discontinuity in sound speed is required, as when modeling an interface between water and 

 sediment. The user indicates this by specifying the sound speed at the top of the layer. If 

 left blank, the program provides the sound speed necessary for continuity. 



A second function of the processing program is to permit a layer to be defined by the 

 sound speed at top and bottom of the layer rather than by one sound speed and one gradient. 

 Note that the profile form as given by eq (5) is a two-parameter curve. 



The last layer extends to infinite depth, so a gradient must be specified at the top of 

 it. However, this gradient can be specified by giving a depth and sound speed point below the 

 last layer. The program handles this by checking to see if the gradient of the last given layer 

 is unspecified. If it is, the number of layers is reduced by one, which causes the last layer to 

 be only the required extra point determining the final gradient. This final gradient must 

 always be negative, as is required by the boundary conditions. The program user must ensure 

 that this gradient is negative and that no gradient is zero. A zero gradient will appear in the 

 denominator of eq (7). 



These functions of the profile processing program are relatively simple, but an addi- 

 tional capability used to model sediment bottoms greatly increases the complexity of the 

 program. The capability required is to specify the absorption in a layer by adding an imagi- 

 nary part to the sound speed. In older versions of this normal mode program an imaginary 

 part, expressed as an absorption coefficient, could be added to the sound speed at the top of 

 the layer. This imaginary part is small compared to the real part. Since the gradient was 

 assumed real at the top of the layer, the imaginary part was initially not changing with depth 

 and it usually changed only a minor amount through the depth of the layer. However, this 

 small change could not always be relied upon. Also Hamilton (ref 8) has published data on 

 absorption gradients in sediment layers, so more precise control of this part of the sound 

 speed function is needed to model sediment layers. Therefore, a more comprehensive profile 

 processing routine has been incorporated in the normal mode program. This curve-fitting 

 process is described below. 



The following quantities can be input for each layer depth starting at the surface: 



Depth of top of the layer 



Sound speed at top of layer 



Sound speed at bottom of layer 



Real part of sound speed gradient at top of layer 



Attenuation in loss per km at the top of the layer 



A similar attenuation at the bottom of the layer 



Density in the layer 



The density is a constant in the layer and as such requires no further curve fitting. Redun- 

 dant parameters are left blank on input cards. In some cases negative values serve as flags to 

 indicate specific treatment. For instance a negative value of absorption at the top of a layer 



Sound Attenuation as a Function of Depth in the Sea Floor, by EL Hamilton; J Acoust Soc Am, vol 59, 

 p 528-535, March 1976. 



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