  We develop three inverse elastic scattering schemes for locating multiple
small, extended and multiscale rigid bodies, respectively. There are some
salient and promising features of the proposed methods. The cores of those
schemes are certain indicator functions, which are obtained by using only a
single far-field pattern of the pressure (longitudinal) wave, or the shear
(transversal) wave, or the total wave field. Though the inverse scattering
problem is known to be nonlinear and ill-posed, the proposed reconstruction
methods are totally "direct" and there are no inversions involved. Hence, the
methods are very efficient and robust against noisy data. Both rigorous
mathematical justifications and numerical simulations are presented in our
study.
