  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 incompressible
materials. The scatterers include non-penetrable rigid obstacles and penetrable
mediums, and we use time-harmonic elastic point signals as the incident input
waves. The scattered waves are collected in a relatively small backscattering
aperture on a bounded surface. A two-stage algorithm is proposed for the
reconstruction and only two incident waves of different wavenumbers are
required. The unknown scatterer is first approximately located by using the
measured data at a small wavenumber, and then the shape of the scatterer is
determined by the computed location of the scatterer together with the measured
data at a regular wavenumber. The corresponding mathematical principle with
rigorous analysis is presented. Numerical tests illustrate the effectiveness
and efficiency of the proposed method.
