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arXiv · 1811.12579

Inverse obstacle scattering problem for elastic waves with phased or phaseless far-field data

Heping Dong·Jun Lai·Peijun Li
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Abstract

This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz decomposition, the model problem is reduced to a coupled boundary value problem of the Helmholtz equations. The relation is established between the compressional or shear far-field pattern for the elastic wave equation and the corresponding far-field pattern for the coupled Helmholtz equations. An efficient and accurate Nystr\"{o}m type discretization for the boundary integral equation is developed to solve the coupled system. The translation invariance of the phaseless compressional and shear far-field patterns are proved. A system of nonlinear integral equations is proposed and two iterative reconstruction methods are developed for the inverse problem. In particular, for the phaseless data, a reference ball technique is introduced to the scattering system in order to break the translation invariance. Numerical experiments are presented to demonstrate the effectiveness and robustness of the proposed method.

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Heping Dong, Jun Lai, Peijun Li. 2018-11-30. Inverse obstacle scattering problem for elastic waves with phased or phaseless far-field data. https://arxiv.org/abs/1811.12579

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