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Spherical-Shell Scattering Computations by Ordinary Exponentials

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The scattered field from a spherically symmetric object composed of concentric fluid and solid shells can be computed by spherical Bessel functions, by dividing each shell into homogeneous sub-shells. As recently shown in the seismological literature, however, wave propagation in the earth can be computed by ordinary exponentials by a division into particular sub-shells, in each of which the P- and S-velocities vary proportionally to the radius. Here, we adapt the exponential-function technique to scattering computations in underwater acoustics. For solid shells, boundary conditions can conveniently be transported by compound matrices. To enhance computational efficiency, each 6×6 compound matrix is factorized with sparse matrices, which are applied in sequence to the pertinent row vector entering from the left. The central compound-matrix factors, involving the exponential functions, become formally identical to corresponding matrices for the range-independent case.
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Document Type: Research Article

Publication date: 01 September 2002

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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