  We consider the time-harmonic elastic wave scattering from a general
(possibly anisotropic) inhomogeneous medium with an embedded impenetrable
obstacle. We show that the impenetrable obstacle can be effectively
approximated by an isotropic elastic medium with a particular choice of
material parameters. We derive sharp estimates to rigorously verify such an
effective approximation. Our study is strongly motivated by the related studies
of two challenging inverse elastic problems including the inverse boundary
problem with partial data and the inverse scattering problem of recovering
mediums with buried obstacles. The proposed effective medium theory readily
yields some interesting applications of practical significance to these inverse
problems.
