This paper focuses on the inverse elastic impedance and the geometry problem by a Cauchy data pair on the access part of the boundary in a two-dimensional case. Through the decomposition of the displacement, the problem is transform the solution of into a coupled boundary value problem that involves two scalar Helmholtz equations. Firstly, a uniqueness result is given, and a non-iterative algorithm is proposed to solve the data completion problem using a Cauchy data pair on a known part of the solution domain's boundary. Next, we introduce a Newton-type iterative method for reconstructing the boundary and the impedance function using the completion data on the unknown boundary, which is governed by a specific type of boundary conditions. Finally, we provide several examples to demonstrate the effectiveness and accuracy of the proposed method.

翻译：本文聚焦于二维情形下基于边界可访问部分上一对柯西数据反演弹性阻抗与几何形状的逆问题。通过对位移进行分解，可将该问题转化为涉及两个标量亥姆霍兹方程的耦合边值问题求解。首先给出唯一性结论，并提出一种利用解域已知边界上柯西数据对完成数据补全问题的非迭代算法。其次，引入基于牛顿型的迭代方法，利用未知边界上的补全数据重建边界结构及满足特定边界条件类型的阻抗函数。最后通过数值算例验证所提方法的有效性与精确性。