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Near-field Imaging Point-like Scatterers and Extended Elastic Solid in a Fluid

Part of:Equations of mathematical physics and other areas of applicationMiscellaneous topics - Partial differential equationsWaves

Published online by Cambridge University Press:  17 May 2016

Tao Yin,
Guanghui Hu and
Liwei Xu
Tao Yin*
Affiliation:
College of Mathematics and Statistics, Chongqing University, Chongqing 400044, P.R. China
Guanghui Hu*
Affiliation:
Beijing Computational Science Research Center, Beijing 100094, P.R. China
Liwei Xu*
Affiliation:
College of Mathematics and Statistics, Chongqing University, Chongqing 400044, P.R. ChinaInstitute of Computing and Data Science, Chongqing University, Chongqing 400044, P.R. China
*
Corresponding author., Email addresses:, taoyincqu@163.com(T. Yin), hu@csrc.ac.cn(G. Hu), xul@cqu.edu.cn(L. Xu)
Corresponding author., Email addresses:, taoyincqu@163.com(T. Yin), hu@csrc.ac.cn(G. Hu), xul@cqu.edu.cn(L. Xu)
Corresponding author., Email addresses:, taoyincqu@163.com(T. Yin), hu@csrc.ac.cn(G. Hu), xul@cqu.edu.cn(L. Xu)

Abstract

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Consider the time-harmonic acoustic scattering from an extended elastic body surrounded by a finite number of point-like obstacles in a fluid. We assume point source waves are emitted from arrayed transducers and the signals of scattered near-field data are recorded by receivers not far away from the scatterers (compared to the incident wavelength). The forward scattering can be modeled as an interaction problem between acoustic and elastic waves together with a multiple scattering problem between the extend solid and point scatterers. We prove a necessary and sufficient condition that can be used simultaneously to recover the shape of the extended elastic solid and to locate the positions of point scatterers. The essential ingredient in our analysis is the outgoing-to-incoming (OtI) operator applied to the resulting near-field response matrix (or operator). In the first part, we justify the MUSIC algorithm for locating point scatterers from near-field measurements. In the second part, we apply the factorization method, the continuous analogue of MUSIC, to the two-scale scattering problem for determining both extended and point scatterers. Numerical examples in 2D are demonstrated to show the validity and accuracy of our inversion algorithms.

Keywords

MUSCInear-field imagingpoint sourcesfactorization methodinverse scatteringfluid-solid interaction problem

MSC classification

Secondary:74J25: Inverse problems74J20: Wave scattering35R30: Inverse problems35Q74: PDEs in connection with mechanics of deformable solids

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 5 , May 2016, pp. 1317 - 1342
Copyright
Copyright © Global-Science Press 2016 

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