UNIQUENESS AND RECONSTRUCTION METHOD FOR INVERSE ELASTIC WAVE SCATTERING WITH PHASELESS DATA

. This paper concerns the inverse elastic scattering of an incident point source by an impenetrable obstacle with phaseless total-field data in two dimensions. To establish the uniqueness results, the reciprocity relation for point source and the mixed reciprocity relation are derived. Then, based on the infinite groups of incident fields superposed by two point sources at a fixed frequency, we prove the uniqueness result from the phaseless total-field data without knowing the boundary condition of the obstacle in advance. In addition, the uniqueness result from the phaseless far-field data is also obtained by using the infinite groups of incident fields superposed by a point source and a fixed plane wave. In order to reconstruct the shape and location of a rigid obstacle, a nonlinear integral equation based iterative algorithm is proposed by using the phaseless total-field data and a fixed incident point source. Numerical experiments are presented to show the effectiveness of the proposed algorithm.