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.
- Inverse scattering
- Trace formulae
ASJC Scopus subject areas
- Computer Science Applications
- Physics and Astronomy (miscellaneous)