Variation of ocean environmental parameters is important to sound ray propagation. This article studies the problem of sound ray propagation in seawater by BELLHOP ray model. The sensitivities of sound ray propagation to the variations of seabed topography and depth of sound source by simulation. The results show that the depth variation of sound source is the main cause for emerging and disappearing of surface sound channel, accumulation area and deep sound channel. The deviation of sound ray propagation is in accordance with seabed topography change.
Sound Ray Propagation; Distance Correlation; Ray Model; Simulation1. Introduction
When propagating in seawater, sound ray may be affected by environmental factors such as sea surface and submarine boundary. The study of sound ray propagation in seawater is mainly ray theory. Sound wave propagation in seawater is looked up as sound ray propagation in medium in the context of high frequency. The change of sound intensity, the time and distance of sound ray propagation in space are mainly studied. Ray acoustics is an approximate method, which is only for the sound wave of high frequency. But in many cases, this method is effective and effective to solve the problem in seawater [1].
Modeling and Simulating of sound wave propagation is important to sonar’s using and optimum designing in water. There are already some simulating study reports on sea sound propagation effect and characteristic of sound channel under perfect environment [2,3].
2. Numerical Model of Acoustic Propagation
To simulation study the difference of sound channel in different condition frames; it is emulational calculated the difference of sound channel by BELLHOP radial model. BELLHOP model by Gaussian approximate method, which was brought out by Porter, etc. [4], deals preferably with energy caustic and absolute shadow zone.
Supposing the sound pressure P on some sound ray propagation is:
is circumference ratio, A is amplitude on the direction of sound ray, is influence function which is perpendicular to the direction of sound ray, s is arc length on the direction of sound ray, n is displacement which is perpendicular to the direction of sound ray centre, is time of sound ray propagation.
In case of cylindrical coordinates, control equations of sound ray propagation are [5]:
and r is horizontal distance, z is horizontal depth, and are two middle variables which have relationship of grazing angle, ,.
3. Simulation Calculation of Sound Ray Spreading Related with Distance
In BELLHOP model, supposing the sound velocity profile is like Figure 1, emulation calculated is under the condition of changing the environmental factors. When upslope, sound source is set as 50 m, 500 m, 1500 m and 4000 m under water; angle of incidence is 1˚, 3˚, 5˚, 8˚, respectively; frequency of sound wave is 1000 Hz; submarine substrate is silt, in accordance with the parameter of geoacoustics by Hamilton [6], substrate parameter: density is, compressional velocity is 1623 m/s, compressional attenuation coefficient is 0.673 dB/kHz; Y
is vertical depth, unit is meter (m), X is horizontal distance, unit is kilometer (km).
When downslope, case 1: sound source is set as 50 m under water, angle of incidence is 1˚, 3˚, 5˚, 8˚, respecttively, frequency of sound wave is 1000 Hz, submarine substrate is silt, Y is vertical depth, unit is meter (m), X is horizontal distance, unit is kilometer (km); case 2: sound source is set as 50 m under water, angle of incidence is –2˚, –1˚, 1˚, 2˚. Frequency of sound wave is 1000 Hz, submarine substrate is silt, Y is vertical depth, unit is meter (m), X is horizontal distance, and unit is kilometer (km).
When wavy terrain, case 1: sound source is set as 50 m, 500 m, 1500 m and 3000 m under water, angle of incidence is 1˚, 3˚, 5˚, 8˚, respectively, frequency of sound wave is 1000 Hz, submarine substrate is silt, Y is vertical depth, unit is meter (m), X is horizontal distance, unit is kilometer (km); case 2: sound source is set as 50 m under water, angle of incidence is –2˚, –1˚, 1˚, 2˚, Frequency of sound wave is 1000 Hz, submarine substrate is silt, Y is vertical depth, unit is meter (m), X is horizontal distance, and unit is kilometer (km).
4. Analysis of Simulation Result
Figure 1 is sound velocity profile. Figures 2-6, Figures 9-12 are the sound ray pictures of upslope and downslope under the conditions of different sound depths by emulation calculation. Figures 7-8 are the sound ray pictures of downslope under the conditions of two sound ray angles. Figure 9 and Figure 13 are the sound ray pictures of wavy terrain under the conditions of two sound ray angles.
ReferencesB. S. Liu and J. Y. Lei, “Hydroacoustics Theory,” 2nd Edition, Harbin Engineering University Press, Harbin, 2010.J. Wang, J. G. Huang and J. Guan, “Wave Guide Modeling and Simulation for Underwater Acoustic Propagation,” Journal of System Simulation, Vol. 13, No. 1, 2001, pp. 37- 39.Y. Z. Dong, X. M. Xu, P. X. Liu, et al., “Study on Modeling of Shallow Water Acoustic Channel and Its Applications,” Journal of System Simulation, Vol. 22, No. 1, 2010, pp. 47-55.M. B. Porter and H. P. Bucher, “Gaussian Beam Tracing for Computing Ocean Acoustic Fields,” Journal of the Acoustical Society of America, Vol. 82, No. 4, 1987, pp. 1349-1359. doi:10.1121/1.395269F. B. Jensen, W. A. Kuperman, M. B. Porter, et al., “Computational Ocean Acoustics,” American Institute of Phys- ics Press, College Park, 1944.E. L. Hamilton, “Geoacoustic Modeling of the Sea Floor,” Journal of the Acoustical Society of America, Vol. 68, No. 5, 1980, pp. 1313-1340. doi:10.1121/1.385100
is circumference ratio, A is amplitude on the direction of sound ray, 
is influence function which is perpendicular to the direction of sound ray, s is arc length on the direction of sound ray, n is displacement which is perpendicular to the direction of sound ray centre, 
is time of sound ray propagation.
and 
are two middle variables which have relationship of grazing angle, 
,
.
, compressional velocity is 1623 m/s, compressional attenuation coefficient is 0.673 dB/kHz; Y