On the inverse scattering problem in the acoustic environment

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 ρρ, and the attenuation γγ are the three parameters reconstructed by the algorithm, given that all of them are laterally invariant. For a medium whose parameters c,ρc,ρ, and γγ have m⩾1m⩾1 continuous derivatives, and data measured for frequencies between 0 and a>0a>0, the error of our scheme decays as 1/am-11/am-1 as a→∞a→∞. In this respect, the algorithm is similar to the Fourier Transform. Our results are illustrated with several numerical examples.