  The concept of scattering coefficients has played a pivotal role in a broad
range of inverse scattering and imaging problems in acoustic, and
electromagnetic media. In view of their promising applications in inverse
problems related to mathematical imaging and elastic cloaking, the notion of
elastic scattering coefficients of an inclusion is presented from the
perspective of boundary layer potentials and a few properties are discussed. A
reconstruction algorithm is developed and analyzed for extracting the elastic
scattering coefficients from multi-static response measurements of the
scattered field in order to cater to inverse scattering problems. The decay
rate, stability and error analyses, and the estimate of maximal resolving order
in terms of the signal-to-noise ratio are discussed. Moreover,
scattering-coefficients-vanishing structures are designed and their utility for
enhancement of nearly elastic cloaking is elucidated.
