|School of Mathematics and Statistics, Xi’an Jiaotong University
There are two aspects of this presentation:
1. Inverse elastic wave scattering by rough surfaces. Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-iterative sampling method is proposed for detecting the rough surface by taking elastic field measurements on a bounded line segment above the surface, based on reconstructing a modified near-field equation associated with a special surface, which generalized our previous work for the Helmholtz equation (SIAM J. Imag. Sci. 10(3) (2017), 1579-1602) to the Navier equation. Several numerical examples are carried out to illustrate the effectiveness of the inversion algorithm.
2. The scattering of electromagnetic field by an elastic body (Vogit’s model). When the elastic body is bounded and the background medium is homogeneous (or two-layered), we have shown that the shape and location of the body is uniquely determined by the fixed energy magnetic (or electric) far-field measurements corresponding to incident plane waves with all polarizations.