{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:11:59Z","timestamp":1760145119246,"version":"build-2065373602"},"reference-count":108,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T00:00:00Z","timestamp":1718582400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["41704138","41974148","2017JJ3069","E51651","E21722"],"award-info":[{"award-number":["41704138","41974148","2017JJ3069","E51651","E21722"]}]},{"name":"Hunan Provincial Science &amp; Technology Department of China","award":["41704138","41974148","2017JJ3069","E51651","E21722"],"award-info":[{"award-number":["41704138","41974148","2017JJ3069","E51651","E21722"]}]},{"name":"Hunan University of Science and Technology","award":["41704138","41974148","2017JJ3069","E51651","E21722"],"award-info":[{"award-number":["41704138","41974148","2017JJ3069","E51651","E21722"]}]},{"name":"Hunan Provincial Key Laboratory of Share Gas Resource Exploitation","award":["41704138","41974148","2017JJ3069","E51651","E21722"],"award-info":[{"award-number":["41704138","41974148","2017JJ3069","E51651","E21722"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Surface gravity inversion attempts to recover the density contrast distribution in the 3D Earth model for geological interpretation. Since airborne gravity is characterized by large data volumes, large-scale 3D inversion exceeds the capacity of desktop computing resources, making it difficult to achieve the appropriate depth\/lateral resolution for geological interpretation. In addition, gravity data are finite and noisy, and their inversion is ill posed. Especially in the absence of a priori geological information, regularization must be introduced to overcome the difficulty of the non-uniqueness of the solutions to recover the most geologically plausible ones. Because the use of Haar wavelet operators has an edge-preserving property and can preserve the sensitivity matrix structure at each level of the multilevel method to obtain faster solvers, we present a multilevel algorithm for large-scale gravity inversion solved by the re-weighted regularized conjugate gradient (RRCG) algorithm to reduce the inversion computational resources and improve the depth\/lateral resolution of the inversion results. The RRCG-based multilevel inversion was then applied to synthetic cases and airborne gravity data from the Quest-South project in British Columbia, Canada. Results from synthetic models and field data show that the RRCG-based multilevel inversion is suitable for obtaining density contrast distributions with appropriate horizontal and vertical resolution, especially for large-scale gravity inversions compared to Occam\u2019s inversion.<\/jats:p>","DOI":"10.3390\/sym16060758","type":"journal-article","created":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T12:48:40Z","timestamp":1718628520000},"page":"758","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multilevel Algorithm for Large-Scale Gravity Inversion"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7033-6077","authenticated-orcid":false,"given":"Shujin","family":"Cao","sequence":"first","affiliation":[{"name":"School of Earth Sciences and Spatial Information Engineering, Hunan University of Science and Technology, Taoyuan Road, Xiangtan 411201, China"},{"name":"School of Geosciences and Info-Physics, Central South University, Lushan South Road, Changsha 410083, China"},{"name":"Institute of Geophysics & Geomatics, China University of Geosciences, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Earth Sciences and Spatial Information Engineering, Hunan University of Science and Technology, Taoyuan Road, Xiangtan 411201, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8014-819X","authenticated-orcid":false,"given":"Guangyin","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Geosciences and Info-Physics, Central South University, Lushan South Road, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6139-9551","authenticated-orcid":false,"given":"Yajing","family":"Mao","sequence":"additional","affiliation":[{"name":"School of Earth Sciences and Spatial Information Engineering, Hunan University of Science and Technology, Taoyuan Road, Xiangtan 411201, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongxin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Geosciences and Info-Physics, Central South University, Lushan South Road, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yihuai","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Earth Sciences and Spatial Information Engineering, Hunan University of Science and Technology, Taoyuan Road, Xiangtan 411201, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinyue","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Earth Sciences and Spatial Information Engineering, Hunan University of Science and Technology, Taoyuan Road, Xiangtan 411201, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1186","DOI":"10.1111\/j.1365-2478.2011.01052.x","article-title":"Large-scale 3D inversion of potential field data","volume":"60","author":"Cuma","year":"2012","journal-title":"Geophys. 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