{"title":"Increasing stability of the acoustic and elastic inverse source problems in multi-layered media","authors":"Tianjiao Wang, Xiang Xu, Yue Zhao","doi":"10.1088/1361-6420/ad7055","DOIUrl":null,"url":null,"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.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1088/1361-6420/ad7055","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
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.