Research and Application of a Cross-Gradient Constrained Time-Lapse Inversion Method for Direct Current Resistivity Monitoring
Abstract
1. Introduction
2. Methodology
2.1. Independent Time-Lapse Inversion
2.2. Constrained Time-Lapse Inversion
2.3. Cross-Gradient Constrained Time-Lapse Inversion
3. Numerical Examples
3.1. Time-Lapse Resistivity
3.2. Time-Lapse Inversion Results
4. Physical Model Experiments
5. Case Study
5.1. Background Information
5.2. Inversion Results
6. Discussion
6.1. Scenario Applicability of the Method
6.2. Cross-Gradient and 4D Inversion
6.3. 2.5D Approximation and 3D Effects
6.4. Justification for the Simplified Medium Assumptions
6.5. Noise Effects and Method Applicability
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Wang, J.; Zhang, S.; Lv, T.-K.; Liu, Y.; Ji, K.-P. Method application of distributed optical fiber Brillouin sensing in slope monitoring. In Proceedings of the IEEE 6th Advanced Information Management, Communication, Electronic and Automation Control Conference (IMCEC), Chongqing, China, 24–26 May 2024. [Google Scholar]
- Wang, B.; Liu, S.-D.; Li, S.-N.; Zhou, F.-B. Double-transmitting and sextuple-receiving borehole transient electromagnetic method and experimental study. Earth Sci. Res. J. 2017, 21, 77–83. [Google Scholar] [CrossRef]
- Farmani, M.B.; Kitterød, N.-O.; Keers, H. Inverse modeling of unsaturated flow parameters using dynamic geological structure conditioned by GPR tomography. Water Resour. Res. 2008, 44, W08401. [Google Scholar] [CrossRef]
- Wang, B.; Jin, B.; Huang, L.-Y.; Liu, S.-D.; Sun, H.-C.; Liu, J.-C.; Ding, X.; Wang, S.-C. A Hilbert polarization imaging method with breakpoint diffracted wave in front of roadway. J. Appl. Geophys. 2020, 177, 104032. [Google Scholar] [CrossRef]
- Whiteley, J.-S.; Chambers, J.-E.; Uhlemann, S.; Wilkinson, P.-B.; Kendall, J.-M. Geophysical monitoring of moisture-induced landslides: A review. Rev. Geophys. 2019, 57, 106–145. [Google Scholar] [CrossRef]
- Slater, L.; Binley, A. Advancing hydrological process understanding from long-term resistivity monitoring systems. WIREs Water 2021, 8, e1513. [Google Scholar] [CrossRef]
- Massarweh, O.; Abushaikha, A.S. CO2 sequestration in subsurface geological formations: A review of trapping mechanisms and monitoring techniques. Earth-Sci. Rev. 2024, 253, 104793. [Google Scholar] [CrossRef]
- Lu, T.; Liu, S.-D.; Wang, B.; Wu, R.-X.; Hu, X.-W. A review of geophysical exploration technology for mine water disaster in China: Applications and trends. Mine Water Environ. 2017, 36, 331–340. [Google Scholar] [CrossRef]
- Barker, R.; Moore, J. The application of time-lapse electrical tomography in groundwater studies. Lead. Edge 1998, 17, 1454–1458. [Google Scholar] [CrossRef]
- Chang, P.-Y.; Chang, L.-C.; Hsu, S.-Y.; Tsai, J.-P.; Chen, W.-F. Estimating the hydrogeological parameters of an unconfined aquifer with the time-lapse resistivity-imaging method during pumping tests: Case studies at the Pengtsuo and Dajou sites, Taiwan. J. Appl. Geophys. 2017, 144, 134–143. [Google Scholar] [CrossRef]
- Thompson, J.; Buda, A.; Shober, A.; Ntarlagiannis, D.; Collick, A.; Kennedy, C.; Mosesso, L.; Reiner, M.; Triantafilis, J.; Pokhrel, S.; et al. Electrical geophysical monitoring of subsurface solute transport in low-relief agricultural landscapes in response to a simulated major rainfall event. J. Hydrol. 2025, 646, 132313. [Google Scholar] [CrossRef]
- Daily, W.; Ramirez, A. Electrical resistance tomography during in-situ trichloroethylene remediation at the Savannah River Site. J. Appl. Geophys. 1995, 33, 239–249. [Google Scholar] [CrossRef]
- Ugbor, C.C.; Ikwuagwu, I.E.; Ogboke, O.J. 2D inversion of electrical resistivity investigation of contaminant plume around a dumpsite near Onitsha expressway in southeastern Nigeria. Sci. Rep. 2021, 11, 11854. [Google Scholar] [CrossRef]
- Nivorlis, A.; Rossi, M.; Dahlin, T. Temporal filtering and time-lapse inversion of geoelectrical data for long-term monitoring with application to a chlorinated hydrocarbon contaminated site. Geophys. J. Int. 2022, 228, 1648–1664. [Google Scholar] [CrossRef]
- Wilkinson, P.; Chambers, J.; Uhlemann, S.; Meldrum, P.; Smith, A.; Dixon, N.; Loke, M.H. Reconstruction of landslide movements by inversion of 4-D electrical resistivity tomography monitoring data. Geophys. Res. Lett. 2016, 43, 1166–1174. [Google Scholar] [CrossRef]
- Palis, E.; Lebourg, T.; Vidal, M.; Levy, C.; Tric, E.; Hernandez, M. Multiyear time-lapse ERT to study short- and long-term landslide hydrological dynamics. Landslides 2017, 14, 1333–1343. [Google Scholar] [CrossRef]
- Lapenna, V.; Perrone, A. Time-lapse electrical resistivity tomography (TL-ERT) for landslide monitoring: Recent advances and future directions. Appl. Sci. 2022, 12, 1425. [Google Scholar] [CrossRef]
- Bergmann, P.; Schmidt-Hattenberger, C.; Kiessling, D.; Rücker, C.; Labitzke, T.; Henninges, J.; Baumann, G.; Schütt, H. Surface-downhole electrical resistivity tomography applied to monitoring of CO2 storage at Ketzin, Germany. Geophysics 2012, 77, B253–B267. [Google Scholar]
- Bergmann, P.; Ivandic, M.; Norden, B.; Rücker, C.; Kiessling, D.; Lüth, S.; Schmidt-Hattenberger, C.; Juhlin, C. Combination of seismic reflection and constrained resistivity inversion with an application to 4D imaging of the CO2 storage site, Ketzin, Germany. Geophysics 2014, 79, B37–B50. [Google Scholar] [CrossRef]
- Khan, S.; Khulief, Y.; Juanes, R.; Bashmal, S.; Usman, M.; Al-Shuhail, A. Geomechanical modeling of CO2 sequestration: A review focused on CO2 injection and monitoring. J. Environ. Chem. Eng. 2024, 12, 112847. [Google Scholar] [CrossRef]
- Liu, S.-C.; Liu, X.-M.; Jiang, Z.-H.; Xing, T.; Chen, M.-Z. Research on electrical prediction for evaluating water conducting fracture zones in coal seam floor. Chin. J. Rock Mech. Eng. 2009, 28, 348–356. [Google Scholar]
- Jin, D.-W.; Zhao, C.-H.; Duan, J.-H.; Qiao, W.; Lu, J.-J.; Li, P.; Zhou, Z.-F.; Li, D.-S. Research on 3D monitoring and intelligent early warning system for water hazard of coal seam floor. J. China Coal Soc. 2020, 45, 2256–2264. [Google Scholar]
- Yang, H.; Liu, S.; Yang, C. Dynamic monitoring of mining destruction on coal seam floor with constrained time-lapse resistivity imaging inversion. IEEE Access 2022, 10, 84799–84808. [Google Scholar] [CrossRef]
- Hayley, K.; Pidlisecky, A.; Bentley, L.R. Simultaneous time-lapse electrical resistivity inversion. J. Appl. Geophys. 2011, 75, 401–411. [Google Scholar] [CrossRef]
- Liu, J.-C.; Zhang, Z.-Y.; Zhou, F.; Li, M.; Ou, Y.-W.; Yang, L.; Yi, K. Two-dimensional joint inversion of DC resistivity method and seismic traveltime tomography method based on the FCM cluster constraint. Chin. J. Geophys. 2023, 66, 3048–3059. [Google Scholar]
- Tao, T.; Han, P.; Ma, H.; Tan, H.-D. 3D time-lapse resistivity inversion. Chin. J. Geophys. 2024, 67, 3973–3988. [Google Scholar]
- Cho, I.-K.; Jeong, D.-B. 4D inversion of resistivity monitoring data with adaptive time domain regularization. J. Appl. Geophys. 2022, 198, 104559. [Google Scholar] [CrossRef]
- De Franco, R.; Biella, G.; Tosi, L.; Teatini, P.; Lozej, A.; Chiozzotto, B.; Giada, M.; Rizzetto, F.; Claude, C.; Mayer, A.; et al. Monitoring the saltwater intrusion by time-lapse electrical resistivity tomography: The Chioggia test site (Venice Lagoon, Italy). J. Appl. Geophys. 2009, 69, 117–130. [Google Scholar] [CrossRef]
- Inim, I.J.; Udosen, N.I.; Tijani, M.N.; Affiah, U.E.; George, N.J. Time-lapse electrical resistivity investigation of seawater intrusion in coastal aquifer of Ibeno, Southeastern Nigeria. Appl. Water Sci. 2020, 10, 1–12. [Google Scholar] [CrossRef]
- Daily, W.; Ramirez, A.; LaBrecque, D.; Nitao, J. Electrical resistivity tomography of vadose water movement. Water Resour. Res. 1992, 28, 1429–1442. [Google Scholar] [CrossRef]
- Liu, B.; Liu, Z.-Y.; Li, S.-C.; Fan, K.-R.; Nie, L.-C.; Zhang, X.-X. An improved time-lapse resistivity tomography to monitor and estimate the impact on the groundwater system induced by tunnel excavation. Tunn. Undergr. Space Technol. 2017, 66, 107–120. [Google Scholar] [CrossRef]
- LaBrecque, D.; Alumbaugh, D.L.; Yang, X.-J.; Paprocki, L.; Brainard, J. Three-dimensional monitoring of vadose zone infiltration using electrical resistivity tomography and cross-borehole ground-penetrating radar. Methods Geochem. Geophys. 2002, 35, 259–272. [Google Scholar]
- Loke, M.H. Constrained time-lapse resistivity imaging inversion. In Proceedings of the Symposium on the Application of Geophysics to Engineering and Environmental Problems (SAGEEP), Denver, CO, USA, 14–19 March 2001. [Google Scholar]
- Oldenborger, G.A.; Knoll, M.D.; Routh, P.S.; LaBrecque, D.J. Time-lapse ERT monitoring of an injection/withdrawal experiment in a shallow unconfined aquifer. Geophysics 2007, 72, F177–F187. [Google Scholar] [CrossRef]
- Miller, C.R.; Routh, P.S.; Brosten, T.R.; McNamara, J.P. Application of time-lapse ERT imaging to watershed characterization. Geophysics 2008, 73, G7–G17. [Google Scholar] [CrossRef]
- Kim, K.-J.; Cho, I.-K. Time-lapse inversion of 2D resistivity monitoring data with a spatially varying cross-model constraint. J. Appl. Geophys. 2011, 74, 114–122. [Google Scholar] [CrossRef]
- Fiandaca, G.; Doetsch, J.; Vignoli, G.; Auken, E. Generalized focusing of time-lapse changes with applications to direct current and time-domain induced polarization inversions. Geophys. J. Int. 2015, 203, 1101–1112. [Google Scholar] [CrossRef]
- Hermans, T.; Kemna, A.; Nguyen, F. Covariance-constrained difference inversion of time-lapse electrical resistivity tomography data. Geophysics 2016, 81, E311–E322. [Google Scholar] [CrossRef]
- Kim, J.-H.; Yi, M.-J.; Park, S.-G.; Kim, J.G. 4-D inversion of DC resistivity monitoring data acquired over a dynamically changing earth model. J. Appl. Geophys. 2009, 68, 522–532. [Google Scholar] [CrossRef]
- Karaoulis, M.C.; Kim, J.-H.; Tsourlos, P.I. 4D active time constrained resistivity inversion. J. Appl. Geophys. 2011, 73, 25–34. [Google Scholar] [CrossRef]
- Karaoulis, M.; Tsourlos, P.; Kim, J.-H.; Revil, A. 4D time-lapse ERT inversion: Introducing combined time and space constraints. Near Surf. Geophys. 2014, 12, 25–34. [Google Scholar] [CrossRef]
- Loke, M.H.; Barker, R.D. Least-squares deconvolution of apparent resistivity pseudosections. Geophysics 1995, 60, 1682–1690. [Google Scholar] [CrossRef]
- Sjödahl, P.; Dahlin, T.; Zhou, B. 2.5 D resistivity modeling of embankment dams to assess influence from geometry and material properties. Geophysics 2006, 71, G107–G114. [Google Scholar] [CrossRef]
- Yi, M.-J.; Kim, J.-H.; Chung, S.-H. Enhancing the resolving power of least-squares inversion with active constraint balancing. Geophysics 2003, 68, 931–941. [Google Scholar] [CrossRef]
- Loke, M.H.; Lane, J.W. The use of constraints in 2D and 3D resistivity modelling. In Proceedings of the 8th Environmental and Engineering Geophysical Society European Section (EEGS-ES) Meeting, Aveiro, Portugal, 21–25 October 2002. [Google Scholar]
- Jaysaval, P.; Hammond, G.E.; Johnson, T.C. Massively parallel modeling and inversion of electrical resistivity tomography data using PFLOTRAN. Geosci. Model Dev. Discuss. 2022, 2022, 1–26. [Google Scholar] [CrossRef]
- Hansen, P.C. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev. 1992, 34, 561–580. [Google Scholar] [CrossRef]
- Loke, M.H.; Dahlin, T.; Rucker, D.F. Smoothness-constrained time-lapse inversion of data from 3D resistivity surveys. Near Surf. Geophys. 2014, 12, 5–24. [Google Scholar] [CrossRef]
- Pollock, D.; Cirpka, O.A. Fully coupled hydrogeophysical inversion of a laboratory salt tracer experiment monitored by electrical resistivity tomography. Water Resour. Res. 2012, 48, W01505. [Google Scholar] [CrossRef]
- Singha, K.; Day-Lewis, F.D.; Johnson, T.; Slater, L.D. Advances in interpretation of subsurface processes with time-lapse electrical imaging. Hydrol. Process. 2015, 29, 1549–1576. [Google Scholar] [CrossRef]
- Adepelumi, A.A.; Solanke, A.A.; Sanusi, O.B.; Shallangwa, A.M. Model tank electrical resistivity characterization of LNAPL migration in a clayey-sand formation. Environ. Geol. 2006, 50, 1221–1233. [Google Scholar] [CrossRef]
- Wu, R.-X.; Wu, Y.-Z.; Sun, B.-Y.; Zhou, G.-Q.; Zheng, L.-L. Monitoring of Overburden Failure with a Large Fractured-Height Working Face in a Deep Jurassic Coal Seam Based on the Electric Method. Appl. Sci. 2024, 14, 10293. [Google Scholar] [CrossRef]
- Du, L.; Zhu, W.-J.; Wang, L.; Li, H.; Jiao, X.-Y.; Qin, T. Using roof borehole electrical resistivity tomography to monitor roof water infiltration in a mine work face. Sci. Rep. 2025, 15, 2621. [Google Scholar] [CrossRef]
- Dimech, A.; Cheng, L.-Z.; Chouteau, M.; Chambers, J.; Uhlemann, S.; Wilkinson, P.; Meldrum, P.; Mary, B.; Fabien-Ouellet, G.; Isabelle, A. A review on applications of time-lapse electrical resistivity tomography over the last 30 years: Perspectives for mining waste monitoring. Surv. Geophys. 2022, 43, 1699–1759. [Google Scholar] [CrossRef] [PubMed]
- Kim, J.-H.; Supper, R.; Tsourlos, P.; Yi, M.-J. Four-dimensional inversion of resistivity monitoring data through Lp norm minimizations. Geophys. J. Int. 2013, 195, 1640–1656. [Google Scholar] [CrossRef]
- Bai, P.; Vignoli, G.; Hansen, T.M. 1D stochastic inversion of airborne time-domain electromagnetic data with realistic prior and accounting for the forward modeling error. Remote Sens. 2021, 13, 3881. [Google Scholar] [CrossRef]
- Engebretsen, K.W.; Zhang, B.; Fiandaca, G.; Madsen, L.M.; Auken, E.; Christiansen, A.V. Accelerated 2.5-D inversion of airborne transient electromagnetic data using reduced 3-D meshing. Geophys. J. Int. 2022, 230, 643–653. [Google Scholar] [CrossRef]
- Wiese, T.; Greenhalgh, S.; Zhou, B.; Greenhalgh, M.; Marescot, L. Resistivity inversion in 2-D anisotropic media: Numerical experiments. Geophys. J. Int. 2015, 201, 247–266. [Google Scholar] [CrossRef]
- Kemna, A.; Binley, A.; Cassiani, G.; Niederleithinger, E.; Revil, A.; Slater, L.; Williams, K.H.; Flores Orozco, A.; Haegel, F.-H.; Hördt, A.; et al. An overview of the spectral induced polarization method for near-surface applications. Near Surf. Geophys. 2012, 10, 453–468. [Google Scholar] [CrossRef]
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Chen, S.; Wang, B.; Yang, H.; Li, Y. Research and Application of a Cross-Gradient Constrained Time-Lapse Inversion Method for Direct Current Resistivity Monitoring. Appl. Sci. 2025, 15, 10330. https://doi.org/10.3390/app151910330
Chen S, Wang B, Yang H, Li Y. Research and Application of a Cross-Gradient Constrained Time-Lapse Inversion Method for Direct Current Resistivity Monitoring. Applied Sciences. 2025; 15(19):10330. https://doi.org/10.3390/app151910330
Chicago/Turabian StyleChen, Sheng, Bo Wang, Haiping Yang, and Yunchen Li. 2025. "Research and Application of a Cross-Gradient Constrained Time-Lapse Inversion Method for Direct Current Resistivity Monitoring" Applied Sciences 15, no. 19: 10330. https://doi.org/10.3390/app151910330
APA StyleChen, S., Wang, B., Yang, H., & Li, Y. (2025). Research and Application of a Cross-Gradient Constrained Time-Lapse Inversion Method for Direct Current Resistivity Monitoring. Applied Sciences, 15(19), 10330. https://doi.org/10.3390/app151910330