Inverse scattering for inhomogeneous viscoelastic media

In this paper, the inverse scattering problems for the full inhomogeneous v iscoelastic medium are studied via the invariant imbedding technique. Speci al attention is paid to the propagation operators of the viscoelastic mediu m and the imbedding equations for these operators are derived. For the inve rse scattering problems, it is shown that the reflection data can be extend ed from one round trip through the iscoelastic slab to arbitrary time with the help of the propagation operators, hence the reconstruction of the rela xation modulus is sufficient to be considered only in one round trip. It is also shown that only one-side measurement reflection data are not sufficie nt to reconstruct the relaxation modulus and the density of the medium simu ltaneously. The corresponding numerical examples are presented. For the cas e that the relaxation modulus of the medium is modeled by two independent f unctions, an iterative inversion procedure is proposed to recover the relax ation modulus and the density simultaneously with the input two-side normal ly reflection data. (C) 2000 American Institute of Physics. [S0022-2488(00) 06705-0].