1. Increasing stability of the acoustic and elastic inverse source problems in multi-layered media.
- Author
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Wang, Tianjiao, Xu, Xiang, and Zhao, Yue
- Subjects
INVERSE problems ,HELMHOLTZ equation - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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