Abstract
In this chapter, we will consider some simple models of the shallow water waveguide. Such models allow us to obtain and understand the main features of SW sound propagation quickly. Such simple models can also be perturbed to take into account more realistic properties of the environment, thus giving them far more power than one might think at first.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The dependence of density on the spatial coordinates can be easily taken into account using a change of functions (see Sect. 3.3). The possibility of some depth dependence of the bottom properties is also discussed.
- 2.
This field is the Green function of the waveguide, determined by the general equation (A.162); in what follows, when not required in the problem, we shall omit the arguments \( {\vec{R}_0},\,\omega \).
- 3.
The function \( g(\xi ) \) is related to the impedance of the bottom\( {Z_1} \) by the equation \( g(\xi ) = i{Z_1}{/}\omega \rho \), where the impedance is defined according to Brekhovskikh (1980); the change in sign from Brekhovskikh (1980) is due to the direction of the z-axis. It also is related to the bottom reflection coefficient by \( V = {{{( {g\sqrt {{{k^2}(H) - {\xi^2}}} + i})}} / {{({g\sqrt {{{k^2}(H) - {\xi^2}}} - i})}}.} \)
- 4.
In other sections we shall neglect the contribution of the continuous spectrum, and the notation \( \Psi \) will be used for the field generated by the discrete spectrum.
- 5.
Strictly speaking we should write for every vertical mode \( {x_l}(y) \) and \( {y_l}(x) \). However, for simplicity we will omit subscript.
References
Apel J.R., Badiey M., Berson J. et al. (1997) An overview of the 1995 SWARM shallow-water internal wave acoustic scattering experiment. IEEE J. Oceanic Eng. V.22(3), pp. 465–500.
Badiey, M., Katsnelson, B., Lynch, J., Pereselkov S., Siegmann, W., (2005) Measurement and modeling of 3-D sound intensity variations due to shallow water internal waves, J. Acoust. Soc. Am., Vol. 117, No. 2, pp. 613–625
Barridge R., Weinberg G. (1977) Horizontal rays and vertical modes In: Wave propagation and underwater acoustics, ed J.B. Keller and J.S. Papadakis [Springer-Verlag, pp. 86–150]
Brekhovskikh L.M. (1980) Waves in layered media, 2nd Ed. [Academic Press, New York]
Brekhovskikh L.M. and Lysanov Yu.P. (1991) Fundamentals of Ocean Acoustics [Springer-Verlag, 270 p.]
Buckingham M.J. (1980) A theoretical model of ambient noise in a low loss, shallow water channel [J. Acoust. Soc. Am., Vol. 67(4), pp. 1186–1192]
Burov V.A., Sergeev S.N. (1991) Processing of acoustic fields in oceanic waveguides with compensation of an unknown distortion of the profile of the vertical receiving antenna In Formation of acoustic fields in waveguides [Nizhnii Novgorod: Izd-vo IPF AN SSSR, p. 214–218] (in Russian)
Burov V.A., Sergeev S.N. (1992) Modern methods of perturbation theory in calculation of hydroacoustic fields [Vestn. Mosk. un-ta Seriya 3, Vol. 33(2), pp. 49–56] (in Russian)
DeSanto J.A. (ed) (1979) Ocean Acoustics [Springer-Verlag]
Doolittle R., Tolstoy A., Buckingham M. (1988) Experimental confirmation of horizontal refraction of cw acoustic radiation from a point source in wedge-shaped ocean environment [J. Acoust. Soc. Am., Vol. 83(6), pp. 2117–2125]
Fock V.A. (1965), Electromagnetic Diffraction and Propagation Problems. Pergamon, New York, pp. 213–234.
Frisk G.V. (1988) Inverse methods in ocean bottom acoustics [WHOI, Woods Hole, MA, USA, 32 p]
Frisk G.V., (1994) “Ocean and Seabed Acoustics”, Prentice Hall, Saddle River, N.J., 299 pp
Gazarian Yu.L. (1958) The sound field generated by a point source in a lying on a half-space [Sov. Phys. Acoust., Vol. 4(3), pp. 237–242]
Gindler I.V. (1990) Perturbation theory for plane-layered open acoustic waveguides [Sov. Phys. Acoust., vol. 36(4), pp. 349–352]
Jensen F.B. (1981) Sound propagation in shallow water [J. Acoust. Soc. Am. Vol. 70(5), pp. 1397–1406]
F. Jensen, W. Kuperman, M. Porter, and H. Schmidt, (1994). “Computational Ocean Acoustics”, AIP Press, 612 pages
G. Jin, Lynch, J.F., Chiu, C.S. and Miller, J.H. (1996) “A theoretical and simulation study of acoustic normal mode coupling effects due to the Barents Sea Polar Front, with applications to acoustic tomography and matched-field processing.” J. Acoust. Soc. Am. Volume 100, Issue 1, pp. 193–205.
Katsnelson B.G., Pereselkov (2000) Horizontal refraction of low frequency sound field due to soliton packets in shallow water. Acoustical Physics
B. Katsnelson, J. Lynch and A. Tsoidze, (2007),“Space-frequency distribution of sound field intensity in the vicinity of a temperature front in shallow water”, [Acoustical Physics, 53(5), 611–617].
Kravtsov Yu.A., Kuz’kin V.M., Petnikov V.G. (1984) Perturbation calculation of the horizontal refraction of sound waves in a shallow sea [Sov. Phys. Acoust., Vol. 30(1), pp. 45–47]
Kravtsov Yu.A., Kuz’kin C.M., Petnikov V.G. (1984) Wave diffraction by regular scatterers in multimode waveguides [Sov. Phys. Acoust., Vol. 30(3), pp. 199–202]
Kravtsov Yu.A., Kuz’kin V.M. and Petnikov V.G. (1988) Resolvability of rays and modes in an ideal waveguide [Sov. Phys. Acoust., vol. 34(4), pp. 387–390]
Kravtsov Yu.A., Orlov Yu.I. (1990) Geometrical optics of inhomogeneous media [Springer-Verlag]
Kuperman W.A., Ferla M.C. (1985) A shallow water experiment to determine the source spectrum level of wind generated noise [J. Acoust. Soc. Am.., Vol. 77(6), pp. 2067– 2073]
Leontovich M.A., and Fock V.A., (1946) “Solution of the problem of propagation of electromagnetic waves along the earth’s surface by the method of parabolic equation,” J. Exp. Theor. Phys. 16, pp 557–573
Lynch J.L., Jin G., Pawlowich R., Ray D., Plueddemann A.J., Chlu C., Miller J.H., Bourke R.H., Parsons A.R., Muench R. (1996) Acoustic travel-time perturbations due to shallow water internal waves and tides in the Barents Sea polar front: theory and experiment [J. Acoust. Soc. Am., Vol. 99(2), pp. 803–821]
Munk, W., and C. Wunsch (1983), Ocean Acoustic Tomography: Rays and Modes, Rev. Geophys., 21(4), 777–793.
Ocean acoustics (ed) L.M. Brekhovskikh. (1974) Moscow, Nauka, in Russian
Pekeris C.L. (1948) Theory of propagation of explosive sound in shallow water [Geol. Soc. Am. Mem., Vol. 27, pp. 1–117]
Rajan S.D., Lynch J.F., Frisk G.V. (1987) Perturbative inversion methods for obtaining bottom geoacoustic parameters in shallow water [J. Acoust. Soc. Am., Vol. 82(3), pp. 998– 1017]
Schiff L., (1968) “Quantum Mechanics.” McGraw-Hill, New York NY. 544 pages.
Stickler D.C, Ammicht E. (1980) Uniform asymptotic evaluation of the continuous spectrum contribution for the Pekeris model [J. Acoust. Soc. Am., Vol. 67(6), p. 2018– 2024]
Tappert F.D. (1977), “The parabolic approximation method,” in Wave Propagation and Underwater Acoustics, edited by J. B. Keller and J. S. Papadakis, Lecture Notes in Physics 70 Springer-Verlag, New York
Tindle C.T., Stamp, A.P, and Guthrie, K.M. (1976), “Virtual modes and the surface boundary condition in underwater acoustics.” [Journal of Sound and Vibration, Volume 49, Issue 2, p. 231–240].
Turbiner A.V. (1984) The eigenvalue spectrum in quantum mechanics and the nonlinearisation procedure [Sov. Phys. Uspekhi, Vol. 27(9), pp. 668–694]
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Katsnelson, B., Petnikov, V., Lynch, J. (2012). Foundations of the Theory of Propagation of Sound. In: Fundamentals of Shallow Water Acoustics. The Underwater Acoustics Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-9777-7_3
Download citation
DOI: https://doi.org/10.1007/978-1-4419-9777-7_3
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-9776-0
Online ISBN: 978-1-4419-9777-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)