COMPARISON OF MULTILAYER SOLID AND LIQUID MODELS 



In Figure 24 is a plot of bottom loss for a model of 100 layers. The curve labeled L 

 is for the liquid layer model (it is also the bottom loss curve for the linear model). The 

 other curves are for a 100 layer sohd model with different values of rigidity. For r = the 

 curve is quite similar to the liquid model except that there is slightly more loss due to some 

 conversion of compressional waves into shear waves. As the rigidity increases there are 

 lower losses than the liquid model at very small grazing angles and higher losses than the 

 liquid model at larger grazing angles. Most likely the propagation to long ranges would be 

 better for the r = 0.1 curve than for the liquid model. 



EFFECT OF BOTTOM INTERACTION ON THE SOUND FIELD 



In this section, a sample case is analyzed where the bottom affects the sound field. 

 The first step is a ray theory calculation in which the most significant (i.e., with the least 

 propagation loss) eigenrays are identified. An eigenray is a ray that travels from the source 

 to the receiver. If the significant eigenrays do not reflect from the bottom then there is no 

 bottom interaction problem unless the frequencies are very low, e.g., < 20 Hz. In many 

 cases the significant eigenrays do have bottom reflections and the ray tracing program can 

 be used to determine the grazing angle of the rays when they reflect at the bottom, 7^^. 



The next step in the analysis is the calculation of a three-dimensional bottom loss 

 surface as shown in Figure 25. Table 3 lists the parameters used for this particular calcula- 

 tion. The values are typical of the deep ocean and are representative of properties pro- 

 vided by E. L. Hamilton's geoacoustic models. Bottom loss is plotted as a function of 

 grazing angle of the ray on the bottom, y^, and frequency. To understand Figure 25, it is 

 useful to consider Figure 26. On the left several sound speeds are plotted as a function of 

 depth. Here c^ is the sound speed in water, cj and C2 are the sound speeds at the top and 

 bottom of the upper sediment layers, and c^ and Cp are the shear speed and the compres- 

 sional speed in the basement. 



A typical ray path is shown on the right side of the figure. We can follow the path 

 of a ray using Snell's law, 



c(z) . , 



— -;^-T = cu = constant . 

 cos(7) n 



In Snell's law (c(z) is the sound speed at depth z, 7 is the grazing angle of the ray at depth 

 z and cj^) the horizontal phase speed of the ray is a constant for any given ray. Using 

 Snell's law, Cj^ can be determined by C|^ = c^/cos7|j and the depth at which the refracted 

 ray becomes horizontal, i.e., at the depth at which c(z) = Cj^. Figure 26 shows the re- 

 fracted ray turning over in the upper sediment layers so cj^ < C2 because the ray with 

 cj^ = C2 will become horizontal at the interface between the upper sediment layers and the 

 basement. The Stoneley wave can exist at the interface between the upper sediment layers 

 and the basement when excited by waves which have a certain relationship between fre- 

 quency and horizontal phase speed. This relation is called a dispersion equation. The high 

 losses at low frequency and low grazing angles are caused by a coupling of energy from 



56 



