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This paper focuses on the inverse elastic impedance and the geometry problemby a Cauchy data pair on the access part of the boundary in a two-dimensionalcase. Through the decomposition of the displacement, the problem is transformthe solution of into a coupled boundary value problem that involves two scalarHelmholtz equations. Firstly, a uniqueness result is given, and a non-iterativealgorithm is proposed to solve the data completion problem using a Cauchy datapair on a known part of the solution domain's boundary. Next, we introduce aNewton-type iterative method for reconstructing the boundary and the impedancefunction using the completion data on the unknown boundary, which is governedby a specific type of boundary conditions. Finally, we provide several examplesto demonstrate the effectiveness and accuracy of the proposed method.

Simultaneously determine elastic impedance and shape by a Newton-type iterative method