{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T20:29:33Z","timestamp":1771705773323,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,17]],"date-time":"2018-08-17T00:00:00Z","timestamp":1534464000000},"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":["51504194"],"award-info":[{"award-number":["51504194"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007128","name":"Natural Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["2018JQ5133"],"award-info":[{"award-number":["2018JQ5133"]}],"id":[{"id":"10.13039\/501100007128","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010228","name":"Natural Science Foundation of Shaanxi Provincial Department of Education","doi-asserted-by":"publisher","award":["17JS106"],"award-info":[{"award-number":["17JS106"]}],"id":[{"id":"10.13039\/501100010228","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Borehole transient electromagnetic (TEM) techniques have been proven to be efficient for nondestructive evaluations (NDEs) of metal casings using eddy-current properties. However, physical limitations and bad borehole conditions restrict the use of eddy-current sensors, which makes downhole casing inspections very different from those of conventional NDE systems. In this paper, we present a uniform linear multi-coil array-based borehole TEM system for NDEs of downhole casings. On the basis of the borehole TEM signal model, a numerical multi-coil array approach using the Gauss\u2013Legendre quadrature is derived. The TEM response can be divided into two independent parts related to the transmitting-receiving distance (TRD) and the observation time and casing thickness. Using this property, the signal received by the multi-coil array is weighted to cancel the influence of the TRDs of the different array elements to obtain the optimal response according to the linearly constrained minimum variance criterion, which can be shown to be identical to that of achieving the maximum signal-to-noise ratio. The effectiveness of the proposed method was verified by applying the uniform linear multi-coil array to a borehole TEM system for NDEs of oil-well casings. Field experiments were conducted, and the results demonstrate the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/s18082707","type":"journal-article","created":{"date-parts":[[2018,8,17]],"date-time":"2018-08-17T10:54:25Z","timestamp":1534503265000},"page":"2707","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["A Uniform Linear Multi-Coil Array-Based Borehole Transient Electromagnetic System for Non-Destructive Evaluations of Downhole Casings"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9258-0764","authenticated-orcid":false,"given":"Bo","family":"Dang","sequence":"first","affiliation":[{"name":"Key Laboratory of Education Ministry for Photoelectric Logging and Detecting of Oil and Gas, Xi\u2019an Shiyou University, Xi\u2019an 710065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9794-9324","authenticated-orcid":false,"given":"Ling","family":"Yang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Education Ministry for Photoelectric Logging and Detecting of Oil and Gas, Xi\u2019an Shiyou University, Xi\u2019an 710065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changzan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yahong","family":"Zheng","sequence":"additional","affiliation":[{"name":"Key Laboratory of Education Ministry for Photoelectric Logging and Detecting of Oil and Gas, Xi\u2019an Shiyou University, Xi\u2019an 710065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Education Ministry for Photoelectric Logging and Detecting of Oil and Gas, Xi\u2019an Shiyou University, Xi\u2019an 710065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruirong","family":"Dang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Education Ministry for Photoelectric Logging and Detecting of Oil and Gas, Xi\u2019an Shiyou University, Xi\u2019an 710065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baoquan","family":"Sun","sequence":"additional","affiliation":[{"name":"Petroleum Engineering Technology Research Institute, Shengli Oilfield Company, SINOPEC, Dongying 257000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chen, C., Liu, F., Lin, J., Zhu, K.G., and Wang, Y.Z. (2016). An Optimized Air-Core Coil Sensor with a Magnetic Flux Compensation Structure Suitable to the Helicopter TEM System. Sensors, 16.","DOI":"10.3390\/s16040508"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.crte.2016.08.001","article-title":"Evaluation and mapping of Dead Sea coastal aquifers salinity using Transient Electromagnetic (TEM) resistivity measurements","volume":"349","author":"Ezersky","year":"2017","journal-title":"C. R. Geosci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.jappgeo.2003.08.004","article-title":"The application of the transient electromagnetic method in hydrogeophysical surveys","volume":"53","author":"Danielsen","year":"2003","journal-title":"J. Appl. Geophys."},{"key":"ref_4","first-page":"222","article-title":"New Borehole Transient Electromagnetic System for Reservoir Monitoring","volume":"53","author":"Dutta","year":"2012","journal-title":"Petrophysics"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1007\/BF01901643","article-title":"Electrical and electromagnetic borehole measurements: A review","volume":"17","author":"Spies","year":"1996","journal-title":"Surv. Geophys."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Huang, S., and Wang, S. (2016). The Pulsed Eddy Current Testing. New Technologies in Electromagnetic Non-Destructive Testing, Springer.","DOI":"10.1007\/978-981-10-0578-7"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2525","DOI":"10.3390\/s110302525","article-title":"Non-Destructive Techniques Based on Eddy Current Testing","volume":"11","year":"2011","journal-title":"Sensors"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.ndteint.2015.11.001","article-title":"Thickness measurement of metal pipe using swept-frequency eddy current testing","volume":"78","author":"Mao","year":"2016","journal-title":"Ndt E Int."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Brill, T.M., Demichel, C., Nichols, E.A., and Bermudez, F.Z. (2012, January 7\u20139). Electromagnetic Casing Inspection Tool for Corrosion Evaluation. Proceedings of the International Petroleum Technology Conference, Bangkok, Thailand.","DOI":"10.2523\/14865-MS"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Bateman, R.M. (2015). Casing Inspection Cased-Hole Log Analysis and Reservoir Performance Monitoring, Springer.","DOI":"10.1007\/978-1-4939-2068-6"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"57","DOI":"10.4283\/JMAG.2016.21.1.057","article-title":"Detection of Corrosion and Wall Thinning in Carbon Steel Pipe Covered With Insulation Using Pulsed Eddy Current","volume":"21","author":"Park","year":"2016","journal-title":"J. Magn."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Rifai, D., Abdallam, A.N., Razali, R., Ali, K., and Faraj, M.A. (2017). An eddy current testing platform system for pipe defect inspection based on an optimized eddy current technique probe design. Sensors, 17.","DOI":"10.3390\/s17030579"},{"key":"ref_13","first-page":"225","article-title":"Theoretical and experimental investigation of eddy current inspection of pipes with arbitrary position of sensor coils","volume":"Volume 5A","author":"Thompson","year":"1986","journal-title":"Review of Progress in Quantitative Nondestructive Evaluation"},{"key":"ref_14","first-page":"1","article-title":"Eddy-Current induction by a coil whose axis is perpendicular to that of a Tube","volume":"53","author":"Wu","year":"2017","journal-title":"IEEE Transact. Magn."},{"key":"ref_15","first-page":"353","article-title":"Investigation of casing inspection through tubing with pulsed eddy current","volume":"27","author":"Fu","year":"2012","journal-title":"NDT E Int."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Dang, B., Yang, L., Du, N., Liu, C., Dang, R., Wang, B., and Xie, Y. (2017). Auxiliary sensor-based borehole transient electromagnetic system for the nondestructive inspection of multipipe strings. Sensors, 17.","DOI":"10.3390\/s17081836"},{"key":"ref_17","first-page":"1673","article-title":"Improved interpretation of the downhole casing inspection logs for two strings of pipes","volume":"Volume 6A","author":"Thompson","year":"1987","journal-title":"Review of Progress in Quantitative Nondestructive Evaluation"},{"key":"ref_18","unstructured":"Dashevsky, A., and Yu, A. (2003). Principles of Induction Logging, Elsevier."},{"key":"ref_19","first-page":"1","article-title":"Synthesized magnetic field focusing using a current-controlled coil array","volume":"7","author":"Bo","year":"2016","journal-title":"IEEE Magn. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1029\/98RS00976","article-title":"A stable algorithm for simulation of array induction and measurement-while-drilling logging tools","volume":"33","author":"Tian","year":"2016","journal-title":"Radio Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/j.rgg.2010.03.009","article-title":"Effect of multicoil electromagnetic tool eccentricity on measured signals","volume":"51","author":"Onegova","year":"2010","journal-title":"Russian Geol. Geophys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"20160714","DOI":"10.1587\/elex.13.20160714","article-title":"Borehole electromagnetic induction system with noise cancelation for casing inspection","volume":"13","author":"Dang","year":"2016","journal-title":"IEICE Electron. Express"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Bourgeois, J., and Minker, W. (2009). Linearly Constrained Minimum Variance Beamforming. Time-Domain Beamforming and Blind Source Separation, Springer.","DOI":"10.1007\/978-0-387-68836-7"},{"key":"ref_24","first-page":"75","article-title":"Three effective inverse Laplace transform algorithms for computing time-domain electromagnetic responses","volume":"81","author":"Li","year":"2016","journal-title":"Geophysics"},{"key":"ref_25","first-page":"400","article-title":"Advances in transient (pulsed) eddy current for inspection of multi-layer aluminum structures in the presence of ferrous fasteners","volume":"1","author":"Desjardins","year":"2012","journal-title":"Am. Inst. Phys."},{"key":"ref_26","first-page":"945","article-title":"On computing the points and weights for Gauss-Legendre Quadratur","volume":"24","author":"Swarztrauber","year":"2002","journal-title":"Soc. Ind. Appl. Math."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/8\/2707\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:19:21Z","timestamp":1760195961000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/8\/2707"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,17]]},"references-count":26,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2018,8]]}},"alternative-id":["s18082707"],"URL":"https:\/\/doi.org\/10.3390\/s18082707","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,17]]}}}