Improving electrical resistivity tomography interpretation with Gray Level Co-Occurrence Matrix textural attributes

Abstract

Electrical resistivity tomography (ERT) provides valuable subsurface structural information but often relies on inverted resistivity thresholds for interpretation. Inversion inherently produces smooth boundaries that can lead to interpretation ambiguity, especially in delineating clay boundaries critical for groundwater exploration. We demonstrate the application of Gray Level Co-Occurrence Matrix (GLCM) textural attributes to enhance ERT interpretation in heterogeneous sedimentary environments. We analyzed a 100 × 100 m 3D ERT survey using three GLCM attributes: Mean, Variance, and Entropy. GLCM Mean improved clay boundary definition by reducing the smoothing effects inherent in L2-norm inversion, enabling more precise delineation of clay lens morphology. GLCM Variance highlighted a potential recharge zone extending up to the surface that was ambiguous in the original inverted ERT results. GLCM Entropy provided enhanced contrast between clay units and groundwater reservoirs, improving discrimination between aquifer zones and confining layers. The integration of these GLCM attributes with traditional ERT interpretation demonstrates significant potential for improving geophysical interpretation in complex geological environments, particularly for groundwater resource assessment and management. This workflow establishes GLCM’s value for extracting additional textural information from electrical resistivity data to aid subsurface characterization.

Introduction

Groundwater is a vital resource for drinking, agricultural, and industrial uses, yet its availability and distribution can be difficult to determine using traditional drilling methods alone, which are often costly and time-consuming. Locating groundwater resources requires accurate understanding of subsurface structures as aquifer distribution and well productivity are directly controlled by subsurface geology^1–3. However, exploring the subsurface is challenging due to the inherent heterogeneity of near surface region. Accurately characterizing subsurface heterogeneity is critical for understanding and modeling groundwater flow and solute transport. Traditional methods often oversimplify the complex spatial variability of hydraulic properties, leading to inaccurate predictions. Therefore, it is necessary to develop and integrate advanced measurement techniques, including geophysical methods, and innovative modeling approaches to better capture this heterogeneity and its dynamic changes over time, which is essential for sustainable water resource management and predicting the fate of contaminants⁴. Geophysical techniques, such as electrical resistivity, seismic refraction, electromagnetic surveys, and ground-penetrating radar (GPR), provide valuable insights into the physical properties of subsurface materials, enabling the identification of potential aquifers and water-bearing zones without the need for extensive drilling^5–10. One of the primary advantages of using geophysical methods is their ability to provide spatially rich information about the depth, extent, and characteristics of groundwater reservoirs⁷. Electrical resistivity methods, for example, are commonly employed to map subsurface structures based on the varying resistivity of different geological materials. This helps to identify permeable formations that are likely to contain groundwater¹¹. By integrating data from multiple geophysical techniques, it is possible construct detailed models of subsurface hydrological systems, improving the accuracy of groundwater resource assessment and management³.

Although geophysical surveys are very useful in locating groundwater in the subsurface, there always is some uncertainty associated with geophysical data. This is even more pronounced in lower resolution methods such as electrical resistivity tomography that also suffer from low signal to noise ratios^3,12,13. Unfortunately, the interpretation of ERT results explicitly relies on modeling and inverse solutions which are based on certain assumptions about the subsurface and its properties; therefore, the final product of an ERT survey can be ambiguous, biased and non-unique^12,14. Therefore, methods that can enhance the ERT results and increase our confidence in the interpretations are needed. Many researchers have focused on improving ERT inversion algorithms to generate sharper, more geologically realistic subsurface images by minimizing smoothing artifacts inherent in some conventional approaches¹⁵. The fundamental choice between smooth and blocky inversion techniques continues to be refined, with blocky methods such as those utilizing Minimum Gradient Support (MGS) being improved through the incorporation of prior geological or geophysical information to better delineate sharp boundaries and complex structures^16,17. While not directly ERT, innovations in related fields, like the use of wavelet-based complexity measures in flexible quasi-2D inversion of AEM data¹⁸, offer potential inspiration for novel regularization strategies in ERT that could better accommodate diverse geological settings and improve the representation of subsurface heterogeneity.

Beyond algorithmic development, significant strides in improving ERT inversion involve enhancing quantitative interpretation, integrating diverse datasets, and rigorously appraising model results. Moving from qualitative images to more quantitative assessments is crucial, supported by robust probabilistic approaches that allow for uncertainty quantification in inverted geoelectric data¹⁹. Understanding the inherent limitations of the method, such as the depth of investigation²⁰, is also vital for reliable interpretation. The integration of external data, such as geochemical analyses and laboratory-derived petrophysical relationships, can significantly constrain inversion models and improve their accuracy for specific applications like resource quantification or environmental site characterization²¹. Post-inversion processing techniques, including watershed algorithms and artificial neural networks, can aid in the objective delineation and reconstruction of discrete targets within the resistivity models^22,23. Furthermore, the use of comprehensive image appraisal tools is essential for critically evaluating the quality and reliability of inversion results²⁴. The increasing focus on monitoring dynamic subsurface processes, particularly in hydrogeology^4,25, drives the need for inversions capable of handling time-lapse (4D) data effectively. Finally, integrating diverse physical property models through techniques like fuzzy c-means cluster analyses can lead to improved subsurface zonation and more accurate petrophysical parameter estimation from inverted models²⁶.

GLCM (Gray Level Co-occurrence Matrix), originally developed by Haralick et al. (1973), quantifies how often different combinations of pixel intensities occur in specified spatial relationships, making it particularly valuable for characterizing complex geological structures²⁷. GLCM analysis provides powerful statistical measures of texture that can reveal subtle patterns and relationships in seismic data that may not be apparent through conventional amplitude analysis alone. In this light, GLCM algorithms represent a new approach for ERT interpretation as they have not been investigated for electrical and electromagnetic methods.

This study demonstrates using GLCM textural analysis as a post-inversion processing technique on an ERT inverted section to improve subsurface structural interpretation, particularly clay lens delineation, in a highly heterogeneous sedimentary environment. The delineation of near surface structures in groundwater studies is important to know where possible recharge zones, heterogeneities, and groundwater reservoirs are located. A previous study acquired 3D ERT data over a 100 × 100 m area with known layered sediments containing aquifers and scattered clay lenses (Fig. 1). Resistivity inversion models identified suspected permeable zones and clay-rich regions, but relied on smooth resistivity thresholds for interpretation with some ambiguity in clay boundaries³. Herein, GLCM textural attributes calculated from the ERT inverted results are used to extract additional information on resistivity spatial relationships.

Fig. 1.

(a) Study location in southwestern Oklahoma. (b) aerial image of survey area³⁹. (c) 3D ERT survey setup where red dashed line shows the relative location of the ERT transect shown in Fig. 3a.

GLCM Applications in geophysical analyses

First used by Gao (2003) in seismic reflection data, GLCM attributes improve definition of channels, deltas, levees, salt, and other sedimentary structures in seismic facies analysis²⁸. The GLCM textural attributes enhanced boundaries between geologic units that were ambiguous in the original seismic data. Following Gao (2003), several researchers have used the GLCM method applied to seismic reflection subsurface data to interpret channels systems^29–31, and sedimentary facies^32–35. GLCM has also been applied to ground penetrating radar studies for varying imaging goals, from searching for archeological features³⁶, to classify sedimentary³⁷ and soil facies³⁸.

Based on the success of GLCM attributes in seismic reflection and GPR, we applied GLCM to ERT inverted results demonstrating GLCM’s utility for extracting supplementary textural information in ERT models to aid resistivity interpretation.

Study area and previous work

The survey area is located in southwestern Oklahoma, near the town of Sentinel, on a poorly cultivated land used primarily for raising cattle (Fig. 1). The site was chosen due to known subsurface heterogeneity and low yield groundwater wells in the vicinity. The topsoil consists of clayey sandy unconsolidated sediments up to 2 m deep, overlying a 4 m thick unsaturated sandy layer. According to a nearby well log, this sandy layer extends to 6 m depth and contains some clay. From 6 to 11 m lies clay with gypsum lenses. The saturated portion from 11 to 14 m comprises primarily clay and claystone based on the well data. Below 14 m depth, interbedded claystone, gypsum, and sandstone are present down to the well’s total depth of 18 m where an unconfined aquifer exists³.

In the 3D ERT survey gathered in McKnight and Saneiyan (2024)³ six 93-meter lines with 32 electrodes spaced 3 m apart in a dipole-dipole, Wenner and Schlumberger configuration⁴⁰ were used; however, this study did not achieve high resolution images of the subsurface. The inverted 3D resistivity model delineated a conductive clay layer underlain by a deeper resistive saturated zone and has a depth of investigation of 30 m after applying the method found in Oldenburg & Li, (1999)²⁰. However, the boundaries between the permeable aquifer zones and less permeable clay lenses remained ambiguous. Further details of the acquisition and ERT results are discussed in McKnight and Saneiyan (2024)³.

Electrical resistivity tomography and its inversion process

The direct current (DC) electrical resistivity method, a popular low-frequency geophysical technique, relies on the conduction of electrical current in materials as described by Ohm’s law. In resistivity surveys, electrical current flows between two current electrodes, and the potential voltage drop is measured across two or more potential electrodes. By understanding the geometry of a four-electrode setup, we can compute the apparent resistivity ( – units of Ωm).

1

where R is resistance (units of ohms or Ω), is potential drop (units of volts), I is current (units of amperes), and K (units of m) is the geometric factor describing the arrangement of survey electrodes¹².

Apparent resistivity () is a theoretical resistivity value that assumes a uniform subsurface and is influenced by the configuration of the electrode array and the electrical properties of the subsurface materials. The actual resistivity distribution () of the subsurface is estimated using an inversion method, which involves iteratively calculating the best-fitting model by a least squares fit between the observed data and the model on a discretized mesh through minimizing the objective function:

2

where d is the vector of observations (i.e., apparent resistivity or transfer resistance), is the vector of parameters (typically a mesh cell is a parameter), and is a data weight matrix, which, assuming uncorrelated errors, is a diagonal matrix with entries equal to the reciprocal of the standard deviation of each measurement. For 3D ERT inversion, parameters are typically the log-transformed resistivities of a given set of mesh cells. Inversion is inherently non-unique, meaning that there are infinite number of models (resistivity distributions) that can explain the observed distribution. Therefore, usually a statistical criterion is defined to find the optimum value of . Typically, once , a solution has been found. , where N is the number of observations (i.e., number of measurements).

In 2D and 3D inversions, Tikhonov regularization⁴¹ is applied to constrain the model to stabilize the inversion and get realistic results. This is applied by the penalty function:

3

where R is a roughness matrix that describes the spatial connectivity of m and is a second derivative operator in 2D and 3D inversion cases.

Thus, the objective function is written as:

4

where is the smoothness factor, which is adjusted at each iteration of the inversion, starting with a sufficiently large value resulting in a very smooth model. In this study, we used ResIPy for 3D inversion which uses a L2-norm inversion routine^12,42,43. The inversion process ideally looks for the best very smooth model by reducing and thus reducing resulting in increasing structures in the model. However, smooth models despite their attractiveness in the electrical resistivity field are not suitable for situations where known electrical contrasts exist (e.g., boundaries of clayey and non-clayey structures).

GLCM Methodology

GLCM analyzes image textures based on the spatial arrangement of grey levels in image pixels²⁷, and calculates statistics, such as frequency, on how often different combinations of grey levels occur for pixel pairs within a moving window at set distances and directions. This captures textural characteristics like image smoothness, coarseness, and regularity. For example, a homogeneous region will have similar grey level pairs recurring frequently, giving high GLCM frequencies along the diagonal. In contrast, a heterogeneous region will have a widespread distribution of dissimilar grey level pairs, increasing off-diagonal GLCM frequencies. Statistical attributes derived from these grey level co-occurrence frequencies provide quantitative textural information. Here, the GLCM attributes were computed using the AASPI glcm3d algorithm⁴⁴, which converts the 32-bit floating point resistivity data to integer grey levels. For each pixel location in the resistivity image, the algorithm constructs a square GLCM matrix from the surrounding analysis window, where each element P(i, j) represents the probability that grey level i occurs adjacent to grey level j. The algorithm examines pixel pairs at 0°, 45°, 90°, and 135° directions within the analysis window, tabulating the frequency of occurrence for each grey level combination to build the co-occurrence matrix. High frequencies along the diagonal (where i = j) indicate homogeneous regions where neighboring pixels have similar values, while off-diagonal frequencies represent textural variations. From each normalized GLCM matrix, statistical attributes are derived: GLCM Mean quantifies the average grey level weighted by occurrence probability, GLCM Variance measures the spread of grey level values indicating textural heterogeneity, and GLCM Entropy evaluates the randomness of grey level distributions with higher values indicating more complex spatial arrangements.

GLCM Mean

GLCM Mean measures the average grey level relating to smoothness²⁷. Mathematically, mean is computed by summing the product of GLCM probabilities P(i, j) and grey levels i, where P(i, j) is the probability of grey level i occurring adjacent to grey level j in the GLCM:

5

A lower GLCM Mean is calculated when adjacent pixels exhibit gradual grey-level changes, leading to frequent occurrences of similar pixel pairs in the GLCM matrix. This suggests a more homogeneous texture. On the other hand, a higher GLCM Mean value indicates abrupt differences, where neighboring pixel pairs are not as similar. This results in higher GLCM values, implying a more heterogeneous texture. So, a high GLCM Mean suggests greater texture variability within the specified subsurface zone, while a low Mean reveals a more consistent and homogeneous geology and sediments.

GLCM Variance

GLCM Variance indicates how widely spread the grey level values are in an image. Low variance arises from a narrow distribution of similar grey levels, associated with homogeneous textures. High variance results from a broad range of dissimilar grey levels, corresponding to increased heterogeneity and texture coarseness²⁷. With a normalized GLCM, Variance is:

6

For subsurface characterization, GLCM Variance can provide valuable insights into the geological or material properties of underground structures. A high GLCM Variance in a subsurface image might suggest the presence of diverse and irregular features with varying textures. This could be indicative of stratigraphic variations, fractures, or the boundaries between different rock formations. Conversely, a low GLCM Variance may point to relatively consistent and homogeneous subsurface layers or materials.

GLCM Entropy

Entropy evaluates the randomness of spatial grey level arrangements. Entropy is calculated as:

7

A higher GLCM Entropy in subsurface data might indicate geologically complex or irregular sediments and rocks, with diverse material compositions. This can correspond to stratigraphic variations, the presence of fractures, or mixed lithologies within the subsurface. Conversely, a low GLCM Entropy may suggest a more uniform subsurface material. This could imply relatively homogeneous geological formations or consistent material properties over the area examined.

Fig. 2.

Overview of GLCM statistical attributes (mean, variance, entropy) and the right panel shows a 5 × 5 pixel calculation box with an example grey level matrix demonstrating how spatial relationships between neighboring pixel pairs are analyzed at different orientations (0°, 45°, 90°, 135°), in this case the arrows show the calculation being done at 90°. The calculation box moves across the resistivity image, computing textural statistics at each location⁴⁵.

Results and Discussion

After loading the inverted resistivity data into the attribute algorithm (Fig. 3a), GLCM Mean was calculated. GLCM Mean improved interface definition between a suspected clay lens and a resistive channel (Fig. 3 – red circle). The inverted ERT section shows this clay bounded by an ambiguous and smooth resistivity transition as a result of L2-norm inversion approach^3,12. However, GLCM Mean increases resistivity contrast at this boundary, better delineating the clay shape. This resistivity segregation confirms the interpreted clay lens is fully connected to the surface, which was ambiguous in the original ERT results.

Fig. 3.

GLCM Mean results (a) initial resistivity profile with smooth layer boundaries (for more please see³), and (b) GLCM Mean showing increased boundary contrasts. Note this transect is shown on Fig. 1 in red dashes.

While the GLCM Mean enhanced the structural bodies in the ERT plot, the GLCM Variance highlights a suspected recharge zone as a high variance anomaly that extends up to the surface (Fig. 4 – red square). This aligns with the previous study’s interpretation based on the resistive anomaly shape³. The GLCM Variance may be particularly enhanced in this region, perhaps due to the increased textural complexity created by water infiltration pathways. Since the data were collected after rainfall, the high variance anomaly may reflect active percolation processes, with water movement creating distinct textural patterns in the resistivity data. In contrast, the conductive clay regions show minimal variance, consistent with their more homogeneous nature. This textural distinction provides additional evidence supporting the interpretation of a recharge zone, as areas of active water movement might be expected to show greater spatial variability in resistivity values compared to the more uniform clay regions.

Fig. 4.

GLCM Variance highlighting a suspected recharge zone (red square) that extends to the surface.

GLCM Entropy better differentiates the groundwater reservoir clay cap from surrounding clays (Fig. 5). ERT inverted section (Fig. 3a) shows little contrast (smooth transition) between these regions but GLCM Entropy encodes higher complexity in the clay cap; delineating the structure better. This improved differentiation agrees with the previous interpretation³ of a clay lens overlying the main aquifer. Entropy also highlights the suspected recharge zone’s textural complexity. Overall, GLCM Entropy provides greater confidence mapping key clay boundaries and hydrogeologic structures compared to L2-norm inversion alone.

Fig. 5.

GLCM Entropy enhancing structures in the ERT inverted plot. The red circle indicates the lower entropy region associated to possible clay cap over the aquifer.

The lithological interpretation process involved systematic analysis of all four datasets (original resistivity plus three GLCM attributes) using a complementary approach. First, the original ERT section (Fig. 3a) provided the baseline resistivity framework for identifying potential clay (low resistivity) and non-clay (higher resistivity) regions. However, where resistivity values fell in ambiguous intermediate ranges, the GLCM attributes provided critical additional information. GLCM Mean (Fig. 3b) was used to enhance boundary definition and resolve resistivity ambiguities. GLCM Variance (Fig. 4) helped identify zones of textural complexity, and GLCM Entropy (Fig. 5) provided discrimination between clay units and groundwater reservoirs. This integrative process was a qualitative visual integration, where each GLCM attribute helped resolve ambiguities in the original resistivity data.

This integrated analysis approach allowed us to build a more confident lithological model where GLCM Mean clearly delineated clay shapes, GLCM Variance confirmed distinct subsurface structures based on textural complexity, and GLCM Entropy improved mapping of boundaries between clay lenses and saturated zones. The combined interpretation provided enhanced geological resolution compared to resistivity thresholds alone. However, while GLCM analysis provides valuable supplementary information, several limitations should be considered. One main limitation is that this method requires careful parameter selection, particularly window size and number of gray levels, which can significantly impact the results. Optimal parameters are inherently dataset-dependent and vary based on the specific geological targets, data resolution, and subsurface heterogeneity. Additionally, depending on the inputs, GLCM can extract detailed textural information from resistivity data, but the outputs may appear less distinct than the original inverted sections and require careful interpretation. Also, certain GLCM attributes, such as mean and variance, may provide complementary but not necessarily superior information compared to traditional resistivity analysis methods.

The primary value of GLCM analysis for ERT appears to be in providing supplementary textural information that helps confirm or refine interpretations based on resistivity values alone. Overall we find that GLCM attributes helped better delineate clay boundaries and potential recharge zones that were ambiguous in the original inverted section. However, like all geophysical analysis methods, GLCM cannot completely resolve the fundamental non-uniqueness inherent in resistivity interpretation. Another limitation of this study is that we did not conduct a systematic sensitivity analysis of GLCM input parameters, as our focus was on demonstrating the method’s applicability to ERT interpretation rather than parameter optimization. The GLCM technique is well-established in geophysical applications, and our parameter choices followed proven methodologies from seismic texture analysis.

While GLCM has proven useful for enhancing ERT interpretation in this environment, further research is needed to establish optimal parameters and workflows specific to resistivity data. Experience from other geophysical applications suggests GLCM attributes may be particularly valuable when integrated into machine learning clustering workflows for automated feature detection^46,47. In these cases, the technique’s primary strength appears to lie in providing complementary information for machine learning classification systems rather than serving as a standalone interpretation tool. This suggests future ERT applications could benefit from incorporating GLCM attributes into broader automated analysis frameworks, particularly for complex, heterogeneous environments where traditional interpretation methods face limitations.

Conclusions

We demonstrate the value of applying GLCM textural analysis to ERT data for improving subsurface structural interpretation. Each GLCM attribute provided unique and complementary information that enhanced the traditional resistivity interpretation. GLCM Mean helped overcome inherent smoothing limitations in L2-norm inversion by better defining clay lens boundaries and interfaces. GLCM Variance proved particularly useful in identifying potential recharge zones, revealing spatial variations that were ambiguous in the original resistivity data. GLCM Entropy enhanced the differentiation between clay units and groundwater reservoirs, providing greater confidence in mapping hydrogeologically significant boundaries.

While GLCM analysis cannot completely resolve the fundamental non-uniqueness in resistivity interpretation, it offers a promising approach for extracting additional textural information from ERT data. The technique’s success in this heterogeneous sedimentary environment suggests broader applicability for subsurface characterization, particularly in settings where traditional resistivity interpretation faces limitations due to smooth inversions or complex geology. Future applications could benefit from integrating GLCM attributes into machine learning frameworks for automated feature detection, especially in large-scale groundwater exploration programs. This demonstration establishes GLCM as a valuable tool for enhancing ERT interpretation, potentially improving our ability to map subsurface structures critical for groundwater resource assessment and management.

Author contributions

J.M., H.B. and S.S.: Conceptualization, Methodology, Data curation, Writing- Original draft preparation, Visualization, Investigation. J.M. and S.S.: Data collection, Operation.

Data availability

Data for this study can be accessed at: http://www.hydroshare.org/resource/d8a8ce239f55408c8db522b785a28669.

Declarations

Competing interests

The authors declare no competing interests.