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Sci. Comput."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>This paper concerns the reconstruction of multiple elastic parameters (Lam\u00e9 parameters and density) of an inhomogeneous medium embedded in an infinite homogeneous isotropic background in $\\mathbb{R}^2$. The direct scattering problem is reduced to an equivalent system on a bounded domain by introducing an exact transparent boundary condition and the well-posedness of the corresponding variational problem is established. The Fr\u00e9chet differentiability of the near-field scattering map is studied with respect to the elastic parameters. Based on the multifrequency measurement data and its phaseless term, two Landweber iterative algorithms are developed for the reconstruction of the multiple elastic parameters. 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