On the inverse scattering problem in the acoustic environment

1 In this report, 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, and can be viewed as extension of the work started in [3]. 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 on the coordinate z. For a medium whose parameters c, ρ, and γ have m ≥ 1 continuous derivatives, and data measured for all frequencies ω on the interval [−a, a], the error of our scheme decays as 1/a m−1 as a → ∞. In this respect, our algorithm is similar to the Fourier Transform. Our results are illustrated with several numerical examples.