A linear sampling approach to inverse elastic scattering in piecewise-homogeneous domains

Bojan B. Guzina, Andrew I. Madyarov

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20 Scopus citations

Abstract

The focus of this study is a 3D inverse scattering problem underlying non-invasive reconstruction of piecewise-homogeneous (PH) defects in a layered semi-infinite solid from near-field, surface elastic waveforms. The solution approach revolves around the use of Green's function for the layered reference domain and a generalization of the linear sampling method to deal with the featured class of PH configurations. For a rigorous treatment of the full-waveform integral equation that is used as a basis for obstacle reconstruction, the developments include an extension of the Holmgren's uniqueness theorem to piecewise-homogeneous domains and an in-depth analysis of the situation when the sampling point is outside the support of the obstacle that employs the method of topological sensitivity. Owing to the ill-posed nature of the featured integral equation, a stable approximate solution is sought via Tikhonov regularization. A set of numerical examples is included to demonstrate the feasibility of 3D obstacle reconstruction when the defects are buried in a multi-layered elastic solid.

Original languageEnglish (US)
Article number007
Pages (from-to)1467-1493
Number of pages27
JournalInverse Problems
Volume23
Issue number4
DOIs
StatePublished - Aug 1 2007

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