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 language | English (US) |
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Article number | 007 |
Pages (from-to) | 1467-1493 |
Number of pages | 27 |
Journal | Inverse Problems |
Volume | 23 |
Issue number | 4 |
DOIs | |
State | Published - Aug 1 2007 |