On an inverse elastic wave imaging scheme for nearly incompressible materials

This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly in compressible materials. The scatterers include non-penetrable rigid obstacles and penetrable media, and we use time-harmonic elastic point signals as the incident input waves. The scattered waves are collected in a relatively small back scattering aperture on a bounded surface. A two-stage algorithm is proposed for the recon struction and only two incident waves of different wave numbers are required. The unknown scatterer is first approx imately located by using the measured data at a small wave number, and then the shape of the scatterer is determined by the computed location of the scatterer together with the measured data at a regular wave number. The corresponding mathematical principle with rigourous analysis is presented. Numerical tests illustrate the effective ness and efficiency of the proposed method.