this reason, these residue 

 contributions are called proper modes . 



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