## 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 / a^{m - 1} as a → ∞. In this respect, the algorithm is similar to the Fourier Transform. Our results are illustrated with several numerical examples.

Original language | English (US) |
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Pages (from-to) | 3209-3231 |

Number of pages | 23 |

Journal | Journal of Computational Physics |

Volume | 228 |

Issue number | 9 |

DOIs | |

State | Published - May 20 2009 |

## Keywords

- Acoustic
- Helmholtz
- Impedance
- Inverse scattering
- Trace formulae

## ASJC Scopus subject areas

- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- General Physics and Astronomy
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics