Recovering an elastic obstacle containing embedded objects by the acoustic far-field measurements. (12th December 2017) - Qu, Fenglong; Yang, Jiaqing; Zhang, Bo
Abstract: Consider the inverse scattering problem of time-harmonic acoustic waves by a 3D bounded elastic obstacle which may contain embedded impenetrable obstacles inside. We propose a novel and simple technique to show that the elastic obstacle can be uniquely recovered by the acoustic far-field pattern at a fixed frequency, disregarding its contents. Our method is based on constructing a well-posed modified interior transmission problem on a small domain and makes use of an a priori estimate for both the acoustic and elastic wave fields in the usual H 1 -norm. In the case when there is no obstacle embedded inside the elastic body, our method gives a much simpler proof for the uniqueness result obtained previously in the literature (Natroshvili et al 2000 Rend. Mat. Serie VII20 57–92; Monk and Selgas 2009 Inverse Problems Imaging 3 173–98).