Uniqueness in inverse scattering of elastic waves by three-dimensional polyhedral diffraction gratings
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Abstract
We consider the inverse elastic scattering problem of determining a three-dimensional diffraction grating profile from scattered waves measured above the structure. In general, a grating profile cannot be uniquely determined by a single incoming plane wave. We completely characterize and classify the bi-periodic polyhedral structures under the boundary conditions of the third and fourth kinds that cannot be uniquely recovered by only one incident plane wave. Thus we have global uniqueness for a polyhedral grating profile by one incident elastic plane wave if and only if the profile belongs to neither of the unidentifiable classes, which can be explicitly described depending on the incident field and the type of boundary conditions. Our approach is based on the reflection principle for the Navier equation and the reflectional and rotational invariance of the total field.
© de Gruyter 2011
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- On the approximations of derivatives of integrated semigroups. II
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- Uniqueness in inverse scattering of elastic waves by three-dimensional polyhedral diffraction gratings
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Articles in the same Issue
- An inverse method for bounded error parameter identification
- An inverse problem for the wave equation
- Shrinkage rules for variational minimization problems and applications to analytical ultracentrifugation
- Reconstruction of initial Tsunami waveforms by a truncated SVD method
- Uniqueness theorems from partial information of the potential on a graph
- On the approximations of derivatives of integrated semigroups. II
- Singular value decomposition and its application to numerical inversion for ray transforms in 2D vector tomography
- Uniqueness in inverse scattering of elastic waves by three-dimensional polyhedral diffraction gratings
- Asymptotic inversion formulas in 3D vector field tomography for different geometries
