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Elastic Scattering Coefficients and Enhancement of Nearly Elastic Cloaking

by T. Abbas and H. Ammari and G. Hu and A. Wahab and J.C. Ye

(Report number 2016-33)

Abstract
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, we introduce the notion of scattering coefficients of an elastic inclusion in this article. First, we define elastic scattering coefficients and substantiate that they naturally appear in the expansions of elastic scattered field and far field scattering amplitudes corresponding to a plane wave incidence. Then an algorithm is developed and analyzed for extracting the elastic scattering coefficients from multi-static response measurements of the scattered field. Moreover, the estimate of the maximal resolving order is provided in terms of the signal-to-noise ratio. The decay rate and symmetry of the elastic scattering coefficients are also discussed. Finally, we design scattering-coefficients-vanishing structures and elucidate their utility for enhancement of nearly elastic cloaking.

Keywords: Elastic scattering, Scattering coefficients, Elastic cloaking, Inverse scattering.

@Techreport{AAHWY16_670,
  author = {T. Abbas and H. Ammari and G. Hu and A. Wahab and J.C. Ye},
  title = {Elastic Scattering Coefficients and Enhancement of Nearly Elastic Cloaking},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2016-33},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2016/2016-33.pdf },
  year = {2016}
}

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