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arXiv · 1902.04123

Multi-frequency iterative methods for the inverse medium scattering problems in elasticity

Gang Bao·Tao Yin·Fang Zeng
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Abstract

This paper concerns the reconstruction of multiple elastic parameters (Lam\'e parameters and density) of an inhomogeneous medium embedded in an infinite homogeneous isotropic background in $\mathbb{R}^2$. The direct scattering problem is reduced to an equivalent system on a bounded domain by introducing an exact transparent boundary condition and the wellposedness of the corresponding variational problem is established. The Fr\'{e}chet differentiability of the near-field scattering map is studied with respect to the elastic parameters. Based on the multi-frequency 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.

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Gang Bao, Tao Yin, Fang Zeng. 2019-02-11. Multi-frequency iterative methods for the inverse medium scattering problems in elasticity. https://arxiv.org/abs/1902.04123

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