Time Domain Electromagnetic Data Modeling based on Zohdy's Technique

Document Type : Research - Paper

Authors

1 Ph.D Student, ACECR-Research Institute of Applied Sciences, Shahid Beheshti University, Tehran, Iran

2 Professor, ACECR-Research Institute of Applied Sciences, Shahid Beheshti University, Tehran, Iran

3 Associate Professor, School of Mining, Petroleum and Geophysics, Shahrood University of Technology, Shahrood, Iran

Abstract

The initial model, Jacobian matrix, Frechet derivatives, and digital look-up tables are essential components in most time-domain electromagnetic (TEM) data modeling methods in layered earth. Computations of these components in the modeling process are time-consuming as their determinations need to use iterative operations. Zohdy introduced an alternative method for the rapid inversion of direct current (DC) resistivity data obtained using the Wenner and Schlumberger electrode configurations. The methodology allows for the inclusion of a flexible number of layers, which are chosen in conjunction with the initial model based on the data-derived knowledge, and avoids large and iterative calculations of Jacobian matrix and Frechet derivatives. This paper presents an endeavor to enhance the outcomes of TEM data modeling or inversion utilizing the Zohdy's technique through the elimination of the look-up tables. In this study, various synthetic models of stratified geological formations are examined using the the above-mentioned methodology. The modeling findings demonstrate robustness even when 5% and 10% noise levels are entered into the dataset. Hence, this approach can be considered as a worthy method for TEM data inversion accompanying some levels of noise in the data.

Keywords

Main Subjects

References

  1. Sattel, D., and Kgotlhang, L. (2004). “Groundwater exploration with AEM in the Boteti area, Botswana”. Exploration Geophysics, 35: 147-156. DOI: 10.1071/EG04147.
  2. Lu, K., Zhou, J., Li, X., Fan, Y. N., Qi, Z., and Cao, H. (2022). “3D large-scale transient electromagnetic modeling using a Shift-and-Invert Krylov subspace method”. Journal of Applied Geophysics, 198: 104573-104573. DOI: 10.1016/j.jappgeo.2022.104573.
  3. Amato, F., Pace, F., Vergnano, A., and Comina, C. (2021). “TDEM prospections for inland groundwater exploration in semiarid climate, Island of Fogo, Cape Verde”. Journal of Applied Geophysics, 184: 104242-42.
  4. El-Kaliouby, H. (2020). “Mapping sea water intrusion in coastal area using time-domain electromagnetic method with different loop dimensions”. Journal of Applied Geophysics, 175: 103963-103963. DOI: 10.1016/j.jappgeo.2020.103963.
  5. Mohanty, I., Nagendran, R., Bisht, L., Thanikai Arasu, A. V., Baskaran, R., Kumar, B. V. L., and Verma, M. B. (2022). “Development of SQUID based TDEM system and its utilization for field survey at Tumallapalle, Andhra Pradesh, India”. Journal of Applied Geophysics, 204: 104746-104746. DOI: 10.1016/j.jappgeo.2022.104746.
  6. Liu, R., Liu, J., Wang, J., Liu, Z., and Guo, R. (2020). “1D EM response modeling with arbitrary source-receiver geometry based on vector potential and its implementation in Matlab”. Geophysics, 1-47. DOI: 10.1190/geo2019-0224.1.
  7. Xiao, L., Gianluca, F., Bo, Z., Auken, E., and Christiansen, A. V. (2022). “Fast 2.5D and 3D Inversion of transient electromagnetic surveys using the octree-based finite element method”. Geophysics, 87(4): 1JA-WB79. DOI: 10.1190/GEO2021-0402.1.
  8. Tang, W., Li, Y., Swidinsky, A., and Liu, J. (2015). “Three-dimensional controlled-source electromagnetic modelling with a well casing as a grounded source: a hybrid method of moments and finite element scheme”. Geophysical Prospecting, 63(6): 1491-1507. DOI: 10.1111/1362478.12330.
  9. Zhang, J., Huang, C., Feng, B., and Shi, Y. (2022). “Inversion of airborne transient electromagnetic data based on reference point lateral constraint”. Journal of Applied Geophysics, 202: 104675-104675. DOI: 10.1016/j.jappgeo.2022.104675.
  10. Feng, B., Zhang, J.-f., Li, D., and Bai, Y. (2020). “Resistivity-depth imaging with the airborne transient electromagnetic method based on an artificial neural network”. Journal of Environmental and Engineering Geophysics, 25(3): 355-368. DOI: 10.32389/JEEG19-087.
  11. Parise, M. (2011). “Fast computation of the forward solution in controlled-source electromagnetic sounding problems”. Progress in Electromagnetics Research, 111: 119-139. DOI: 10.2528/PIER10101409.
  12. Farquharson, C. G., Oldenburg, D. W., and Routh, P. S. (2003). “Simultaneous 1D inversion of loop-loop electromagnetic data for both magnetic susceptibility and electrical conductivity”. Geophysics, 68: 1857-1869. DOI: 10.1190/1.1635038.
  13. Singh, N. P., Utsugi, M., and Kagiyama, T. (2009). “TEM response of a large loop source over a homogeneous earth model: A generalized expression for arbitrary source-receiver offsets”. International Journal of Geophysics 7 Pure and Applied Geophysics, 166(12): 2037-2058. DOI: 10.1007/s00024-009-0532-z.
  14. Aji Hapsoro, C., Srigutomo, W., Purqon, A., and Warsa. (2019). “3-D Modeling of Layered Earth Structure in the Geothermal Systems Using Time Domain Electromagnetics (TDEM) Method”. IOP Conference Series: Earth and Environmental Science, 318(1): 012015. DOI: https://doi.org/10.1088/1755-1315/318/1/012015.
  15. Cao, H., Liu, Y., and Wang, K. P. (2013). “Improved Magnetotelluric Zohdy-Oldenburg Direct Inversion, Mathematical Problems in Engineering”. Mathematical Problems in Engineering, 2013: 174586. DOI: https://doi.org/10.1155/2013/174586.
  16. Spies, B. R., and Eggers, D. E. (1986). “The use and misuse of apparent resistivity in electromagnetic methods”. Geophysics, 51: 1462-1471. DOI: 10.1190/1.1442194.
  17. Christiansen, A. V., Auken, E., Kirkegaard, C., Schamper, C., and Vignoli, G. (2016). “An efficient hybrid scheme for fast and accurate inversion of airborne transient electromagnetic data”. Exploration Geophysics, 47(4): 323-330. DOI: 10.1071/EG14121.
  18. Huang, H., and Palacky, G. J. (1991). “Damped least-squares inversion of time-domain airborne EM data based on singular value decomposition”. Geophysical Prospecting, 39(6): 827-844. DOI: 10.1111/j.1365-2478.1991.tb00346.x.
  19. Lane, R., Green, A., Golding, C., Owers, M., Pik, P., Plunkett, C., Sattel, D., and Thorn, B. (2000). “An example of 3D conductivity mapping using the TEMPEST AEM system”. Exploration Geophysics, 31: 162-172. DOI: 10.1071/EG00162.
  20. Leeming, P., Moehadu, M., Nikiel-Tshabangu, B., and Sarma, D. (2001). “An integrated approach with DIGHEMV to groundwater exploration -Tsabong, Botswana”. 15th Conference and Exhibition, Australian Society of Exploration Geophysicists, Extended Abstracts, 1-4. DOI: 10.1071/ASEG2001ab069.
  21. Qi, Z., Zhang, Y., Li, X., and Li, H. (2022). “S-Inversion of electrical source semi-airborne TEM data to determine the electric interface underground”. Journal of Applied Geophysics, 204: 104744-104744. DOI: 10.1016/j.jappgeo.2022.104744.
  22. Schaa, R., and Fullagar, P. K. (2012). “Vertical and horizontal resistive limit formulas for a rectangular-loop source on a conductive half-space”. Geophysics, 77: E91-E99. DOI: 10.1190/geo2011-0141.1.
  23. Krivochieva, S., and Chouteau, M. (2002). “Whole-space modeling of a layered earth in time-domain electromagnetic measurements”. Journal of Applied Geophysics, 50(4): 375-391. DOI: https://doi.org/10.1016/S0926-9851(02)00164-7.
  24. Sattel, D., Lane, R., Pears, G., Smith, R., and Vrbancich, J. (2004). “Novel ways to process and model GEOTEM data”. 17th Conference and Exhibition, Australian Society of Exploration Geophysicists, Extended Abstracts. DOI: 10.1071/ASEG2004ab127.
  25. Smith, R. S., Lee, T. J., Annan, P. A., and Connell, M. D. (2005). “Approximate apparent conductance (or conductivity) from the realizable moments of the impulse response”. Geophysics, 70: G29-G32. DOI: 10.1190/1.1852776.
  26. Sattel, D. (2005). “Inverting airborne electromagnetic (AEM) data with Zohdy’s method”. Geophysics, 70: G77-G85. DOI: 10.1190/1.1990217.
  27. شیرزادی‏تبار، ف.، کازرانی، ص.؛ 1395؛ "به کارگیری روش زهدی در تفسیر داده‏های الکترومغناطیسی هوابرد حوزه فرکانس". سی و پنجمین گردهمایی ملی علوم زمین.
  28. Tiwari, A. K., Maurya, S. P., and Singh, N. P. (2018). “TEM response of a large loop source over the multilayer earth models”. International Journal of Geophysics, 2018: 9891548. DOI: doi.org/10.1155/2018/9891548.
  29. Ward, S. H., and Hohmann, G. W. (1987). “Electromagnetic theory for geophysical applications”. In: Nabighian, M. N. (Ed.), Electromagnetic Methods in Applied Geophysics, v. 1- Theory: SEG, 53-129. DOI: 10.1190/1.9781560802631.ch4.
  30. Spies, B. R. (1989). “Depth of investigation in electromagnetic sounding methods”. Geophysics, 54: 872-888. DOI: 10.1190/1.1442716.
  31. Wait, J. R. (1987). “Electromagnetic wave theory”. John Wiley & sons.
  32. Zohdy, A. A. R. (1989). “A new method for the automatic interpretation of Schlumberger and Wenner sounding curves”. Geophysics, 54: 245-253. DOI: 10.1190/1.1442648.
  33. Nekut, A. G. (1987). “Direct inversion of time-domain electromagnet data”. Geophysics, 52: 1431-1435. DOI: 10.1190/1.1442256.
  34. Xue, G., Li, X., Gelius, L. J., Qi, Z., Zhou, N., and Chen, W. (2015). “A new apparent resistivity formula for in-loop fast sounding TEM theory and application”. Journal of Environmental and Engineering Geophysics, 20(2): 107-118. DOI: doi.org/10.2113/JEEG20.2.107.
  35. Xue, G. Q., Yan, S., and Zhou, N. N. (2011). “Theoretical study on the errors caused by dipole hypothesis of large-loop TEM response”. Diqiu Wuli Xuebao, 54(9): 2389-2396. DOI: 10.3969/j.issn.0001-5733.2011.09.022.
  36. Zhao, Y.-w., Zhu, Z.-q., Lu, G.-y., and Han, B. (2018). “The optimal digital filters of sine and cosine transforms for geophysical transient electromagnetic method”. Journal of Applied Geophysics, 150: 267-277. DOI: 10.1016/j.jappgeo.2018.01.008.
  37. Guptasarma, D., and Singh, B. (1997). “New digital linear filters for Hankel J0 and J1 transforms”. Geophysical Prospecting, 45(5): 745-762. DOI.org/10.1046/j.1365-2478.1997.500292.x.
  38. Key, K. (2012). “Is the fast Hankel transform faster than quadrature?”. Geophysics, 77(3): F21-F30. DOI: doi.org/10.1190/geo2011-0237.1.
  39. Ingeman-Nielsen, T., and Baumgartner, F. (2006). “CR1Dmod: A Matlab program to model 1D complex resistivity effects in electrical and electromagnetic surveys”. Computers & Geosciences, 32(9): 1411-1419. DOI: 10.1016/j.cageo.2006.01.001.

Files

History

  • Receive Date: 01 February 2023
  • Revise Date: 07 November 2023
  • Accept Date: 16 August 2023

Share

How to cite

Statistics