{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T08:20:58Z","timestamp":1765354858545,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,4,30]],"date-time":"2022-04-30T00:00:00Z","timestamp":1651276800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["42074161","42104143","2021JJ30806","2021zzts0270"],"award-info":[{"award-number":["42074161","42104143","2021JJ30806","2021zzts0270"]}]},{"name":"Natural Science Foundation of Hunan Province, China","award":["42074161","42104143","2021JJ30806","2021zzts0270"],"award-info":[{"award-number":["42074161","42104143","2021JJ30806","2021zzts0270"]}]},{"name":"Fundamental Research Funds for the Central Universities of Central South University","award":["42074161","42104143","2021JJ30806","2021zzts0270"],"award-info":[{"award-number":["42074161","42104143","2021JJ30806","2021zzts0270"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>High-precision detection of the underground pipelines is an indispensable part of the development and construction of cities. At present, the inversion technology for ground-penetrating radar (GPR) data is an effective means of realizing shallow-underground-space visualization in the field of geophysical exploration. However, the traditional full-waveform inversion (FWI) method usually faces the problems of strong nonlinearity of the objective function, high dependence on the initial model, and huge calculation cost. For improving the accuracy and efficiency of GPR data inversion, a wavefield reconstruction inversion (WRI) strategy is used for GPR data imaging to reduce the nonlinearity of the inversion problem and the dependence on the initial model. Then, the frequency weighting strategy and the multi-scale method are adopted to avoid the high-frequency component data dominating the optimization process and enhance the stability of inversion. In this paper, two numerical experiments of pipeline models with different materials and spacing or buried depths verified that the proposed method can effectively reconstruct the subsurface pipelines, and further performance of our algorithm on the field data verified the reliability of high-precision imaging of urban underground pipelines, which shows great potential of application in the field of high-precision detection of the urban underground pipelines.<\/jats:p>","DOI":"10.3390\/rs14092162","type":"journal-article","created":{"date-parts":[[2022,5,2]],"date-time":"2022-05-02T07:08:58Z","timestamp":1651475338000},"page":"2162","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Wavefield Reconstruction Inversion Based on the Multi-Scale Cumulative Frequency Strategy for Ground-Penetrating Radar Data: Application to Urban Underground Pipeline"],"prefix":"10.3390","volume":"14","author":[{"given":"Deshan","family":"Feng","sequence":"first","affiliation":[{"name":"School of Geosciences and Info-Physics, Central South University, Changsha 410083, China"},{"name":"Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education, Changsha 410083, China"}]},{"given":"Siyuan","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Geosciences and Info-Physics, Central South University, Changsha 410083, China"},{"name":"Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education, Changsha 410083, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3039-4683","authenticated-orcid":false,"given":"Xun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Geosciences and Info-Physics, Central South University, Changsha 410083, China"},{"name":"Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education, Changsha 410083, China"}]},{"given":"Xuan","family":"Su","sequence":"additional","affiliation":[{"name":"School of Geosciences and Info-Physics, Central South University, Changsha 410083, China"},{"name":"Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education, Changsha 410083, China"}]},{"given":"Shuo","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Geosciences and Info-Physics, Central South University, Changsha 410083, China"},{"name":"Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education, Changsha 410083, China"}]},{"given":"Cen","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Geosciences and Info-Physics, Central South University, Changsha 410083, China"},{"name":"Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education, Changsha 410083, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Iftimie, N., Savin, A., Steigmann, R., and Dobrescu, G.S. (2021). Underground Pipeline Identification into a Non-Destructive Case Study Based on Ground-Penetrating Radar Imaging. Remote Sens., 13.","DOI":"10.3390\/rs13173494"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Daniels, D.J. (2004). Ground Penetrating Radar, Institution of Electrical Engineers. [2nd ed.].","DOI":"10.1049\/PBRA015E"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bianchini Ciampoli, L., Tosti, F., Economou, N., and Benedetto, F. (2019). Signal Processing of GPR Data for Road Surveys. Geosciences, 9.","DOI":"10.3390\/geosciences9020096"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Solla, M., P\u00e9rez-Gracia, V., and Fontul, S. (2021). A Review of GPR Application on Transport Infrastructures: Troubleshooting and Best Practices. Remote Sens., 13.","DOI":"10.3390\/rs13040672"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Li, J.X., Guo, T., Leung, H., Xu, H., Liu, L., Wang, B.J., and Liu, Y. (2019). Locating Underground Pipe Using Wideband Chaotic Ground Penetrating Radar. Sensors, 19.","DOI":"10.3390\/s19132913"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Park, B., Kim, J., Lee, J., Kang, M.-S., and An, Y.-K. (2018). Underground Object Classification for Urban Roads Using Instantaneous Phase Analysis of Ground-Penetrating Radar (GPR) Data. Remote Sens., 10.","DOI":"10.3390\/rs10091417"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"H27","DOI":"10.1190\/geo2017-0617.1","article-title":"Improving estimates of buried pipe diameter and infilling material from ground-penetrating radar profiles with full-waveform inversion","volume":"83","author":"Jazayeri","year":"2018","journal-title":"Geophysics"},{"key":"ref_8","first-page":"4647","article-title":"Fast Ground Penetrating Radar double-parameter inversion based on GPU-parallel by time-domain full waveform optimization conjugate gradient method","volume":"61","author":"Feng","year":"2018","journal-title":"Chin. J. Geophys. Chin. Ed."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4417","DOI":"10.1109\/TGRS.2019.2891206","article-title":"A Machine Learning-Based Fast-Forward Solver for Ground Penetrating Radar With Application to Full-Waveform Inversion","volume":"57","author":"Giannakis","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Persico, R., and Morelli, G. (2020). Combined Migrations and Time-Depth Conversions in GPR Prospecting: Application to Reinforced Concrete. Remote Sens., 12.","DOI":"10.3390\/rs12172778"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1093\/gji\/ggac058","article-title":"High-resolution velocity estimation from surface-based common-offset GPR reflection data","volume":"230","author":"Liu","year":"2022","journal-title":"Geophys. J. Int."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"H51","DOI":"10.1190\/geo2019-0696.1","article-title":"Estimating reservoir permeability with borehole radar","volume":"85","author":"Zhou","year":"2020","journal-title":"Geophysics"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Meng, X., Liu, S., Xu, Y., and Fu, L. (2019). Application of Laplace Domain Waveform Inversion to Cross-Hole Radar Data. Remote Sens., 11.","DOI":"10.3390\/rs11161839"},{"key":"ref_14","first-page":"1","article-title":"Wavefield Reconstruction Inversion of GPR Data for Permittivity and Conductivity Models in the Frequency Domain Based on Modified Total Variation Regularization","volume":"60","author":"Feng","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1093\/gji\/ggt528","article-title":"Two-dimensional permittivity and conductivity imaging by full waveform inversion of multioffset GPR data: A frequency-domain quasi-Newton approach","volume":"197","author":"Brossier","year":"2014","journal-title":"Geophys. J. Int."},{"key":"ref_16","unstructured":"Watson, F.M. (2016). Better Imaging for Landmine Detection: An Exploration of 3D Full-Wave Inversion for Ground-Penetrating Radar. [Ph.D. Thesis, The University of Manchester]."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.jappgeo.2018.02.025","article-title":"Inverts permittivity and conductivity with structural constraint in GPR FWI based on truncated Newton method","volume":"151","author":"Ren","year":"2018","journal-title":"J. Appl. Geophys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1111\/j.1365-2478.1990.tb01846.x","article-title":"Inverse Theory Applied to Multi-Source Cross-Hole Tomography. Part 1: Acoustic Wave-Equation Method 1","volume":"38","author":"Pratt","year":"1990","journal-title":"Geophys. Prospect."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"R1","DOI":"10.1190\/1.3073002","article-title":"Simultaneous multifrequency inversion of full-waveform seismic data","volume":"74","author":"Hu","year":"2009","journal-title":"Geophysics"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.jappgeo.2011.12.001","article-title":"Taming the non-linearity problem in GPR full-waveform inversion for high contrast media","volume":"78","author":"Meles","year":"2012","journal-title":"J. Appl. Geophys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"920","DOI":"10.1111\/j.1365-2478.2011.00973.x","article-title":"Discontinuous Galerkin frequency domain forward modelling for the inversion of electric permittivity in the 2D case","volume":"59","author":"Lanteri","year":"2011","journal-title":"Geophys. Prospect."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"H79","DOI":"10.1190\/geo2012-0045.1","article-title":"Quantitative conductivity and permittivity estimation using full-waveform inversion of on-ground GPR data","volume":"77","author":"Busch","year":"2012","journal-title":"Geophysics"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3947","DOI":"10.1109\/TGRS.2013.2278297","article-title":"Improved characterization of fine-texture soils using on-ground GPR full-waveform inversion","volume":"52","author":"Busch","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1949","DOI":"10.1109\/TGRS.2020.3004465","article-title":"A frequency-domain quasi-Newton-based biparameter synchronous imaging scheme for ground-penetrating radar with applications in full waveform inversion","volume":"59","author":"Feng","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1190\/1.1443880","article-title":"Multiscale seismic waveform inversion","volume":"60","author":"Bunks","year":"1995","journal-title":"Geophysics"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1109\/LGRS.2020.2976146","article-title":"Multiparameter Full-Waveform Inversion of 3-D On-Ground GPR With a Modified Total Variation Regularization Scheme","volume":"18","author":"Wang","year":"2020","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1093\/gji\/ggt258","article-title":"Mitigating local minima in full-waveform inversion by expanding the search space","volume":"195","author":"Herrmann","year":"2013","journal-title":"Geophys. J. Int."},{"key":"ref_28","first-page":"015007","article-title":"A penalty method for PDE-constrained optimization in inverse problems","volume":"32","author":"Herrmann","year":"2015","journal-title":"Inverse Probl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1190\/tle36010094.1","article-title":"Constraints versus penalties for edge-preserving full-waveform inversion","volume":"36","author":"Peters","year":"2017","journal-title":"Lead. Edge"},{"key":"ref_30","unstructured":"Fang, Z. (2018). Source Estimation and Uncertainty Quantification for Wave-Equation Based Seismic imaging and Inversion. [Ph.D. Thesis, University of British Columbia]."},{"key":"ref_31","first-page":"015004","article-title":"Wavefield reconstruction inversion with a multiplicative cost function","volume":"34","author":"Yao","year":"2017","journal-title":"Inverse Probl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1192","DOI":"10.1109\/TGRS.2019.2944464","article-title":"Compound regularization of full-waveform inversion for imaging piecewise media","volume":"58","author":"Aghamiry","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1316","DOI":"10.1093\/gji\/ggz369","article-title":"ADMM-based multiparameter wavefield reconstruction inversion in VTI acoustic media with TV regularization","volume":"219","author":"Aghamiry","year":"2019","journal-title":"Geophys. J. Int."},{"key":"ref_34","first-page":"R381","article-title":"Multiparameter wavefield reconstruction inversion for wavespeed and attenuation with bound constraints and total variation regularization","volume":"85","author":"Aghamiry","year":"2020","journal-title":"Geophysics"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"R879","DOI":"10.1190\/geo2020-0743.1","article-title":"A dual formulation of wavefield reconstruction inversion for large-scale seismic inversion","volume":"86","author":"Rizzuti","year":"2021","journal-title":"Geophysics"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"103836","DOI":"10.1016\/j.jappgeo.2019.103836","article-title":"An exact PML to truncate lattices with unstructured-mesh-based adaptive finite element method in frequency domain for ground penetrating radar simulation","volume":"170","author":"Feng","year":"2019","journal-title":"J. Appl. Geophys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1006\/jcph.1994.1159","article-title":"A perfectly matched layer for the absorption of electromagnetic waves","volume":"114","author":"Berenger","year":"1994","journal-title":"J. Comput. Phys."},{"key":"ref_38","unstructured":"Nocedal, J., and Wright, S. (2006). Numerical Optimization, Springer Science & Business Media."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2807","DOI":"10.1109\/TGRS.2007.901048","article-title":"Full-waveform inversion of crosshole radar data based on 2-D finite-difference time-domain solutions of Maxwell\u2019s equations","volume":"45","author":"Ernst","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/9\/2162\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:05:12Z","timestamp":1760137512000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/9\/2162"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,30]]},"references-count":39,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["rs14092162"],"URL":"https:\/\/doi.org\/10.3390\/rs14092162","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2022,4,30]]}}}