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：本文研究二维情形下利用边界可访问部分的柯西数据对反演弹性阻抗与几何形状问题。通过位移分解，将问题转化为包含两个标量亥姆霍兹方程的耦合边值问题。首先给出唯一性结果，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求解数据完备问题。随后引入基于牛顿型迭代的重构方法，利用未知边界上受特定边界条件约束的完备数据重构边界形状与阻抗函数。最后通过数值算例验证该方法的有效性与精度。