On the inverse scattering problem in the acoustic environment

  • Authors:

  • Yu Chen;Ran Duan;Vladimir Rokhlin

  • Affiliations:

  • Departments of Mathematics, Courant Institute, New York University, New York, NY 10012, USA;Departments of Physics, Yale University, 217 Prospect Street, New Haven, CT 06511, USA;Departments of Computer Science, Mathematics and Physics, Yale University, New Haven, CT 06511, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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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 @r, and the attenuation @c are the three parameters reconstructed by the algorithm, given that all of them are laterally invariant. For a medium whose parameters c,@r, and @c have m=1 continuous derivatives, and data measured for frequencies between 0 and a0, the error of our scheme decays as 1/a^m^-^1 as a-~. In this respect, the algorithm is similar to the Fourier Transform. Our results are illustrated with several numerical examples.