{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:33:51Z","timestamp":1787236431207,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100013290","name":"National Key Research and Development Program of China Stem Cell and Translational Research","doi-asserted-by":"publisher","award":["2023YFA1009100"],"award-info":[{"award-number":["2023YFA1009100"]}],"id":[{"id":"10.13039\/501100013290","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013290","name":"National Key Research and Development Program of China Stem Cell and Translational Research","doi-asserted-by":"publisher","award":["2024YFA1012303"],"award-info":[{"award-number":["2024YFA1012303"]}],"id":[{"id":"10.13039\/501100013290","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071430"],"award-info":[{"award-number":["12071430"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Laboratory of Collaborative Sensing and Autonomous Unmanned Systems of Zhejiang Province"},{"name":"Open Research Project of Innovation Center of Yangtze River Delta, Zhenjiang University"},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12371421"],"award-info":[{"award-number":["12371421"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2025,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>This paper is concerned with the stability estimates for inverse random source problems of the stochastic elastic wave equation. The source is assumed to be either a generalized microlocally isotropic Gaussian random field such that its covariance operator is a classical pseudo-differential operator or to be a white noise. In the case of a generalized microlocally isotropic Gaussian random field, we derive a stability estimate of determining the micro-correlation strength of the random source at multiple frequencies. For the white noise, a stability estimate is established for recovering the strength of the random source at a fixed frequency. In the analysis, we employ the correlation boundary measurements. Besides providing quantitative estimates of the stability, we show that the stability improves as more frequencies of data are used, which exhibits the phenomenon of increasing stability.<\/jats:p>","DOI":"10.1137\/24m1672997","type":"journal-article","created":{"date-parts":[[2025,4,23]],"date-time":"2025-04-23T04:04:21Z","timestamp":1745381061000},"page":"777-797","source":"Crossref","is-referenced-by-count":2,"title":["Stability for the Inverse Random Source Scattering Problems in Elastic Waves"],"prefix":"10.1137","volume":"23","author":[{"given":"Tianjiao","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang University, Hangzhou, 310058 China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0626-7609","authenticated-orcid":true,"given":"Xiang","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Institute of Fundamental and Transdisciplinary Research, Zhejiang University, Hangzhou, 310058 China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yue","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, and Key Lab NAA\u2013MOE, Central China Normal University, Wuhan, 430079 China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,4,23]]},"reference":[{"key":"ref1","volume-title":"Mathematical Methods in Elasticity Imaging","author":"Ammari H.","year":"2015"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/16M1067470"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/16M1088922"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/31\/9\/093001"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2019.06.006"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/21\/2\/R01"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1142\/S0219530519500015"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2015.11.030"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1090\/mbk\/082"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.bioeng.5.040202.121623"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141001383564"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/b138659"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-008-0416-6"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1080\/03605302.2020.1774895"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1137\/21M1467663"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1137\/22M1497183"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1137\/23M1586331"},{"key":"ref18","unstructured":"P. Li, Y. Liang, and X. Wang, Stability Estimates of Inverse Random Source Problems for the Wave Equations by Using Correlation-Based Data, preprint, arXiv:2410.07938, 2024."},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1137\/19M1309456"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1177\/016173469101300201"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1137\/24M1655974"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ad99f7"},{"key":"ref23","unstructured":"J. Zhai and Y. Zhao, Increasing Stability for the Inverse Scattering Problem of the Schr\u00f6dinger Equation, arXiv:2306.10211, 2023."}],"container-title":["Multiscale Modeling &amp; Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/24M1672997","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:34:45Z","timestamp":1787232885000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M1672997"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,23]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,6,30]]}},"alternative-id":["10.1137\/24M1672997"],"URL":"https:\/\/doi.org\/10.1137\/24m1672997","relation":{},"ISSN":["1540-3459","1540-3467"],"issn-type":[{"value":"1540-3459","type":"print"},{"value":"1540-3467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,23]]}}}