The application of an integral-equation-based automatic inversion algorithm for Interpretation of vertical electrical sounding data

Document Type : Research Paper

Authors

1 Institute of Geophysics, University of Tehran, Tehran, Iran.

2 School of Computing and Engineering, University of West London (UWL), London, United Kingdom of Great Britain.

3 The Faringdon Research Centre for Non-Destructive Testing and Remote Sensing, University of West London, London, United Kingdom of Great Britain and Northern Ireland.

4 School of Mining Engineering, Faculty of Engineering, University of Tehran, Iran.

5 Faculty of Sciences, Razi University, Kermanshah, Iran.

10.22059/ijmge.2025.386171.595207

Abstract

This study presents the implementation of an automatic inversion algorithm designed for the analysis of direct current (DC) vertical electrical sounding (VES) data, utilizing a one-dimensional (1D) linear integral equation approach. The forward modelling problem was derived from a three-dimensional (3D) integral equation, which was elegantly simplified through numerical integration across horizontal dimensions. The inverse problem was tackled through a minimum length solution that integrated a depth-weighting function and optimized the regularization parameter based on the maximum value of the forward operator. The efficacy of this algorithm was validated by inverting synthetic datasets as well as by its application to real field data. The results highlighted the limitations inherent in 1D inversion, particularly in cases where a layered Earth is significantly violated, as evidenced by comparisons with two-dimensional inversion models. In contrast, in contexts characterized by predominantly layered subsurface structures, the algorithm successfully produced accurate representations of the subsurface models. These findings underscore the method's efficacy in various geological environments, offering a robust tool for geophysical exploration.

Keywords

Main Subjects


[1] Hosseini, S. H., Habibian Dehkordi, B., Abedi, M., & Oskooi, B. (2021). Implications for a geothermal reservoir at Abgarm, Mahallat, Iran: magnetic and magnetotelluric signatures. Natural Resources Research, 30, 259-272.
[2] Talebi, M. A., Hosseini, S. H., Abedi, M., & Moradzadeh, A. (2023). 3D inverse modeling of electrical resistivity and chargeability data through unstructured meshing: a case study for travertine exploration. International Journal of Mining and Geo-Engineering, 57(2), 131-140.
[3] Ghanbarifar, S., Ghiasi, S. M., Hosseini, S. H., Abedi, M., Oskooi, B., & Smirnov, M. Y. (2024). Geoelectrical image of the Sabalan geothermal reservoir from magnetotelluric studies. Journal of Applied Geophysics, 224, 105359.
[4] Ghanbarifar, S., Hosseini, S. H., Ghiasi, S. M., Abedi, M., & Afshar, A. (2024). Joint Euler deconvolution for depth estimation of potential field magnetic and gravity data. International Journal of Mining and Geo-Engineering, 58(2), 121-134.
[5] Ghari, H., Parnow, S., Varfinezhad, R., Milano, M., Fourie, F. D., & Tosti, F. (2024). Cross-Gradient Joint Inversion of DC Resistivity and Gravity Gradient Data: A Multi-Disciplinary Approach for Geoscience, Heritage, and the Built Environment. Remote Sensing, 16(23), 4468.
[6] Ghari, H., Varfinezhad, R., & Parnow, S. (2023). 3D joint interpretation of potential field, geology, and well data to evaluate a salt dome in the Qarah‐Aghaje area, Zanjan, NW Iran. Near Surface Geophysics, 3`w(3), 233-246.
[7] Varfinezhad, R., Parnow, S., Florio, G., Fedi, M., & Mohammadi Vizheh, M. (2023). DC resistivity inversion constrained by magnetic method through sequential inversion. Acta Geophysica, 71(1), 247-260.
[8] Najaftomraei, M., Moghadam, S., Varfinezhad, R., Goudarzi, A., & Faghih, A. (2024). Subsurface characterization in southeastern Asaluyeh using DC resistivity and ground penetrating radar. International Journal of Mining and Geo-Engineering, 58(4), 423-429.
[9] Parnow, S., Oskooi, B., & Florio, G. (2021). Improved linear inversion of low induction number electromagnetic data. Geophysical Journal International, 224(3), 1505-1522.[10] Hamzah, U., Samsudin, A. R., & Malim, E. P. (2007). Groundwater investigation in Kuala Selangor using vertical electrical sounding (VES) surveys. Environmental Geology, 51(8), 1349-1359.
[11] Kumar, D., Ahmed, S., Krishnamurthy, N. S., & Dewandel, B. (2007). Reducing ambiguities in vertical electrical sounding interpretations: A geostatistical application. Journal of Applied Geophysics, 62(1), 16-32.
[12] Okoro, E. I., Egboka, B. C. E., & Onwuemesi, A. G. (2010). Evaluation of the aquifer characteristic of Nanka Sands using hydrogeological method in combination with Vertical Electrical Sounding (VES). Journal of Applied Sciences and Environmental Management, 14(2).
[13] Sikandar, P., Bakhsh, A., Arshad, M., & Rana, T. (2010). The use of vertical electrical sounding resistivity method for the location of low salinity groundwater for irrigation in Chaj and Rachna Doabs. Environmental Earth Sciences, 60(5), 1113-1129.
[14] Moghaddam, S., Dezhpasand, S., Kamkar Rohani, A., Parnow, S., & Ebrahimi, M. (2017). Detection and determination of groundwater contamination plume using time-lapse electrical resistivity tomography (ERT) method. Journal of Mining and Environment, 8(1), 103-110.
[15] Pérez-Flores, M., Méndez-Delgado, S., & Gómez-Treviño, E. (2001). Imaging low-frequency and DC electromagnetic fields using a simple linear approximation. Geophysics, 66(5), 1067-1081.
[16] Varfinezhad R., Fedi M., & Milano M. (2022). The role of model weighting functions in the gravity and DC resistivity inversion. IEEE Transactions on Geoscience and Remote Sensing, 60(1), 1-15.
[17] Menke, W. (2012). Geophysical data analysis: discrete inverse theory. Academic Press.
[18] Varfinezhad R., Oskooi B., & Fedi M. (2020). Joint inversion of DC resistivity and magnetic data constrained by cross gradients: compactness and depth weighting. Pure and Applied Geophysics, 177(4325-4343).
[19] Varfinezhad, R., & Oskooi B. (2020). 2D DC resistivity forward modeling based on the integral equation method and a comparison with the RES2DMOD results. Journal of Earth and Space Physics.
[20] Ekinci, Y. L., Demirci, A., & Ertekin, C. (2008). Delineation of the seawater-freshwater interface from the coastal alluvium of Kalekoy-Gokceada, NW Turkey. Journal of Applied Sciences, 8, 1977-1981.
[21] Ekinci, Y. L., & Demirci, A. (2008). A damped least-squares inversion program for the interpretation of Schlumberger sounding curves. Journal of Applied Sciences, 8, 4070–4078.
[22] Temel, R.O., & Ciftci, N.B. (2002). Stratigraphy and depositional environments of the tertiary sedimentary units in Gelibolu Peninsula and islands of Gokceada and Bozcaada (Northern Aegean Region, Turkey). TAPG Bulletin, 14(2), 17-40.