WIAS Preprint No. 1782, (2013)

The factorization method for inverse elastic scattering from periodic structures


  • Hu, Guanghui
  • Lu, Yulong
  • Zhang, Bo

2010 Mathematics Subject Classification

  • 35R30 74B05 78A46 35Q93


  • Inverse elastic scattering, factorization method, Dirichlet boundary condition, Navier equation, uniqueness


This paper is concerned with the inverse scattering of time-harmonic elastic waves from rigid periodic structures. We establish the factorization method to identify an unknown grating surface from knowledge of the scattered compressional or shear waves measured on a line above the scattering surface. Near-field operators are factorized by selecting appropriate incident waves derived from quasi-periodic half-space Green's tensor to the Navier equation. The factorization method gives rise to a uniqueness result for the inverse scattering problem by utilizing only the compressional or shear components of the scattered field corresponding to all quasi-periodic incident plane waves with a common phase-shift. A number of computational examples are provided to show the accuracy of the inversion algorithms, with an emphasis placed on comparing reconstructions from the scattered near-field and those from its compressional and shear components.

Appeared in

  • Inverse Problems, 29 (2013) pp. 115005/1--115005/25.

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