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：本文针对二维情形下边界可访问部分由柯西数据对确定的逆弹性阻抗与几何问题。通过位移分解，将问题转化为涉及两个标量亥姆霍兹方程的耦合边值问题。首先给出唯一性结论，并提出一种非迭代算法，利用解域已知边界上的柯西数据对完成数据补全。接着引入牛顿型迭代方法，利用未知边界上的补全数据（该边界受特定类型边界条件控制）重构边界形态与阻抗函数。最后通过多个算例验证所提方法的有效性与精度。