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Published July 16, 2019 | Submitted + Published
Journal Article Open

Multifrequency Iterative Methods for the Inverse Medium Scattering Problems in Elasticity

Abstract

This paper concerns the reconstruction of multiple elastic parameters (Lamé parameters and density) of an inhomogeneous medium embedded in an infinite homogeneous isotropic background in ℝ^2. The direct scattering problem is reduced to an equivalent system on a bounded domain by introducing an exact transparent boundary condition and the well-posedness of the corresponding variational problem is established. The Fréchet differentiability of the near-field scattering map is studied with respect to the elastic parameters. Based on the multifrequency measurement data and its phaseless term, two Landweber iterative algorithms are developed for the reconstruction of the multiple elastic parameters. Numerical examples, indicating that plane pressure incident wave is a better choice, are presented to show the validity and accuracy of our methods.

Additional Information

© 2019 Society for Industrial and Applied Mathematics. Submitted to the journal's Computational Methods in Science and Engineering section October 15, 2018; accepted for publication (in revised form) April 30, 2019; published electronically July 16, 2019. The work of the first author was partially supported by an NSFC Innovative Group Fund (11621101), an Integrated Project of the Major Research Plan of NSFC (91630309), and an NSFC A3 Project (11421110002). The work of the third author was supported by NSFC grants (11501063, 11771068), the Chongqing Research Program of Basic Research and Frontier Technology (CSTC2017JCYJAX0294), and the Fundamental Research Funds for the Central University (106112016CDJXY100004). The authors also would like to thank Prof. Peijun Li for his suggestions on this work. We thank the referees for their constructive comments, which helped to improve the paper.

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August 19, 2023
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