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In this paper we study the inverse inhomogeneous penetrable obstacle scattering problems in a stratified medium. On the basis of the uniqueness and existence of solutions for the direct scattering by an inhomogeneous penetrable obstacle in a stratified medium, we first establish an a priori estimate of the solution on some part of the penetrable interfaces S i (i = 1, 2), which plays an important role in the inverse scattering problems, and then we prove that both the penetrable interfaces S idoi:10.1186/s13661-017-0747-3 fatcat:huaapbkcjbadnbintokdfautpy