Stable methods for an inverse problem in acoustic scattering by an obstacle and an inhomogeneous medium

摘要

AbstractWe consider (in two‐dimensional Euclidean space) the scattering of a plane, time‐harmonic acoustic wave by an inhomogeneous medium Ω with compact support and a bounded obstacleDlying completely outside of the inhomogeneous medium. We show that one may determine the shape ofDand the local speed of sound in Ω from a knowledge of the asymptotic behavior of the scattered wave (i.e. the far field). This is done by considering a constrained optimization problem and employing integral equation and conformal mapping techniques.By assuming a priori that the functions which determine the shape ofDand the local speed of sound in Ω lie in given compact sets, we show that the problem is stable, in the sense that the solution of the inverse scattering problem depends continuously on the far fiel