Simultaneous recovery of a locally rough interface and its buried obstacles and homogeneous medium

Consider the inverse scattering of time--harmonic point sources by an infinite rough interface with buried obstacles in the lower half-space. The interface is assumed to be a local perturbation of a plane, which allows us to reduce the model problem to an equivalent integral equation formulation defined in a bounded domain. The well--posedness is thus obtained by employing the classical Fredholm theory. For the inverse problem, a global uniqueness theorem is established which shows that the locally rough interface, the wave number in the lower half-space and the buried obstacle can be uniquely determined by near-field data measured only above the interface.