Low frequency elastic wave scattering by an inclusion: Limits of applications

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The present investigation considers various approximations for the problem of low frequency elastic waves scattered by a single, small inclusion of constant elastic parameters. For the Rayleigh approximation containing both near and far field terms, the scattered amplitudes are investigated as a function of distance from the scatterer. Near field terms are found to be dominant for distances up to two wavelengths, after which far field solutions correctly describe the scattered field. At a distance of two wavelengths the relative error between the total and the far field solution is about 15% and decreases with increasing, distance. Deriving solutions for ... continued below

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31 p.

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Gritto, R.; Korneev, V.A. & Johnson, L.R. May 1, 1995.

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Description

The present investigation considers various approximations for the problem of low frequency elastic waves scattered by a single, small inclusion of constant elastic parameters. For the Rayleigh approximation containing both near and far field terms, the scattered amplitudes are investigated as a function of distance from the scatterer. Near field terms are found to be dominant for distances up to two wavelengths, after which far field solutions correctly describe the scattered field. At a distance of two wavelengths the relative error between the total and the far field solution is about 15% and decreases with increasing, distance. Deriving solutions for the linear and quadratic Rayleigh-Born approximation, the relative error between the nonlinear Rayleigh approximation and the linear and quadratic Rayleigh-Born approximation as a function of the scattering angle and the parameter perturbation is investigated. The relative error reveals a strong dependence on the scattering angle, while the addition of the quadratic term significantly improves the approximation for all scattering angles and parameter perturbations. An approximation for the error caused by linearization of the problem, based entirely on the perturbations of the parameters from the background medium, and its validity range given. We also investigate the limit of the wave parameter for Rayleigh scattering and find higher values than previously assumed. By choosing relative errors of 5%, 10% and 20% between the exact solution and the Rayleigh approximation, we find the upper limits for the parameter k{sub p}R to be 0.55, 0.7 and 0.9, respectively.

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31 p.

Notes

OSTI as DE95015140

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  • Other Information: PBD: May 1995

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  • Other: DE95015140
  • Report No.: LBL--37238
  • Grant Number: AC03-76SF00098
  • DOI: 10.2172/94647 | External Link
  • Office of Scientific & Technical Information Report Number: 94647
  • Archival Resource Key: ark:/67531/metadc793428

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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Creation Date

  • May 1, 1995

Added to The UNT Digital Library

  • Dec. 19, 2015, 7:14 p.m.

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  • April 5, 2016, 10:18 a.m.

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Gritto, R.; Korneev, V.A. & Johnson, L.R. Low frequency elastic wave scattering by an inclusion: Limits of applications, report, May 1, 1995; California. (digital.library.unt.edu/ark:/67531/metadc793428/: accessed December 17, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.