Abstract: In this paper, the inverse problem for the viscoelastic medium is investigated in the time domain, in which the wave impedance of the medium is discontinuous at the rear interface. The differentio-integral equations governing the behavior of the scattering and propagation operators are utilized to reconstruct the relaxation modulus of the viscoelastic medium. A new approach, in which only the one-side measurement reflection data for one round trip through the viscoelastic layer, is developed. The numerical examples are given at the end of the paper. It is shown that the curves of the reconstructed moduli coincide very well with the original relaxation moduli.

Key words: viscoelastic medium, inverse scattering, inversion procedure, Volterra integral equation, relaxation modulus, one round trip, numerical examples