Skip to main content
SpringerLink
Log in

Numerical Modeling for 4-D Self-Potential Resistivity Model

  • Published:
Pure and Applied Geophysics Aims and scope Submit manuscript

Abstract

Geoelectric models, such as self-potential (SP) resistivity models, are sometimes variable, i.e., subsurface geophysical properties such as resistivity distributions and causative sources vary in time and space. How to conduct numerical modeling of such dynamic models efficiently is a difficult problem. Conventional numerical algorithms simply repeat and accumulate the static single simulation at different moments so that the total calculation time is proportional to the number of single calculations required by the dynamic process. However, only a small part of the properties in dynamic models changes over time and space, and the numerical calculation process has some repeated elements among different single simulations. Herein, the concepts of frames and dynamic and static blocks in video technology were introduced into a conventional numerical algorithm to construct a dynamic scheme for 3-D time-series (4-D) models. Specifically, a 3-D finite–infinite element coupling method integrating irregular hexahedral finite elements and unidirectional mapping of infinite elements was proposed in conjunction with a dynamic update strategy to realize the numerical modeling of dynamic resistivity models. Two tests demonstrated the correctness and effectiveness of the algorithm, and two dynamic SP resistivity models concerning contaminant plume diffusion and solute transport processes were simulated to verify the effect of the dynamic algorithm. The results suggest that the proposed algorithm is effective for dynamic SP resistivity models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Akram, M., & Izquierdo, E. (2013). Fast motion estimation for surveillance video compression. Signal, Image and Video Processing, 7, 1103–1112.

    Article  Google Scholar 

  • Arora, T., Linde, N., Revil, A., & Castermant, J. (2007). Non-intrusive characterization of the redox potential of landfill leachate plumes from self-potential data. Journal of Contaminant Hydrology, 92, 274–292.

    Article  Google Scholar 

  • Astley, R. J., Macaulay, G. J., & Coyette, J. P. (1994). Mapped wave envelope elements for acoustical radiation and scattering. Journal of Sound and Vibration, 170(1), 97–118.

    Article  Google Scholar 

  • Astley, R. J., Macaulay, G. J., Coyette, J. P., et al. (1998). Three-dimensional wave-envelope elements of variable order for acoustic radiation and scattering, Part I, Formulation in the frequency domain. Journal of the Acoustical Society of America, 103(1), 49–63.

    Article  Google Scholar 

  • Barros, R. S., Olabarriaga, S. D., Borst, J., et al. (2016). Dynamic CT perfusion image data compression for efficient parallel processing. Medical & Biological Engineering & Computing, 54, 463–473.

    Article  Google Scholar 

  • Beer, G., & Meek, J. L. (1981). Infinite domain element. International Journal for Numerical Methods in Engineering, 17, 43–52.

    Article  Google Scholar 

  • Bettess, P. (1977). Infinite element. International Journal for Numerical Methods in Engineering, 11, 53–64.

    Article  Google Scholar 

  • Bettess, P., & Zienkiewicz, O. C. (1977). Diffraction and refraction of surface waves using finite and infinite elements. International Journal for Numerical Methods in Engineering, 13(11), 1271–1290.

    Article  Google Scholar 

  • Bouwmans, T., Javed, S., Sultana, M., & Jung, S. K. (2019). Deep neural network concepts for background subtraction: A systematic review and comparative evaluation. Neural Networks, 117, 8–66.

    Article  Google Scholar 

  • Burnett, D. S. (1994). A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion. The Journal of the Acoustical Society of America, 96(5), 2798–2816.

    Article  Google Scholar 

  • Christensen, T. H., Bjerg, P. L., Banwart, S. A., Jakobsen, R., Heron, G., & Albrechtsen, H.-J. (2000). Characterization of redox conditions in groundwater contaminant plumes. Journal of Contaminant Hydrology, 45, 165–241.

    Article  Google Scholar 

  • Cui, Y., Liu, L., & Zhu, X. (2017). Unscented Kalman filter assimilation of time-lapse self-potential data for monitoring solute transport. Journal of Geophysics and Engineering, 14, 920–929.

    Article  Google Scholar 

  • Gao, J., Smirnov, M., Smirnova, M., & Egbert, G. (2020). 3-D DC resistivity forward modeling using the multi-resolution grid. Pure and Applied Geophysics, 177, 2803–2819.

    Article  Google Scholar 

  • Li, Y., & Spitzer, K. (2002). Three-dimensional DC resistivity forward modelling using finite elements in comparison with finite-difference solutions. Geophysical Journal International, 151, 924–934.

    Article  Google Scholar 

  • Lipton, A. J., Fujiyoshi, H., & Patil, R. (1998). Moving target classification and tracking from real-time video. In IEEE workshop on applications of computer vision (pp. 8–14).

  • Liu, G. R., & Quek, S. S. (2014). The finite element method. Butterworth Heinemann, Oxford: Elsevier.

    Book  Google Scholar 

  • Marques, J. M. M. C., & Owen, D. R. J. (1984). Infinite elements in quasi-static materially nonlinear problems. Computers & Structures, 18(4), 739–751.

    Article  Google Scholar 

  • Matsuyama, T., Ohya, T., & Habe, H. (2000). Background subtraction for non-stationary scene. In: Proceedings of Asian conference on computer vision, Taipei (pp. 622–667).

  • Mendonça, C. A. (2008). Forward and inverse self-potential modeling in mineral exploration. Geophysics, 73(1), F33–F43.

    Article  Google Scholar 

  • Naudet, V., Revil, A., Rizzo, E., Bottero, J. Y., & Bégassat, P. (2004). Groundwater redox conditions and conductivity in a contaminant plume from geoelectrical investigations. Hydrology and Earth System Sciences, 8(1), 8–22.

    Article  Google Scholar 

  • Ren, Z., Tang, J., Kalscheuer, T., & Maurer, H. (2017). Fast 3-D large-scale gravity and magnetic modeling using unstructured grids and an adaptive multilevel fast multipole method. Journal of Geophysical Research-Solid Earth, 122(1), 79–109.

    Article  Google Scholar 

  • Revil, A., & Jardani, A. (2013). The self-potential method: Theory and applications in environmental geosciences. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Revil, A., Mendonça, C. A., Atekwana, E. A., Kulessa, B., Hubbard, S. S., & Bohlen, K. J. (2010). Understanding biogeobatteries: Where geophysics meets microbiology. Journal of Geophysical Research, 115, G00G02.

    Article  Google Scholar 

  • Rücker, C., Günther, T., & Spitzer, K. (2006). Three-dimensional modelling and inversion of dc resistivity data incorporating topography—I. Modelling. Geophysical Journal International, 166(2), 495–505.

    Article  Google Scholar 

  • Sanchez, V., Nasiopoulos, P., & Abugharbieh, R. (2008). Efficient 4D motion compensated lossless compression of dynamic volumetric medical image data. In Proceedings of IEEE international conference on acoustics, speech and signal processing (pp. 549–552).

  • Sezer, O. G., Harmanci, O., & Guleryuz, O. G. (2008). Sparse orthonormal transforms for image compression. In 15th IEEE international conference on image processing, San Diego, CA (pp. 149–152).

  • Sheffer, M. R. (2007). Forward modelling and inversion of streaming potential for the interpretation of hydraulic conditions from self-potential data. Ph.D. thesis, the University of British Columbia.

  • Sheikh, Y., Javed, O., & Kanade, T. (2009). Background Subtraction for Freely Moving Cameras. In 2009 IEEE 12th international conference on computer vision, Kyoto (pp. 1219–1225).

  • Tang, J., & Gong, J. (2010). 3D DC resistivity forward modeling by finite-infinite element coupling method. Chinese Journal of Geophysics, 53(3), 717–728.

    Google Scholar 

  • Ungless, R. F. (1973). An infinite element. Master thesis, University of British Columbia.

  • Vetro, A., Haga, T., Sumi, K., & Sun, H. (2003). Object-based coding for long-term archive of surveillance video. In 2003 International conference on multimedia and expo. ICME ’03. Proceedings (Cat. No. 03TH8698), Baltimore, MD, USA (pp. II–417).

  • Wang, L., Hu, W., & Tan, T. (2002). A survey of visual analysis of human motion. Chinese Journal of Computers, 25(3), 225–237.

    Google Scholar 

  • Wang, L., Li, Z., Li, D., & Wu, T. (2012). An improved video object segmentation algorithm based on background reconstruction. In 2012 International conference on information management, innovation management and industrial engineering, Sanya (pp. 523–526).

  • Xie, J., Cui, Y., Fanidi, M., Zhang, L., Guo, Y., Luo, Y., & Liu, J. (2021a). Numerical modeling of marine self-potential from seafloor hydrothermal ore deposit. Pure and Applied Geophysics, 178, 1731–1744.

    Article  Google Scholar 

  • Xie, J., Cui, Y., Zhang, J., Guo, Y., Wang, J., Fanidi, M., & Liu, J. (2021b). Numerical modeling of biogeobattery system from microbial degradation of underground organic contaminant. SN Applied Sciences, 2, 208.

    Article  Google Scholar 

  • Xie, J., Cui, Y., Zhang, L., Ma, C., Yang, B., Chen, X., & Liu, J. (2020). 3D forward modeling of seepage self-potential using finite-infinite element coupling method. Journal of Environmental & Engineering Geophysics, 25(3), 381–390.

    Article  Google Scholar 

  • Yu, Y., & Doermann, D. (2005). Model of object-based coding for surveillance video. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, 2, 693–696.

    Google Scholar 

  • Yuan, Y., Qiang, J., Tang, J., Ren, Z., & Xiao, X. (2016). 2.5D direct-current resistivity forward modeling and inversion by finite-element-infinite-element coupled method. Geophysical Prospecting, 64(3), 767–779.

    Article  Google Scholar 

  • Zhao, S., & Lin, H. (2014). Design and implement of dynamic block-divided interlaced scanning algorithm. Journal of Chengdu University of Information Technology, 29(6), 630–634.

    Google Scholar 

  • Zienkiewicz, O. C., Emson, C., & Bettess, P. (1983). A novel boundary infinite element. International Journal for Numerical Methods in Engineering, 19, 393–404.

    Article  Google Scholar 

  • Zuo, Q., & Wu, J. (2008). A screen sharing scheme based on block collection and data compression. Computer Technology and Development, 18(4), 206–209.

    Google Scholar 

Download references

Funding

This study was funded by the National Natural Science Foundation of China (grant numbers 42174170, 41874145, 72088101).

Author information

Authors and Affiliations

  1. School of Geosciences and Info Physics, Central South University, Changsha, 410083, China

    Jing Xie, Yi-an Cui, Yijian Luo, Lijuan Zhang, Youjun Guo & Jianxin Liu

  2. Hunan Key Laboratory of Non-Ferrous Resources and Geological Hazard Detection, Changsha, 410083, China

    Jing Xie, Yi-an Cui, Yijian Luo, Lijuan Zhang, Youjun Guo & Jianxin Liu

  3. Key Laboratory of Metalorganic Prediction of Nonferrous Metals and Geological Environment Monitoring (Central South University), Ministry of Education, Changsha, 410083, China

    Jing Xie, Yi-an Cui, Yijian Luo, Lijuan Zhang, Youjun Guo & Jianxin Liu

  4. POWERCHINA Guiyang Engineering Corporation Limited, Guiyang, 550081, China

    Xingzhong Du

Authors
  1. Jing Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xingzhong Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yi-an Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yijian Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Lijuan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Youjun Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Jianxin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yi-an Cui.

Ethics declarations

Conflict of Interest

The authors declare no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xie, J., Du, X., Cui, Ya. et al. Numerical Modeling for 4-D Self-Potential Resistivity Model. Pure Appl. Geophys. 180, 205–213 (2023). https://doi.org/10.1007/s00024-022-03208-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-022-03208-4

Keywords

Search

Navigation