提高多层介质中声学和弹性反源问题的稳定性

IF 2 2区数学 Q1 MATHEMATICS, APPLIED

Inverse Problems Pub Date : 2024-08-27 DOI:10.1088/1361-6420/ad7055

Tianjiao Wang, Xiang Xu, Yue Zhao

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引用次数: 0

摘要

本文研究了多层介质中亥姆霍兹方程和纳维方程的反源问题，分别考虑了二维和三维情况。研究表明，每种情况下的稳定性都在不断提高，其特点是有两个主要项：一个是与数据差异相关的霍尔德项，另一个是对数项，随着考虑的频率越多，对数项越小。在二维情况下，对界面和远场数据的测量至关重要。通过采用自由空间的基本解作为测试函数，并利用解的渐近行为和延续原理，可以得到稳定的结果。在三维情况下，需要对界面和人工边界进行测量，并通过应用均质介质中反源问题的论证得出稳定性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Increasing stability of the acoustic and elastic inverse source problems in multi-layered media

This paper investigates inverse source problems for the Helmholtz and Navier equations in multi-layered media, considering both two and three-dimensional cases respectively. The study reveals a consistent increase in stability for each scenario, characterized by two main terms: a Hölder-type term associated with data discrepancy, and a logarithmic-type term that diminishes as more frequencies are considered. In the two-dimensional case, measurements on interfaces and far-field data are essential. By employing the fundamental solution in free-space as the test function and utilizing the asymptotic behavior of the solution and continuation principle, stability results are obtained. In the three-dimensional case, measurements on interfaces and artificial boundaries are taken, and the stability result can be derived by applying the arguments for inverse source problems in homogeneous media.

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来源期刊

Inverse Problems 数学-物理：数学物理

CiteScore

4.40

自引率

14.30%

发文量

115

审稿时长

2.3 months

期刊介绍： An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, numerical and practical approaches to their solution. As well as applied mathematicians, physical scientists and engineers, the readership includes those working in geophysics, radar, optics, biology, acoustics, communication theory, signal processing and imaging, among others. The emphasis is on publishing original contributions to methods of solving mathematical, physical and applied problems. To be publishable in this journal, papers must meet the highest standards of scientific quality, contain significant and original new science and should present substantial advancement in the field. Due to the broad scope of the journal, we require that authors provide sufficient introductory material to appeal to the wide readership and that articles which are not explicitly applied include a discussion of possible applications.