On the Far Field Pattern for Acoustic Scattering by a Piecewise Homogeneous Obstacle in Two Dimensions

A time-harmonic plane acoustic wave is scattered by a piecewise homogeneous obstacle with penetrable or impenetrable core. We construct in the close form an integral representation for far field pattern which we have incorporated physical and geometrical characteristics of scatterer. Through this representation, obtain prove scattering relations between patterns two problems due to distinct incident waves on same In particular, reciprocity general theorems. The optical theorem, connecting total power that scatterer extracts from either radiation absorption corresponding wave, recovered as corollary theorem. Moreover, if consider be both spherical, derive mixed define operators using these relations, some properties can used solving inverse problems.