BOTTOM LOSS MODELS THAT ACCOUNT FOR GRADIENTS 



The variation of sound speed in the ocean, configuration of the bottom, and 

 bottom and subbottom properties are generally the most important environmental factors 

 for the determination of underwater sound transmission. The bottom properties can vary 

 considerably from one area to another. The more common types of sediments are sand, 

 sand and mud, or mud. The areas of mud-size particles can vary in compactness from hard 

 clay to a loose suspension. Not enough is known of the acoustic properties of the immedi- 

 ate bottom materials and the variation of these properties as a function of depth into the 

 bottom as discussed in Part L We do observe that the bottom characteristics have an 

 important effect in some areas on sound transmission. In other areas the bottom has very 

 Httle effect and the sound speed profile is the controHing factor. It is important to develop 

 realistic models of the bottom which use sediment characteristics to predict the reflection 

 coefficient R as a function of grazing angle for determining the acoustic transmission of 

 an area. 



LIQUID MULTILAYER MODEL 



We next want to consider multilayered sediment models that can be used either to 

 represent actual layering (e.g., it is not uncommon to find alternating layers of sand and silt 

 in shallow water) or to account for gradients. For the layered hquid case the solution is 

 very simple. Figure 17 shows n sediment layers and a half-space labeled (n + 1). In each 

 layer the potential function is the sum of an upgoing and a downgoing plane wave (e.g., 

 i^j^ = Aj^ exp(iCj^ z^) + Bjj exp(-i£j^ z^^)) and in the halfspace the potential function 

 represents a downgoing wave (i/'n+l ~ exp(iCj^+j Zj^+j)). 



Let P represent the pressure and Q the vertical component of particle velocity. Then 

 start at the interface between layer n and the half-space with the expressions for P and Q 

 that follow. P and Q are easily evaluated at the n/(n+l) interface where Zj^+j is zero. Be- 

 cause P and Q are continuous functions they have the same values at the bottom of layer n 

 (at Zj^ = dj^) that they have at the top of the half-space (at Zj^+] - 0). Therefore, A^^ and Bj^ 

 can be calculated. From these calculate P and Q at the top of layer n (at z^ = 0). Continue 

 working up the layers until Aq and B^ are calculated. The value of R is obtained from 

 R = B„/A„. 



nKn+\) ] P " P*^ = Pn+ 1 ' Q = < d^/^z) = iH^^ j 

 Layer | ^n = 1/2 exp(-ien d„) [P/p^ + Q/(ie„)] 



Interface! ^ = V^n + B„) 

 ^"-^^/" ^ Q = iyA„-B„) 

 Continue until A^ and B^ are calculated 

 Reflection coefficient: R = B„/A„ 



49 



