On the inverse scattering problem in the acoustic environment

Yu Chen, Ran Duan, Vladimir Rokhlin

Research output: Contribution to journalArticle

Abstract

In this paper, we construct numerical algorithms for the solution of inverse scattering problems in layered acoustic media. Our inverse scattering schemes are based on a collection of so-called trace formulae. The speed c of propagation of sound, the density ρ, and the attenuation γ are the three parameters reconstructed by the algorithm, given that all of them are laterally invariant. For a medium whose parameters c, ρ, and γ have m ≥ 1 continuous derivatives, and data measured for frequencies between 0 and a > 0, the error of our scheme decays as 1 / am - 1 as a → ∞. In this respect, the algorithm is similar to the Fourier Transform. Our results are illustrated with several numerical examples.

Original languageEnglish (US)
Pages (from-to)3209-3231
Number of pages23
JournalJournal of Computational Physics
Volume228
Issue number9
DOIs
StatePublished - May 20 2009

Fingerprint

inverse scattering
Acoustics
Scattering
acoustics
Fourier transforms
attenuation
Acoustic waves
Derivatives
propagation
decay

Keywords

  • Acoustic
  • Helmholtz
  • Impedance
  • Inverse scattering
  • Trace formulae

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy (miscellaneous)

Cite this

On the inverse scattering problem in the acoustic environment. / Chen, Yu; Duan, Ran; Rokhlin, Vladimir.

In: Journal of Computational Physics, Vol. 228, No. 9, 20.05.2009, p. 3209-3231.

Research output: Contribution to journalArticle

Chen, Yu ; Duan, Ran ; Rokhlin, Vladimir. / On the inverse scattering problem in the acoustic environment. In: Journal of Computational Physics. 2009 ; Vol. 228, No. 9. pp. 3209-3231.
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