Iranian Journal of Geophysics

Iranian Journal of Geophysics

Estimating depth of investigation in electrical resistivity tomography Inverse modelling

Document Type : Research Article

Authors
Reza Ghanati 1
Fateme Farahmand 2
1 M.Sc. Graduated, Department of Earth Physics, Institute of Geophysics, University of Tehran,Tehran,Iran
2 Associate Professor, Department of Earth Physics, Institute of Geophysics, University of Tehran,Tehran,Iran
10.30499/ijg.2024.482592.1643
Abstract
Correct and appropriate estimation of the depth of investigation (DOI) in electrical resistivity tomography (ERT) studies is crucial for constructing geologic and hydrological models from field data sets. Understanding the DOI allows for the validation of models resulting from inverse modeling. The investigation depth typically refers to the depth below which surface (or airborne) geophysical data obtained are not sensitive to the physical properties of subsurface layers of the Earth. In other words, it is the depth at which the geophysical techniques used in an investigation become insensitive to subsurface changes. Estimating this depth is essential for resistivity (DC) and induced polarization (IP) investigations when interpreting the models obtained from inverse modeling. This is because the structure beneath it has a greater depth of uncertainty compared to other parts of the inverted model and must be carefully interpreted from a geological perspective. The depth of investigation is influenced by various factors, such as receiver sensitivity, measurement accuracy, operating frequencies, ambient noise level, exploration target characteristics, host rock, and data processing and interpretation techniques. Several resolution indicators can be used to estimate the depth of investigation or to identify possible artifacts in the electrical structures. Understanding the quantitative relationship between survey depth and these factors is crucial for users to achieve their geological objectives, minimize unnecessary survey costs, and uncover meaningful geological features. In electrical resistivity or induced polarization (IP) tomography studies, the data, including apparent resistivity or apparent induced polarization, is used to solve a nonlinear inverse problem. This problem is addressed through an iterative process known as the Occam’s inversion method with appropriate physical constraints to avoid unrealistic subsurface features. Accurate interpretation of the subsurface geological model relies on the distribution of specific physical parameters, such as electrical resistance and chargeability, and enables reliable depth assessment. This study presents an approach to calculate the detectable depth (DOI) in electrical resistivity tomograms. Additionally, the sensitivity matrix (SM) and the sensitivity index to the primary model (SIM) are employed for further investigation. To evaluate the proposed method, a synthetic model and a real dataset are utilized. Numerical results obtained from synthetic and real data demonstrate a strong agreement among all three criteria i.e., DOI, SM, and SIM. It is worth noting that insufficient information (data) leads to increased uncertainty in the inverted cross-section, resulting in a decrease in the DOI index, a decrease in sensitivity, and an increase in the SIM value.
 
Keywords
Depth of investigation (DOI), electrical resistivity tomography (ERT), fré
chet derivatives, uncertainty quantification
Adrian, J., Tezkan, B. and Candansayar, M.E. (2022). Exploration of a copper ore deposit in Elbistan/Turkey using 2D inversion of the time-domain induced polarization data by using unstructured mesh, Pure Appl. Geophys. 179, 2255–2272
Apparao, A., Rao, T. G., Sastry, R. S., and Sarma, V. S. (1992). Depth of detection of buried conductive targets with different electrode arrays in resistivity prospecting1, Geophysical Prospecting, 40(7), 749–760.
Asch, T., Abraham, J., and Irons, T. (2015). A discussion on depth of investigation in geophysics and AEM inversion results, SEG Technical Program Expanded Abstracts 2015.
Banerjee B. and Pal B.P. (1986). A simple method for determination of depth of investigation characteristics in resistivity prospecting. Exploration Geophysics 17, 93–95.
Barker, R. D. (1979). Signal contribution sections and their use in resistivity studies. Geophysical Journal International, 59(1), 123-139.
Barker, R. D. (1989). Depth of investigation of collinear symmetrical four electrode arrays, Geophysics, 54(8), 1031–1037.
Constable, S. C., Parker, R. L., & Constable, C. G. (1987). Occam’s inversion: A practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics, 52(3), 289–300.
Christiansen A.V. and Auken E. (2012). A global measure for depth of investigation. Geophysics 77, WB171-WB177.
Dey, A., & Morrison, H. F. (1979). Resistivity modeling for arbitrarily shaped two-dimensional structures. Geophysical Prospecting, 27(1), 106–136
Edwards, L. S. (1977). A modified pseudo-section for resistivity and IP. Geophysics, 42(5), 1020–1036.
 
Evjen, H. M. (1938). Depth factors and resolving power of electrical measurements, geophysics, 3(2), 78–95.
Ghanati, R., and Fallahsafari, M. (2022). Fréchet Derivatives calculation for electrical resistivity imaging using forward matrix method. Iranian Journal of Geophysics, 15(4), 153-163.
Koefoed O. 1979. Geo-sounding Principles, 1: Resistivity Sounding Measurements Elsevier.
Loke, M. H., & Barker, R. D. (1996). Rapid least-squares inversion of apparent resistivity pseudo-sections by a quasi-Newton method1. Geophysical Prospecting, 44(1), 131-152
Loke, M. H., & Barker, R. D. (1995). Practical techniques for 3D resistivity surveys and data inversion. Geophysical Prospecting, 44(3), 499–523.
Martin, R. (2009). Development and application of 2D and 3D transient electromagnetic inverse solutions based on adjoint Green functions: A feasibility study for the spatial reconstruction of conductivity distributions by means of sensitivities. PhD thesis, University of Cologne, Germany.
Oldenburg, D. W., and Li, Y. (1999). Estimating depth of investigation in dc resistivity and IP surveys, Geophysics, 64(2), 403–416.
Parker R. 1984. The inverse problem of resistivity sounding. Geophysics, 49, 2143–2158.
Roy, A., and Apparao, A. (1971). Depth of investigation in direct current methods, Geophysics, 36(5), 943–959.
Roy, A. (1972). Depth of investigation in wenner, three-electrode and dipole-dipole dc resistivity methods, Geophysical Prospecting, 20(2), 329–340.
Roy A. and Apparao A. (1971). Depth of investigation in direct current methods. Geophysics 36(5), 943–959.
Schlumberger, C., 1920, Etude sur la prospection electrique du sours-sol: Gauthier-Villars et Cie., Paris.
 
Siripunvaraporn, W., & Egbert, G. (2000). An efficient data-subspace inversion method for 2D magneto-telluric data. Geophysics, 65(3), 791–803.
Van Nostrand, R. G. (1953). Limitations on resistivity methods as inferred from the buried sphere problem, Geophysics, 18(2), 423-433.
Yogeshwar, P. (2014). A resistivity-depth model of the central Azraq basin area, Jordan: 2D forward and inverse modeling of time domain electromagnetic data. PhD thesis, University of Cologne, Germany.
Yogeshwar, P., & Tezkan, B. (2017). Two-dimensional basement modeling of central loop transient electromagnetic data from the central Azraq basin area, Jordan. Journal of Applied Geophysics, 136, 198.
gravity anomalies due to faulted thin slabs. Geophysics, 68: 535–543.
 
 
Iranian Journal of Geophysics
Volume 19, Issue 4
September and October 2025
Pages 121-136