WIAS Preprint No. 2348, (2016)

Direct and inverse elastic scattering from anisotropic media


  • Bao, Gang
  • Hu, Guanghui
  • Yin, Tao
  • Sun, Jiguang

2010 Mathematics Subject Classification

  • 35R30 74B05 78A46


  • linear elasticity, Lamé system, variational approach, Fréchet derivative, Dirichlet-to-Neumann map, inverse scattering




Assume a time-harmonic elastic wave is incident onto a penetrable anisotropic body embedded into a homogeneous isotropic background medium. We propose an equivalent variational formulation in a truncated bounded domain and show uniqueness and existence of weak solutions by applying the Fredholm alternative and using properties of the Dirichlet-to-Neumann map in both two and three dimensions. The Fréchet derivative of the near-field solution operator with respect to the scattering interface is derived. As an application, we design a descent algorithm for recovering the interface from the near-field data of one or several incident directions and frequencies. Numerical examples in 2D are demonstrated to show the validity and accuracy of our methods.

Appeared in

  • J. Math. Pures Appl., 117 (2018), pp. 263--301.

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