{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T08:32:57Z","timestamp":1786523577881,"version":"build-2736575974"},"reference-count":41,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T00:00:00Z","timestamp":1786492800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Jilin Province, China","award":["YDZJ202301ZYTS222"],"award-info":[{"award-number":["YDZJ202301ZYTS222"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42507058"],"award-info":[{"award-number":["42507058"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"award":["42507058"],"award-info":[{"award-number":["42507058"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Gradient-based inversion methods are widely used for time-domain airborne electromagnetic (AEM) data, but their results are commonly affected by the initial model and regularization-induced smoothing. These limitations are particularly evident when thin layers or alternating high- and low-resistivity structures need to be resolved. To address this problem, we propose a gradient-guided iterative enhancement (GGIE) inversion that combines a limited-iteration Gauss\u2013Newton (GN) inversion with a lightweight U-Net. In each GGIE inversion iteration, the GN module first produces a coarse inverted model (IM) that preserves the main data-driven geoelectric trend but is still affected by regularization-induced smoothing. The trained U-Net then predicts a structurally enhanced model (PM) from the observed data and the IM. A data-misfit-guided adaptive approach is proposed to calculate the weight coefficients of the IM and PM and to construct an update model (UM). These coefficients are further smoothed by a momentum term so that the relative contributions of the IM and the PM are adjusted adaptively during the iterations. This design reduces error propagation from either component alone and dynamically balances learned structural enhancement with physics-based data consistency. The UM then serves as the initial model for the subsequent GN inversion. GGIE inversion is tested on synthetic data, and the results show that it is most beneficial for complex multilayer structures, for which it reduces the mean relative error and root mean squared error (RMSE) by 49.0% and 28.6%, respectively. Compared with the physics-informed neural network (PINN) baseline, GGIE inversion reduces the model relative error, log-domain RMSE, and data misfit by 19.4%, 7.0%, and 71.7%, respectively. Moreover, compared with U-Net alone, GGIE inversion reduces the data misfit by 85.4%. The proposed method is further applied to field data acquired from the Fox River area in Wisconsin, USA. The main advantage of GGIE inversion is its ability to resolve complex multilayered structures, thin layers, and sharp resistivity contrasts with improved accuracy and stability.<\/jats:p>","DOI":"10.3390\/s26165099","type":"journal-article","created":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T07:57:26Z","timestamp":1786521446000},"page":"5099","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Time-Domain Airborne Electromagnetic Inversion with Gradient Guidance and Structural Enhancement"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-1304-9008","authenticated-orcid":false,"given":"Dajun","family":"Li","sequence":"first","affiliation":[{"name":"College of Surveying and Prospecting Engineering, Jilin Jianzhu University, Changchun 130118, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-7250-9803","authenticated-orcid":false,"given":"Yuan","family":"Gao","sequence":"additional","affiliation":[{"name":"College of Surveying and Prospecting Engineering, Jilin Jianzhu University, Changchun 130118, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-0930-1157","authenticated-orcid":false,"given":"Yaoming","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Surveying and Prospecting Engineering, Jilin Jianzhu University, Changchun 130118, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Su","sequence":"additional","affiliation":[{"name":"College of Surveying and Prospecting Engineering, Jilin Jianzhu University, Changchun 130118, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xingwang","family":"Li","sequence":"additional","affiliation":[{"name":"College of Surveying and Prospecting Engineering, Jilin Jianzhu University, Changchun 130118, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuanlong","family":"Shan","sequence":"additional","affiliation":[{"name":"College of Earth Sciences, Jilin University, Changchun 130012, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1109\/PROC.1978.10902","article-title":"Time-Domain Electromagnetics and Its Applications","volume":"66","author":"Bennett","year":"1978","journal-title":"Proc. IEEE"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1016\/j.oregeorev.2015.10.029","article-title":"A geological assessment of airborne electromagnetics for mineral exploration through deeply weathered profiles in the southeast Yilgarn Cratonic margin, Western Australia","volume":"73","author":"Salama","year":"2016","journal-title":"Ore Geol. Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"629","DOI":"10.3997\/1873-0604.2009043","article-title":"A review of helicopter-borne electromagnetic methods for groundwater exploration","volume":"7","author":"Siemon","year":"2009","journal-title":"Near Surf. Geophys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3875","DOI":"10.5194\/hess-19-3875-2015","article-title":"Performance evaluation of groundwater model hydrostratigraphy from airborne electromagnetic data and lithological borehole logs","volume":"19","author":"Marker","year":"2015","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3471","DOI":"10.1109\/TAP.2025.3650631","article-title":"Measurement and Calibration Methods for Full-Polarization Characteristics of Radar Targets at Subterahertz Frequencies","volume":"74","author":"Xu","year":"2026","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1137\/1021044","article-title":"Solutions of Ill-Posed Problems (A. N. Tikhonov and V. Y. Arsenin)","volume":"21","author":"Willoughby","year":"1979","journal-title":"SIAM Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1007\/s10712-017-9435-1","article-title":"Application of 3-D Electromagnetic Inversion in Practice: Challenges, Pitfalls and Solution Approaches","volume":"38","author":"Miensopust","year":"2017","journal-title":"Surv. Geophys."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Butler, D.K. (2005). Inversion for Applied Geophysics: A Tutorial. Near-Surface Geophysics, Society of Exploration Geophysicists.","DOI":"10.1190\/1.9781560801719"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Haber, E. (2014). Computational Methods in Geophysical Electromagnetics, Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9781611973808"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1190\/1.1442303","article-title":"Occam\u2019s Inversion; a Practical Algorithm for Generating Smooth Models from Electromagnetic Sounding Data","volume":"52","author":"Constable","year":"1987","journal-title":"Geophysics"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2658","DOI":"10.1109\/TAP.2009.2027161","article-title":"Overview and Classification of Some Regularization Techniques for the Gauss-Newton Inversion Method Applied to Inverse Scattering Problems","volume":"57","author":"Mojabi","year":"2009","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1624","DOI":"10.1190\/1.1442973","article-title":"Nonlinear One-Dimensional Seismic Waveform Inversion Using Simulated Annealing","volume":"56","author":"Sen","year":"1991","journal-title":"Geophysics"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1794","DOI":"10.1190\/1.1442992","article-title":"Nonlinear Multiparameter Optimization Using Genetic Algorithms: Inversion of Plane-Wave Seismograms","volume":"56","author":"Stoffa","year":"1991","journal-title":"Geophysics"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1111\/j.1365-246X.1992.tb00100.x","article-title":"Genetic Algorithms in Seismic Waveform Inversion","volume":"109","author":"Sambridge","year":"1992","journal-title":"Geophys. J. Int."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"e2021RG000742","DOI":"10.1029\/2021RG000742","article-title":"Deep Learning for Geophysics: Current and Future Trends","volume":"59","author":"Yu","year":"2021","journal-title":"Rev. Geophys."},{"key":"ref_16","unstructured":"Yu, S., and Ma, J. (2020). Data-Driven Geophysics: From Dictionary Learning to Deep Learning. arXiv."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"166474","DOI":"10.1109\/ACCESS.2025.3612575","article-title":"Time to Frequency Domain Conversion for Transient Electromagnetic Data With Neural Networks","volume":"13","author":"Li","year":"2025","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2007912","DOI":"10.1109\/TGRS.2022.3222507","article-title":"Rapid Surrogate Modeling of Electromagnetic Data in Frequency Domain Using Neural Operator","volume":"60","author":"Peng","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1093\/gji\/ggz204","article-title":"Deep Learning Electromagnetic Inversion with Convolutional Neural Networks","volume":"218","author":"Puzyrev","year":"2019","journal-title":"Geophys. J. Int."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1080\/08123985.2019.1668240","article-title":"Imaging Subsurface Resistivity Structure from Airborne Electromagnetic Induction Data Using Deep Neural Network","volume":"51","author":"Noh","year":"2020","journal-title":"Explor. Geophys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"E209","DOI":"10.1190\/geo2020-0760.1","article-title":"Physics-Driven Deep-Learning Inversion with Application to Transient Electromagnetics","volume":"86","author":"Colombo","year":"2021","journal-title":"Geophysics"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"922","DOI":"10.1093\/jge\/gxae046","article-title":"Three-Dimensional Inversion for Short-Offset Transient Electromagnetic Data Based on 3D U-Net","volume":"21","author":"Zhao","year":"2024","journal-title":"J. Geophys. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"T337","DOI":"10.1190\/geo2023-0615.1","article-title":"Review of Physics-Informed Machine-Learning Inversion of Geophysical Data","volume":"89","author":"Schuster","year":"2024","journal-title":"Geophysics"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1109\/MSP.2022.3198805","article-title":"Physics-Embedded Machine Learning for Electromagnetic Data Imaging: Examining Three Types of Data-Driven Imaging Methods","volume":"40","author":"Guo","year":"2023","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1774","DOI":"10.1093\/gji\/ggae244","article-title":"Physics-Guided Deep Learning-Based Inversion for Airborne Electromagnetic Data","volume":"238","author":"Wu","year":"2024","journal-title":"Geophys. J. Int."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"7001705","DOI":"10.1109\/TMAG.2023.3247023","article-title":"Physics-Informed Neural Networks for Inverse Electromagnetic Problems","volume":"59","author":"Baldan","year":"2023","journal-title":"IEEE Trans. Magn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"7500505","DOI":"10.1109\/LGRS.2024.3485686","article-title":"Physics-Guided Deep Learning 3-D Inversion Based on Magnetic Data","volume":"22","author":"Shi","year":"2025","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"WA61","DOI":"10.1190\/geo2024-0210.1","article-title":"Deep Joint Inversion of Multiple Geophysical Data with U-Net Reparameterization","volume":"90","author":"Guo","year":"2025","journal-title":"Geophysics"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"7501405","DOI":"10.1109\/LGRS.2024.3505607","article-title":"Enhanced Electrical Resistivity Tomography With Prior Physical Information","volume":"22","author":"Jia","year":"2025","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"H97","DOI":"10.1190\/geo2019-0754.1","article-title":"Joint Inversion of Full-Waveform Ground-Penetrating Radar and Electrical Resistivity Data: Part 1","volume":"85","author":"Domenzain","year":"2020","journal-title":"Geophysics"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"5564","DOI":"10.1109\/TGRS.2020.2967344","article-title":"Well-Logging Constrained Seismic Inversion Based on Closed-Loop Convolutional Neural Network","volume":"58","author":"Wang","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1111\/j.1365-246X.2011.05347.x","article-title":"Computational recipes for electromagnetic inverse problems","volume":"189","author":"Egbert","year":"2012","journal-title":"Geophys. J. Int."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.cageo.2015.09.015","article-title":"SimPEG: An Open Source Framework for Simulation and Gradient Based Parameter Estimation in Geophysical Applications","volume":"85","author":"Cockett","year":"2015","journal-title":"Comput. Geosci."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Ronneberger, O., Fischer, P., and Brox, T. (2015). U-Net: Convolutional Networks for Biomedical Image Segmentation. Medical Image Computing and Computer-Assisted Intervention, Springer.","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"ref_35","unstructured":"Simonyan, K., and Zisserman, A. (2014). Very Deep Convolutional Networks for Large-Scale Image Recognition. arXiv."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"106063","DOI":"10.1016\/j.cageo.2025.106063","article-title":"TorchTEM3D: PyTorch-Driven Forward Modeling Platform for Fast 3D Transient Electromagnetic Modeling and Efficient Sensitivity Matrix Calculation","volume":"207","author":"Li","year":"2026","journal-title":"Comput. Geosci."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Qu, Z., Gao, Y., Xing, K., and Zhang, X. (2025). Deep-TEMNet: A Hybrid U-Net\u20132D LSTM Network for Efficient and Accurate 2.5D Transient Electromagnetic Forward Modeling. Remote Sens., 17.","DOI":"10.3390\/rs17020264"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Li, D., Wang, Z., Li, Y., and Jin, L. (2023). A General Forward Solver for 3D CSEMs with Multitype Sources and Operating Environments. Front. Earth Sci., 11.","DOI":"10.3389\/feart.2023.1206784"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"3833","DOI":"10.1109\/TMTT.2025.3650181","article-title":"Plasmonic skyrmion-based microfluidic-integrated flexible microwave meta-resonator for noninvasive intelligent flow rate sensing","volume":"74","author":"Wang","year":"2026","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","article-title":"Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","volume":"378","author":"Raissi","year":"2019","journal-title":"J. Comput. Phys."},{"key":"ref_41","unstructured":"Crosbie, J.W., Minsley, B.J., Hart, D.J., Fitzpatrick, W., Muldoon, M.A., Stewart, E.K., Hunt, R.J., Komiskey, M.J., and Duncker, J.J. (2023). Airborne Electromagnetic (AEM) Survey in Southwest and Southeast Areas, Wisconsin, 2022, U.S. Geological Survey Data Release."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/16\/5099\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T07:59:52Z","timestamp":1786521592000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/16\/5099"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,12]]},"references-count":41,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2026,8]]}},"alternative-id":["s26165099"],"URL":"https:\/\/doi.org\/10.3390\/s26165099","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,12]]}}}