{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T08:20:55Z","timestamp":1765354855548,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,3,9]],"date-time":"2022-03-09T00:00:00Z","timestamp":1646784000000},"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":["42130805","42074151","42004106"],"award-info":[{"award-number":["42130805","42074151","42004106"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Ground-penetrating radar (GPR) crosshole tomography is widely applied to subsurface media images. However, the inadequacies of ray methods may limit the resolution of crosshole radar images, since the ray method is a type of high-frequency approximation. To solve this problem, the full waveform method is introduced for GPR inversion. However, full waveform inversion is computationally expensive. In this paper, we introduce a trained neural network that can be evaluated very quickly to replace a computationally intensive forward model. Additionally, the forward error of the trained neural network can be statistically analyzed. We demonstrate a methodology for a full waveform inversion of crosshole ground-penetrating radar data using the Markov chain Monte Carlo (MCMC) method. An accurate forward model based on Maxwell\u2019s equations is replaced by a quickly trained neural network. This method achieves a high computation efficiency, which is four orders of magnitude faster than the accurate forward model. The inversion result of the synthetic waveform data shows a good performance of the trained neural network, which greatly improves the calculation efficiency.<\/jats:p>","DOI":"10.3390\/rs14061320","type":"journal-article","created":{"date-parts":[[2022,3,10]],"date-time":"2022-03-10T02:10:35Z","timestamp":1646878235000},"page":"1320","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["MCMC Method of Inverse Problems Using a Neural Network\u2014Application in GPR Crosshole Full Waveform Inversion: A Numerical Simulation Study"],"prefix":"10.3390","volume":"14","author":[{"given":"Shengchao","family":"Wang","sequence":"first","affiliation":[{"name":"College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China"}]},{"given":"Liguo","family":"Han","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China"}]},{"given":"Xiangbo","family":"Gong","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China"}]},{"given":"Shaoyue","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China"}]},{"given":"Xingguo","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Instrumentation & Electrical Engineering, Jilin University, Changchun 130026, China"}]},{"given":"Pan","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"102293","DOI":"10.1016\/j.ndteint.2020.102293","article-title":"An experimental and numerical approach to combine Ground Penetrating Radar and computational modeling for the identification of early cracking in cement concrete pavements","volume":"115","author":"Rasol","year":"2020","journal-title":"NDT E Int."},{"key":"ref_2","first-page":"1366","article-title":"Non-destructive testing for the analysis of moisture in the masonry arch bridge of Lubians (Spain)","volume":"20","author":"Solla","year":"2013","journal-title":"Struct. 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