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Mathematical Methods in Elasticity Imaging$
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Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

Print publication date: 2015

Print ISBN-13: 9780691165318

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691165318.001.0001

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Backpropagation and Multiple Signal Classification Imaging of Small Inclusions

Backpropagation and Multiple Signal Classification Imaging of Small Inclusions

(p.80) Chapter Five Backpropagation and Multiple Signal Classification Imaging of Small Inclusions
Mathematical Methods in Elasticity Imaging

Habib Ammari

Elie Bretin

Josselin Garnier

Hyeonbae Kang

Hyundae Lee

Abdul Wahab

Princeton University Press

This chapter deals with direct imaging of small inclusions and cracks in the static regime, focusing on MUSIC- and migration-type algorithms for detecting the small defects. MUSIC, reverse-time migration, and Kirchhoff migration algorithms take advantage of the smallness of the elastic inclusions. Even though only the two-dimensional case is considered, the same algorithms can be applied in three dimensions. These direct location search algorithms are extended to the general case of linear isotropic elasticity. After describing least-squares algorithms for locating small elastic inclusions, the chapter introduces a MUSIC-type location search algorithm in the static regime and extends it to the time-harmonic regime. It also performs three-dimensional simulations to illustrate relevant features of the MUSIC algorithm.

Keywords:   direct imaging, small inclusion, crack, static regime, reverse-time migration, Kirchhoff migration, elastic inclusion, search algorithm, time-harmonic regime, MUSIC algorithm

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