标题： 基于噪声数据通过时间谐波弹性波方程的单调性方法重构包络形状 显示英文标题

标题： Shape reconstruction of inclusions based on noisy data via monotonicity methods for the time harmonic elastic wave equation

摘要： 本文中，我们将研究关于时间谐波弹性波方程反问题的标准单调性和线性化单调性方法，并引入这些方法针对噪声数据的修正。更具体地，当使用噪声数据时，这些方法必须提供一致的结果，以便能够用真实世界的数据（例如实验室数据）进行模拟。因此，我们考虑扰动的Neumann-to-Dirichlet算子，并修改特征值界以用于利用噪声数据重建未知夹杂物的单调性测试中。通过这样做，我们证明了存在一个噪声水平 $\delta_0$，使得对于所有噪声水平 $\delta < \delta_0$，夹杂物都能被检测到且其形状可以被重建。最后，我们基于噪声数据呈现了一些数值模拟。 显示英文摘要

摘要： In this paper, we extend our research concerning the standard and linearized monotonicity methods for the inverse problem of the time harmonic elastic wave equation and introduce the modification of these methods for noisy data. In more detail, the methods must provide consistent results when using noisy data in order to be able to perform simulations with real world data, e.g., laboratory data. We therefore consider the disturbed Neumann-to-Dirichlet operator and modify the bound of the eigenvalues in the monotonicity tests for reconstructing unknown inclusions with noisy data. In doing so, we show that there exists a noise level $\delta_0$ so that the inclusions are detected and their shape is reconstructed for all noise levels $\delta < \delta_0$. Finally, we present some numerical simulations based on noisy data.