By Hans A Bethe; A Guran; Herbert Überall; et al
Read Online or Download Acoustic interactions with submerged elastic structures. : Part III, Acoustic propagation and scattering, wavelets, and time frequency analysis a Herbert Überall festschrift volume PDF
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Additional info for Acoustic interactions with submerged elastic structures. : Part III, Acoustic propagation and scattering, wavelets, and time frequency analysis a Herbert Überall festschrift volume
6 RANGE (km) 1.. 0 Figure 3b. Predicted propagation field by S A F A R I for 30Hz signal. 2 36 J. 7. /true%o, J. Yuan, 77. MteraH a"^ R". CAottyam i- n. 2 Figure 3c. Predicted propagation-field by K R A K E N C for 30Hz signal. Figure 3d. Predicted propagation field by FEPES for 30Hz signal Figure 3a is a contour plot using the 30Hz measured transmission loss data as a function of range and depth. Figures 3b, 3c, and 3d are the estimated propagation according to SAFARI. K R A K E N C , and FEPES, respectively.
The highest frequency of 30Hz can excite a total of four trapped modes as shown in Figure 1. For this same case S A F A R I displayed the possible existence of at least one additional m o d e as shown by the peaks of the integrand in Figure 2. This mode is part of the radiating spectrum and it is not possible to detect it by K R A K E N C . This additional contribution is of much concern when using K R A K E N C in this case because the ranges are relatively short. The m i n i m u m range of one kilometer is about seven times the water depth.
Since the integrand oscillates rapidly w e approximate the integral by assuming that the amplitude of the integrand is constant and given by its value at 0J^. (x-xl) ^y The integrals in this expression can be evaluated exactly to give (23) vi ^ fU! 1 '^ fL" 1 '^ This result shows that a reflection coefficient must be applied to each image source with the amplitude of the reflection coefficient determined by the angle of incidence on each surface between each source and the observer. This corresponds to using a ray tracing approach in which each ray is specularly reflected from the bottom with an amplitude reduction corresponding to the reflection coefficient for the angle of incidence of the ray.
Acoustic interactions with submerged elastic structures. : Part III, Acoustic propagation and scattering, wavelets, and time frequency analysis a Herbert Überall festschrift volume by Hans A Bethe; A Guran; Herbert Überall; et al