  This paper is concerned with the inverse problem of scattering of
time-harmonic acoustic waves from a penetrable and buried obstacles. By
introducing a related transmission scattering problem, a Newton iteration
method is proposed to simultaneously reconstruct both the penetrable interface
and the buried obstacle inside from far-field data. A main feature of our
method is that we do not need to know the type of boundary conditions on the
buried obstacle. In particular, the boundary condition on the buried obstacle
can also be determined simultaneously by the method. Finally, numerical
examples using multi-frequency data are carried out to illustrate the
effectiveness of our method.
