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Inverse Elastic Scattering for Multiscale Rigid Bodies with A Single Far-field Pattern

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.