Recovering an elastic obstacle containing embedded objects by the acoustic far-field measurements

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 VII 20 57-92; Monk and Selgas 2009 Inverse Problems Imaging 3 173-98).

A novel method in determining a layered periodic structure

“…In this paper we intend to develop a novel method, which differs from the approach used in [34], to prove the uniqueness on the identification of the penetrable periodic structure in the three-dimensional space from the measured data only above the structure with respect to a countably infinite number of quasiperiodic incident plane waves. The technique developed in this paper can date back to the work [27,36] on the inverse scattering problems of determining the support of penetrable electromagnetic obstacles or to [28] for the fluid-solid interaction problem of identifying the bounded solid obstacle, [29] for the cavity scattering case.…”

Locating a complex inhomogeneous medium with an approximate factorization method

“…In the current paper, we are interested in the inverse problem of reconstructing the shape and location of the inhomogeneous medium D from a knowledge of the far-field pattern u ∞ for incident plane waves. The uniqueness of this inverse problem has been established in [25] for the case when n is an unknown constant, in [23] for the case when n is an unknown piecewise constant, and in [11,16,24] for other related inverse medium scattering problems.…”

The uniqueness of the inverse elastic wave scattering problem based on the mixed reciprocity relation

“…the impenetrable scattering, then for our main problem, i.e. inverse transmission elastic scattering problem (see [39] and [44]).…”