This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle with buried objects inside. We prove under certain conditions that the factorization method can be applied to reconstruct the penetrable obstacle from far-field data without knowing the buried objects inside. Numerical examples are also provided illustrating the inversion algorithm.
Introduction.In this paper, we study the problem of scattering of timeharmonic acoustic plane waves by an inhomogeneous penetrable obstacle with buried objects inside. This type of problem occurs in various applications such as radar, remote sensing, geophysics, medical imaging, and nondestructive testing. Let D 0 denote an impenetrable obstacle which is embedded in a bounded, penetrable obstacle D with C 2 -boundary ∂D, that is, D 0 ⊂ D. Assume that D 1 := D \ D 0 is filled with an inhomogeneous material characterized by the refractive index n ∈ L ∞ (D 1 ) with Re[n(x)] > 0 and Im[n(x)] ≥ 0 for almost all x ∈ D 1 and D 2 := R 3 \ D is filled with a homogeneous material with the constant refractive index 1. Then the scattering of time-harmonic acoustic waves by D and D 0 can be modeled by the Helmholtz equation with boundary conditions on the interface ∂D and boundary ∂D 0 :