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Eigenproblem for an ocean acoustic waveguide with random depth dependent sound speed

Published in Institute of Electrical and Electronics Engineers Inc.

2014

A recently developed deterministic FE model for range and depth dependent acoustic waveguides (Vendhan et al, J. Acoust. Am., 126, 3319-3326, 2010) may be extended to a medium with random properties. Such a model would require the eigensolution for a depth dependent waveguide at the far field of the FE domain. The aim of the present paper is to study the depth eigenproblem with random sound speed, which may be written as d2Z/dz2 + (1/k1z)Z = 0 (1) where z denotes the depth coordinate, Z(z) the depth function and kz the depth wavenumber given by k2z = (ω2/c2(z)-k1r) (2) In Eq.2, r k denotes the radial wavenumber of a cylindrically symmetric waveguide and c(z) the sound speed which is assumed to be random variable in the form c(z) = c (z) (1+a) where a denotes a small random fluctuation of the sound speed with c(z)as the mean value. The depth eigenmodes of a deterministic isovelocity waveguide are adopted to set up a Rayleigh-Ritz approximation for the depth eigenproblem (see Eq.1) in the form [K]{ψ} = λ [M]{ψ} (3) Choosing a perturbation approach (Nakagiri and Hisada, Proc. Intl. Conf. on FEM, 206-211, 1982; Ghanem and Spanos, Stochastic Finite Elements: A Spectral Approach, Springer Verlag, 1991) an approximate solution may be written in the form of a Taylor series as [M] = [M] + α [M1] + α2/2[M2] (4a)λ = λ + αλ1 + (α2/2)λ2 (4b){ψ} = {ψ} + α{ψ1} + α2/2{ψ2} (4c) where an over bar denotes deterministic quantity. © 2014 IEEE.

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About the journal

Journal | Data powered by Typeset2014 USNC-URSI Radio Science Meeting (Joint with AP-S Symposium), USNC-URSI 2014 - Proceedings |
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Publisher | Data powered by TypesetInstitute of Electrical and Electronics Engineers Inc. |

Open Access | No |

Concepts (12)

- Stochastic systems
- Ultrasonic velocity measurement
- Waveguides
- ACOUSTIC WAVEGUIDES
- Approximate solution
- DETERMINISTIC QUANTITY
- PERTURBATION APPROACH
- RANDOM FLUCTUATION
- RANDOM PROPERTIES
- STOCHASTIC FINITE ELEMENTS
- SYMMETRIC WAVEGUIDES
- Eigenvalues and eigenfunctions