We consider acoustic scattering from an obstacle inside an inhomogeneo
us structure. We prove in the paper that if the outside inhomogeneity
is known then the obstacle and possible inside inhomogeneity are uniqu
ely determined by the fixed energy far field data. The proof is based
on new mapping properties of layer potentials in spaces that specify o
ne point. (C) 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.