{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T09:15:55Z","timestamp":1775812555024,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,5,21]],"date-time":"2024-05-21T00:00:00Z","timestamp":1716249600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["42374170"],"award-info":[{"award-number":["42374170"]}]},{"name":"National Natural Science Foundation of China","award":["Z181100005718001"],"award-info":[{"award-number":["Z181100005718001"]}]},{"name":"Beijing Science and Technology Plan \u201cDeep Earth Exploration Technology Breakthrough\u201d special project of China","award":["42374170"],"award-info":[{"award-number":["42374170"]}]},{"name":"Beijing Science and Technology Plan \u201cDeep Earth Exploration Technology Breakthrough\u201d special project of China","award":["Z181100005718001"],"award-info":[{"award-number":["Z181100005718001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In geophysical inversion issues, the Jacobian matrix computation takes the greatest time, and it is the most significant factor limiting the inversion\u2019s calculation speed. We think that the correctness of the inverse problem is determined by the difference between the inversion data and the real data, not the precision of the gradient solution in each iteration. Based on this, we present an approximate computation approach for the Jacobian matrix that may rapidly solve the inverse issue by estimating the gradient information. In this research, the approximate gradient information is solved in each iteration process, and the approximate gradient is utilized for computation; nevertheless, the poor fitting of the evaluation data is correctly evaluated, and the inversion model that fits the criteria is achieved. We employed this approach of estimating the Jacobian matrix to invert the 3D airborne transient electromagnetic method (ATEM) on synthetic data, and it was able to significantly minimize the time necessary for the inversion while maintaining inversion accuracy. When the model mesh is more precise, this technique outperforms the previous way of finding the exact Jacobian matrix in terms of acceleration.<\/jats:p>","DOI":"10.3390\/rs16111830","type":"journal-article","created":{"date-parts":[[2024,5,22]],"date-time":"2024-05-22T06:54:09Z","timestamp":1716360849000},"page":"1830","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Parallel Inversion of 3D Airborne Transient Electromagnetic Data Using an Approximate Jacobi Matrix"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9687-894X","authenticated-orcid":false,"given":"Da","family":"Lei","sequence":"first","affiliation":[{"name":"CAS Engineering Laboratory for Deep Resources Equipment and Technology, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China"},{"name":"Innovation Academy for Earth Science, Chinese Academy of Sciences, Beijing 100029, China"},{"name":"College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Hao","family":"Ren","sequence":"additional","affiliation":[{"name":"College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Ruo","family":"Wang","sequence":"additional","affiliation":[{"name":"CAS Engineering Laboratory for Deep Resources Equipment and Technology, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China"},{"name":"Innovation Academy for Earth Science, Chinese Academy of Sciences, Beijing 100029, China"},{"name":"College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Zhongxing","family":"Wang","sequence":"additional","affiliation":[{"name":"CAS Engineering Laboratory for Deep Resources Equipment and Technology, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China"},{"name":"Innovation Academy for Earth Science, Chinese Academy of Sciences, Beijing 100029, China"},{"name":"College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0368-0238","authenticated-orcid":false,"given":"Changmin","family":"Fu","sequence":"additional","affiliation":[{"name":"CAS Engineering Laboratory for Deep Resources Equipment and Technology, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China"},{"name":"Innovation Academy for Earth Science, Chinese Academy of Sciences, Beijing 100029, China"},{"name":"College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"W17","DOI":"10.1190\/geo2014-0544.1","article-title":"Review on airborne electromagnetic inverse theory and applications","volume":"80","author":"Yin","year":"2015","journal-title":"Geophysics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1007\/s10589-012-9476-9","article-title":"Convergence analysis of a proximal Gauss-Newton method","volume":"53","author":"Salzo","year":"2012","journal-title":"Comput. 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