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This paper is concerned with the inverse scattering of time-harmonic acoustic plane waves by a multi-layered fluid–solid medium in the three dimensional space. We establish the global uniqueness in identifying the embedded penetrable solid obstacle, the surrounding fluid medium and its wave number from the acoustic far-field pattern for all incident plane waves at a fixed frequency. The proof depends on constructing different kinds of interior transmission problems in appropriate small domains and the a priori estimates derived for both the elastic wave fields in the embedded solid obstacle and the acoustic wave fields in the surrounding fluid medium.

Consider the time-harmonic acoustic scattering of an incident point source inside an inhomogeneous cavity. By constructing an equivalent integral equation, the well-posedness of the direct problem is proved in $L^p$ with using the classical Fredholm theory. Motivated by the previous work [ 10 ], a novel uniqueness result is then established for the inverse problem of recovering the refractive index of piecewise constant function from the wave fields measured on a closed surface inside the cavity.

This paper is concerned with direct and inverse scattering by a locally perturbed infinite plane (called a locally rough surface in this paper) on which a Neumann boundary condition is imposed. A novel integral equation formulation is proposed for the direct scattering problem which is defined on a bounded curve (consisting of a bounded part of the infinite plane containing the local perturbation and the lower part of a circle) with two corners and some closed smooth artificial curve. It is a nontrivial extension of our previous work on direct and inverse scattering by a locally rough surface from the Dirichlet boundary condition to the Neumann boundary condition [{\em SIAM J. Appl. Math.}, 73 (2013), pp. 1811-1829]. In this paper, we make us of the recursively compressed inverse preconditioning (RCIP) method developed by Helsing to solve the integral equation which is efficient and capable of dealing with large wave numbers. For the inverse problem, it is proved that the locally rough surface is uniquely determined from a knowledge of the far-field pattern corresponding to incident plane waves. Further, based on the novel integral equation formulation, a Newton iteration method is developed to reconstruct the locally rough surface from a knowledge of multiple frequency far-field data. Numerical examples are also provided to illustrate that the reconstruction algorithm is stable and accurate even for the case of multiple-scale profiles.

Consider the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous medium with complex refractive index. We show that an approximate factorization method can be applied to reconstruct the support of the complex inhomogeneous medium from the far-field data. Numerical examples are also provided to illustrate the practicability of the inversion algorithm.

This paper is concerned with problems of scattering of time-harmonic electromagnetic and acoustic waves from an innite penetrable medium with a certain non-trapping and geometric conditions.