  This paper is concerned with the problem of scattering of time-harmonic
acoustic waves from an impenetrable obstacle in a piecewise homogeneous medium.
The well-posedness of the direct problem is established, employing the integral
equation method and then used, in conjunction with the representation in a
combination of layer potentials of the solution, to prove a priori estimates of
solutions on some part of the interface between the layered media. The inverse
problem is also considered in this paper. An uniqueness result is obtained for
the first time in determining both the penetrable interface and the
impenetrable obstacle with its physical property from a knowledge of the far
field pattern for incident plane waves. In doing so, an important role is
played by the a priori estimates of the solution for the direct problem.
