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Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.10 P.1463~1472

http://doi.org/10.1631/jzus.A0720064


Mathematical treatment of wave propagation in acoustic waveguides with n curved interfaces


Author(s):  Jian-xin ZHU, Peng LI

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   zjx@zju.edu.cn

Key Words:  Helmholtz equation, Local orthogonal transform, Dirichlet-to-Neumann (DtN) reformulation, Marching method, Curved interface, Multilayer medium


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Jian-xin ZHU, Peng LI. Mathematical treatment of wave propagation in acoustic waveguides with n curved interfaces[J]. Journal of Zhejiang University Science A, 2008, 9(10): 1463~1472.

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author="Jian-xin ZHU, Peng LI",
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T1 - Mathematical treatment of wave propagation in acoustic waveguides with n curved interfaces
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DOI - 10.1631/jzus.A0720064


Abstract: 
There are some curved interfaces in ocean acoustic waveguides. To compute wave propagation along the range with some marching methods, a flattening of the internal interfaces and a transforming equation are needed. In this paper a local orthogonal coordinate transform and an equation transformation are constructed to flatten interfaces and change the helmholtz equation as a solvable form. For a waveguide with a flat top, a flat bottom and n curved interfaces, the coefficients of the transformed helmholtz equation are given in a closed formulation which can be thought of as an extension of the formal work related to the equation transformation with two curved internal interfaces. In the transformed horizontally stratified waveguide, the one-way reformulation based on the Dirichlet-to-Neumann (DtN) map is then used to reduce the boundary value problem to an initial value problem. Numerical implementation of the resulting operator Riccati equation uses a large range step method to discretize the range variable and a truncated local eigenfunction expansion to approximate the operators. This method is particularly useful for solving long range wave propagation problems in slowly varying waveguides. Furthermore, the method can also be applied to wave propagation problems in acoustic waveguides associated with varied density.

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Reference

[1] Evans, R., 1998. The flattened surface parabolic equation. J. Acoust. Soc. Am., 104(4):2167-2173.

[2] Jensen, F.B., Kuperman, W.A., Porter, M.B., Schmidt, H., 1994. Computational Ocean Acoustics. American Institute of Physics, New York.

[3] Lu, Y.Y., McLaughlin, J.R., 1996. The Riccati method for the Helmholtz equation. J. Acoust. Soc. Am., 100(3):1432-1446.

[4] Lu, Y.Y., Zhu, J.X., 2004. A local orthogonal transform for acoustic waveguides with an internal interface. J. Comput. Acoust., 12(1):37-53.

[5] Lu, Y.Y., Huang, J., McLaughlin, J.R., 2001. Local orthogonal transformation and one-way methods for acoustics waveguides. Wave Motion, 34(2):193-207.

[6] Tessmer, E., Kosloff, D., Behle, A., 1992. Elastic wave propagation simulation in the presence of surface topography. Geophys. J. Int., 108(2):621-632.

[7] Zhu, J.X., Li, P., 2007. Local orthogonal transform for a class of acoustic waveguide. Prog. Nat. Sci., 17(10):18-28.

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