Iranian Journal of Geophysics

Iranian Journal of Geophysics

Simultaneous estimation of smooth and blocky structures in tomographic inversion of electrical resistivity data

Document Type : Research Article

Authors
Pardis Salehi 1
Reza Ghanati 2
1 M.Sc. Graduated, Institute of Geophysics, University of Tehran,Tehran, Iran
2 Associate Professor, Institute of Geophysics, University of Tehran,Tehran, Iran
10.30499/ijg.2025.490854.1652
Abstract
Electrical resistivity tomography is a non-invasive, near-surface geophysical technique commonly used for creating detailed images of the subsurface. It plays a crucial role in diverse geoscientific fields, such as subsurface resource exploration, environmental and engineering studies, soil characteristics determination, mapping hydrogeophysical properties. Electrical resistivity tomography is a technique that allows the spatial distribution of electrical conductivity (or equivalently resistivity) to be determined by passing an electric current through the Earth subsurface and measuring the Earth's response in terms of electrical voltage. Subsequently, numerical methods are used to solve nonlinear inverse problems and interpret the results. The method's adaptability and precision have made it indispensable in applications ranging from groundwater exploration and contamination assessment to archaeological investigations and infrastructure stability evaluations. Recent advancements in Electrical resistivity tomography technology, including higher resolution imaging and improved inversion algorithms, have further expanded its utility and accuracy in complex geology. In this study, the focus is on achieving a more accurate characterization of the physical properties of the subsurface Earth. The goal is to develop a model that can accurately predict the characteristics of smooth and sharp anomalies as well as the boundaries of subsurface layers. Two regularization methods including Tikhonov regularization and total variation regularization are considered. Tikhonov regularization utilizes the Gauss-Newton technique, while total variation regularization employs the Iteratively Reweighted Least Squares (IRLS) algorithm as a fast and practical approach for minimizing the overall objective function and obtaining the final model. IRLS is an optimization technique commonly used to solve problems where the objective function can be expressed as a weighted least squares problem. Tikhonov regularization leads to a smooth model of subsurface structures, while total variation regularization emphasizes edge enhancement. Since subsurface layers may simultaneously contain smooth and sharp (edge-like) structures, using only one of these methods would result in the loss of the other features. Therefore, to preserve both characteristics, this study proposes a novel strategy based on the simultaneous use of both Tikhonov and total variation regularization within a common objective function to obtain a model of electrical conductivity variations in subsurface layers that closely matches reality. The performance of the proposed algorithm is first evaluated on several synthetic models with different features. Then, its functionality is assessed through its application to field data. Numerical results demonstrate that the proposed approach enables the creation of a model of subsurface electrical conductivity distribution that bears a closer resemblance to subsurface reality.
Keywords
Electrical reisitivity tomography
tikhonov regularization
total variation
ill-posedness
IRLS
Gauss-Newton
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Iranian Journal of Geophysics
Volume 19, Issue 5
November and December 2025
Pages 1-16