{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T10:56:38Z","timestamp":1777028198775,"version":"3.51.4"},"reference-count":47,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,2,8]],"date-time":"2021-02-08T00:00:00Z","timestamp":1612742400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41774125"],"award-info":[{"award-number":["41774125"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42030806"],"award-info":[{"award-number":["42030806"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41530320"],"award-info":[{"award-number":["41530320"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Strategic Priority Research Program of the Chinese Academy of Sciences","award":["XDA14020102"],"award-info":[{"award-number":["XDA14020102"]}]},{"name":"Key National Research Project of China","award":["2017YFC0601900"],"award-info":[{"award-number":["2017YFC0601900"]}]},{"name":"Key National Research Project of China","award":["2016YFC0303100"],"award-info":[{"award-number":["2016YFC0303100"]}]},{"name":"the S&amp;T Program of Beijing","award":["Z181100005718001"],"award-info":[{"award-number":["Z181100005718001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Airborne electromagnetic (AEM) method uses aircraft as a carrier to tow EM instruments for geophysical survey. Because of its huge amount of data, the traditional AEM data inversions take one-dimensional (1D) models. However, the underground earth is very complicated, the inversions based on 1D models can frequently deliver wrong results, so that the modeling and inversion for three-dimensional (3D) models are more practical. In order to obtain precise underground electrical structures, it is important to have a highly effective and efficient 3D forward modeling algorithm as it is the basis for EM inversions. In this paper, we use time-domain spectral element (SETD) method based on Gauss-Lobatto-Chebyshev (GLC) polynomials to develop a 3D forward algorithm for modeling the time-domain AEM responses. The spectral element method combines the flexibility of finite-element method in model discretization and the high accuracy of spectral method. Starting from the Maxwell's equations in time-domain, we derive the vector Helmholtz equation for the secondary electric field. We use the high-order GLC vector interpolation functions to perform spectral expansion of the EM field and use the Galerkin weighted residual method and the backward Euler scheme to do the space- and time-discretization to the controlling equations. After integrating the equations for all elements into a large linear equations system, we solve it by the multifrontal massively parallel solver (MUMPS) direct solver and calculate the magnetic field responses by the Faraday's law. By comparing with 1D semi-analytical solutions for a layered earth model, we validate our SETD method and analyze the influence of the mesh size and the order of interpolation functions on the accuracy of our 3D forward modeling. The numerical experiments for typical models show that applying SETD method to 3D time-domain AEM forward modeling we can achieve high accuracy by either refining the mesh or increasing the order of interpolation functions.<\/jats:p>","DOI":"10.3390\/rs13040601","type":"journal-article","created":{"date-parts":[[2021,2,10]],"date-time":"2021-02-10T04:33:46Z","timestamp":1612931626000},"page":"601","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["3D Airborne EM Forward Modeling Based on Time-Domain Spectral Element Method"],"prefix":"10.3390","volume":"13","author":[{"given":"Changchun","family":"Yin","sequence":"first","affiliation":[{"name":"College of Geo-exploration Sciences and Technology, Jilin University, Changchun 130026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zonghui","family":"Gao","sequence":"additional","affiliation":[{"name":"China Petroleum Logging CO., LTD Technology Center, Xi\u2019an 710000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Su","sequence":"additional","affiliation":[{"name":"College of Geo-exploration Sciences and Technology, Jilin University, Changchun 130026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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":"Xin","family":"Huang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Exploration Technologies for Oil and Gas Resource, Yangtze University, Wuhan 430100, 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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Xiong","sequence":"additional","affiliation":[{"name":"College of Earth Sciences, Guilin University of Technology, Guilin 541002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.jappgeo.2007.07.001","article-title":"A comparison of helicopter-borne electromagnetics in frequency- and time-domain at the Cuxhaven valley in Northern Germany","volume":"67","author":"Steuer","year":"2009","journal-title":"J. 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