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contrasts with surround rocks and try to interpret them with single survey data. The conventional three-dimensional (3-D) inversions significantly rely on the size of the grids, which should be smaller than the smallest geological target to achieve a good recovery to anomalous electric conductivity. However, this will create a large amount of unknowns to be solved and cost significant time and memory. In this paper, we present a multi-scale (MS) stochastic inversion scheme based on shearlet transform for airborne electromagnetic (AEM) data. The shearlet possesses the features of multi-direction and multi-scale, allowing it to effectively characterize the underground conductivity distribution in the transformed domain. To address the practical implementation of the method, we use a compressed sensing method in the forward modeling and sensitivity calculation, and employ a preconditioner that accounts for both the sampling rate and gradient noise to achieve a fast stochastic 3-D inversion. By gradually updating the coefficients from the coarse to fine scales, we obtain the multi-scale information on the underground electric conductivity. The synthetic data inversion shows that the proposed MS method can better recover multiple geological bodies with different sizes and depths with less time consumption. Finally, we conduct 3-D inversions of a field dataset acquired from Byneset, Norway. The results show very good agreement with the geological information.<\/jats:p>","DOI":"10.3390\/rs16163070","type":"journal-article","created":{"date-parts":[[2024,8,22]],"date-time":"2024-08-22T04:26:57Z","timestamp":1724300817000},"page":"3070","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Multiscale 3-D Stochastic Inversion of Frequency-Domain Airborne Electromagnetic Data"],"prefix":"10.3390","volume":"16","author":[{"given":"Yang","family":"Su","sequence":"first","affiliation":[{"name":"College of Geo-Exploration Sciences and Technology, Jilin University, Changchun 130026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiuyan","family":"Ren","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Sciences and Technology, Jilin University, Changchun 130026, China"},{"name":"SinoProbe Laboratory, Chinese Academy of Geological Sciences, Beijing 100094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changchun","family":"Yin","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Sciences and Technology, Jilin University, Changchun 130026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Libao","family":"Wang","sequence":"additional","affiliation":[{"name":"Shandong Huichuang Technology Co., Ltd., Changyi 261300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3634-9832","authenticated-orcid":false,"given":"Yunhe","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Sciences and Technology, Jilin University, Changchun 130026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Sciences and Technology, Jilin University, Changchun 130026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luyuan","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Sciences and Technology, Jilin University, Changchun 130026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,21]]},"reference":[{"key":"ref_1","first-page":"3370","article-title":"Exploration capability of airborne TEM systems for typical targets in the subsurface","volume":"58","author":"Yin","year":"2015","journal-title":"Chin. 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