On the inverse scattering problem in the acoustic environment

JOURNAL OF COMPUTATIONAL PHYSICS

卷:228

Article

Chen, Yu²  Duan, Ran¹  Rokhlin, Vladimir^3,4 

[1] Yale Univ, Dept Phys, New Haven, CT 06511 USA

[2] NYU, Courant Inst, Dept Math, New York, NY 10012 USA

[3] Yale Univ, Dept Comp Sci, New Haven, CT 06511 USA

[4] Yale Univ, Dept Math & Phys, New Haven, CT 06511 USA

关键词: Inverse scattering;    Helmholtz;    Impedance;    Trace formulae;    Acoustic;   

DOI  :  10.1016/j.jcp.2008.12.034

来源: Elsevier

【 摘 要 】

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 rho, and the attenuation gamma are the three parameters reconstructed by the algorithm, given that all of them are laterally invariant. For a medium whose parameters c, rho, and gamma have m >= 1 continuous derivatives, and data measured for frequencies between 0 and a > 0, the error of our scheme decays as 1/a(m-1) as a -> infinity. In this respect, the algorithm is similar to the Fourier Transform. Our results are illustrated with several numerical examples. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free