Abstract
In this paper, the inverse scattering problems for the full inhomogeneous viscoelastic medium are studied via the invariant imbedding technique. Special attention is paid to the propagation operators of the viscoelastic medium and the imbedding equations for these operators are derived. For the inverse scattering problems, it is shown that the reflection data can be extended from one round trip through the iscoelastic slab to arbitrary time with the help of the propagation operators, hence the reconstruction of the relaxation modulus is sufficient to be considered only in one round trip. It is also shown that only one-side measurement reflection data are not sufficient to reconstruct the relaxation modulus and the density of the medium simultaneously. The corresponding numerical examples are presented. For the case that the relaxation modulus of the medium is modeled by two independent functions, an iterative inversion procedure is proposed to recover the relaxation modulus and the density simultaneously with the input two-side normally reflection data.
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