Effective Medium Theory for Embedded Obstacles in Elasticity with Applications to Inverse Problems

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