Recovering an elastic obstacle containing embedded objects by the acoustic far-field measurements. (12th December 2017)

• Record Type: Journal Article
• Authors: Qu, Fenglong; Yang, Jiaqing; Zhang, Bo
• Is Part Of: Inverse problems. Volume 34:Number 1(2018:Jan.)
• Publication Date: 2017-12-12
• Subjects: inverse scattering -- uniqueness -- fluid-solid interaction -- far-field pattern -- embedded obstacles; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa9c26
• Languages: English
• ISSNs: 0266-5611

Abstract

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).