Determining a Multi-layered Fluid-solid Medium from the Acoustic Measurements

Consider the inverse problem of recovering a multi-layered fluid-solid medium from many acoustic measurements corresponding to time-harmonic acoustic plane waves. We prove that both the supports of the embedded solid obstacle and the surrounding layered fluid medium can be uniquely identified by means of acoustic far-field pattern for all incident wave fields at a fixed frequency. Our proof is based on the constructions of some well-posed partial differential equation systems in sufficiently small domains combined with the a priori estimates for the solutions of the forward scattering problem.