{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T03:49:45Z","timestamp":1778125785468,"version":"3.51.4"},"reference-count":47,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,30]],"date-time":"2025-03-30T00:00:00Z","timestamp":1743292800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"ational Natural Science Foundation of China (NSFC)","award":["42074172"],"award-info":[{"award-number":["42074172"]}]},{"name":"ational Natural Science Foundation of China (NSFC)","award":["42204089"],"award-info":[{"award-number":["42204089"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The deep learning-based gravity anomaly inversion method addresses the complex challenge of deriving subsurface density variation models from surface gravity anomaly data. In order to generate various geological environments and their corresponding surface gravity anomaly datasets, three-dimensional density models considering different spatial locations and density variations are created in this paper. At the same time, the residual module and spatial attention mechanism are introduced into the U-Net architecture to improve the learning ability and inversion accuracy of complex geological structures. Experimental results demonstrate that the proposed method achieves the high-precision reconstruction of density variation models in complex anomaly environments, with a model residual error lower than 3%. Additionally, the inversion results of the density change and the gravity change in the Longshoushan fault zone show that the 2022 Menyuan MS6.9 earthquake is in the middle of the positive and negative density changes, which verifies the applicability of the U-Net network in the field of gravity change data, highlighting the method\u2019s value in the real-world environment.<\/jats:p>","DOI":"10.3390\/sym17040523","type":"journal-article","created":{"date-parts":[[2025,3,31]],"date-time":"2025-03-31T05:21:04Z","timestamp":1743398464000},"page":"523","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Inversion of Gravity Anomalies Based on U-Net Network"],"prefix":"10.3390","volume":"17","author":[{"given":"Fei","family":"Yu","sequence":"first","affiliation":[{"name":"Institute of Seismology, China Earthquake Administration, Wuhan 430071, China"},{"name":"Hubei Earthquake Agency, Wuhan 430071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guiju","family":"Wu","sequence":"additional","affiliation":[{"name":"Institute of Seismology, China Earthquake Administration, Wuhan 430071, China"},{"name":"Hubei Earthquake Agency, Wuhan 430071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yufei","family":"Xi","sequence":"additional","affiliation":[{"name":"Institute of Hydrogeology and Environmental Geology, Chinese Academy of Geological Sciences, Shijiazhuang 050061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fan","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Seismology, China Earthquake Administration, Wuhan 430071, China"},{"name":"Hubei Earthquake Agency, Wuhan 430071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5412-790X","authenticated-orcid":false,"given":"Jiapei","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Seismology, China Earthquake Administration, Wuhan 430071, China"},{"name":"Hubei Earthquake Agency, Wuhan 430071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-9539-102X","authenticated-orcid":false,"given":"Rui","family":"Zhang","sequence":"additional","affiliation":[{"name":"Institute of Seismology, China Earthquake Administration, Wuhan 430071, China"},{"name":"Hubei Earthquake Agency, Wuhan 430071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qinghong","family":"Long","sequence":"additional","affiliation":[{"name":"Institute of Seismology, China Earthquake Administration, Wuhan 430071, China"},{"name":"Hubei Earthquake Agency, Wuhan 430071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1190\/1.1441501","article-title":"Compact gravity inversion","volume":"48","author":"Last","year":"1983","journal-title":"Geophysics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1354","DOI":"10.1190\/1.1441761","article-title":"Gravity and magnetic inversion with minimization of a specific functional","volume":"49","author":"Guillen","year":"1984","journal-title":"Geophysics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1190\/1.1443534","article-title":"Generalized compact gravity inversion","volume":"59","author":"Barbosa","year":"1994","journal-title":"Geophysics"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1190\/1.1444302","article-title":"3-D inversion of gravity data","volume":"63","author":"Li","year":"1998","journal-title":"Geophysics"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"696","DOI":"10.1190\/1.2168010","article-title":"Interactive gravity inversion","volume":"71","author":"Silva","year":"2006","journal-title":"Geophysics"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"I9","DOI":"10.1190\/1.3092775","article-title":"3D gravity inversion through an adaptive-learning procedure","volume":"74","author":"Dias","year":"2009","journal-title":"Geophysics"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1046\/j.1365-246X.2002.01664.x","article-title":"Non-smooth gravity problem with total variation penalization functional","volume":"149","author":"Cherkaev","year":"2002","journal-title":"Geophys. 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