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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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Time-Reversal Imaging of Extended Source Terms

Time-Reversal Imaging of Extended Source Terms

(p.125) Chapter Eight Time-Reversal Imaging of Extended Source Terms
Mathematical Methods in Elasticity Imaging

Habib Ammari

Elie Bretin

Josselin Garnier

Hyeonbae Kang

Hyundae Lee

Abdul Wahab

Princeton University Press

This chapter describes the use of time-reversal imaging techniques for extended source terms from far-field measurements. A target or a source term is called extended when its characteristic size times the operating frequency (wavenumber) is considerably larger than one. For the scalar wave equation, the main idea of time reversal is to take advantage of its reversibility in order to backpropagate signals to the sources that emitted them. The chapter focuses on the homogeneous isotropic elastic wave equation in a d-dimensional open medium with d = 2, 3. It first reconstructs shape changes of an extended target before introducing a number of algorithms and analyzing their resolution and stability for the linearized reconstruction problem. Finally, it discusses optimal control approaches for solving the nonlinear problem.

Keywords:   time-reversal imaging, extended source term, far-field measurement, scalar wave equation, elastic wave equation, shape change, extended target, linearized reconstruction problem, optimal control, nonlinear problem

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