Apparent Resistivity Measurements Research Articles

Petrophysical interpretation of logging-while-drilling borehole measurements in the presence of electrical anisotropy, mud-filtrate invasion, noise, and well deviation effects

Petrophysical interpretation of logging-while-drilling (LWD) borehole measurements in the presence of electrical anisotropy, mud-filtrate invasion, noise, and well deviation effects remains a challenge in formation evaluation. In high-angle and horizontal (HAHZ) wells penetrating electrically anisotropic sandstones, phase and attenuation apparent resistivity logs often exhibit values larger than resistivity parallel to bedding planes. Consequently, traditional interpretation methods often fail to accurately estimate hydrocarbon saturation when using only the long-spacing phase apparent resistivity log (P40H) in petrophysical calculations. We implement two approaches (analytical and Bayesian) to estimate horizontal and vertical resistivities from apparent resistivity measurements. The first analytical approach is based on the numerical simulation of LWD resistivity measurements using synthetic models under various conditions of electrical anisotropy and well inclination to derive analytical models. The relative error of analytical approximations is less than 6%. In the presence of measurement noise and shoulder-bed effects, we implement a Bayesian method for well-log inversion and uncertainty quantification. The relative error of Bayesian inversion is less than 2%. Estimates of horizontal and vertical resistivities then can be used for petrophysical analysis. A challenging set of synthetic and field examples of HAHZ wells penetrating electrically anisotropic formations is selected for examination and verification of the new methods. For radial lengths of invasion less than 20 cm (8 in), sensitivity analysis indicates that the effects of conductive mud-filtrate invasion on long-spacing resistivity logs are negligible. The long-spacing phase (P40H) and attenuation (A40H) apparent resistivities are used to estimate horizontal and vertical resistivities. In the field examples under study, electrical anisotropy is caused by intercalated laminations of coarse- and fine-grained sandstones; the volumetric concentration of shale is negligible. Considering that Archie’s parameters are direction dependent, sensitivity analysis indicates that the effective value of the saturation exponent parallel to bedding planes is less sensitive to the volumetric concentration of fine-grained sandstone layers compared with the saturation exponent perpendicular to bedding planes. Thus, water saturation of grain-laminated sandstones in HAHZ wells can be estimated using horizontal resistivity with Archie’s parameters that are consistent with petrophysical interpretations performed in vertical wells. Estimates of water saturation in the field examples using horizontal resistivity agree with saturation-height models. Compared with conventional interpretation methods that use P40H as the formation resistivity, the new approach improved the estimation of hydrocarbon saturation by 10%.

Contaminant source and aquifer characterization: An application of ES-MDA demonstrating the assimilation of geophysical data

Contaminant source and aquifer characterization (CSAC) is critical in groundwater pollution evaluation and remediation. The ensemble smoother with multiple data assimilation (ES-MDA) is utilized to jointly identify contaminant source information and hydraulic conductivities by assimilating time-lapse electrical resistivity tomography (ERT) data. In a synthetic profile with a time-varying release history in a heterogeneous aquifer, we verify the performance of the proposed data assimilation framework. The results show that the CSAC problem could be handled by the proposed approach. The time-varying release history and the high permeability area can be identified with adequate time-lapse ERT measurements. Further reproduction of the evolution of the plume after CSAC also shows consistency with the reference plume. The poor conditioning inversion caused by the filter inbreeding is analyzed by comparing four scenarios with different apparent resistivity measurements. Furthermore, we also evaluate the impact of uncertainties in the petrophysical properties and geophysical observations on our data assimilation framework. The results show that the proposed ES-MDA data assimilation framework could provide a convincing inversion of the time-varying release history and hydraulic conductivities.

Electrical resistivity tomography results analyzed with two inversion methods to determine chloride profiles on BFS concrete having very high electrical resistivity

Non-destructive evaluation techniques are increasingly used for the investigation of reinforced concrete structures in marine environment. In this paper, the possibility of evaluating chloride profiles by Electrical Resistivity Tomography (ERT) on Blast furnace slag (BFS) concrete at a long curing period so having high electrical resistivity was studied. This was carried out by monitoring the chloride profile for two 6-years old concretes (with and without slag) during a diffusion campaign using a Non-Destructive Evaluation (NDE) methodology. The methodology is based on determining the electrical resistivity profiles by carrying out surface apparent resistivity measurements submitted to two different inversion processes. The resistivity profiles are then converted to chlorides profiles using calibration curves. The chlorides profiles were also compared by those assessed by Destructive Evaluation (DE) at three different exposure periods, which displays a high similarity between DE and NDE profiles.

Near-bit apparent resistivity measurement method based on SPWM excitation

In order to improve the measurement accuracy of near-bit apparent resistivity and its measurement range, this paper excites the underground transmitting antenna by a sinusoidal pulse-width modulated (SPWM) current excitation method, which can improve the response of the receiving antenna and circuit in the resistivity measurement system under the usual square wave excitation, thus improving the measurement accuracy of near-bit apparent resistivity. In this paper, the effect of square wave, SPWM wave and sine wave excitation on resistivity measurement was studied, and the modulation algorithm and hardware control are programmed by DSP (Digital Signal Processor), and the SPWM signal is output by full-bridge inverter circuit and tuned antenna. The indoor experimental results show that the near-bit apparent resistivity measurement method based on the SPWM wave pulse excitation can achieve the measurement in the range of formation equivalent resistor value of less than 600kΩ. There is a high trend matching between near-bit apparent resistivity LWD curve and RT resistivity curve of well completion electrical logging in field tests of formation resistivity less than 2000Ω·m, which proves that the method can improve the accuracy of near-bit apparent resistivity measurement.

Influence analysis of calculated horizontally layered soil parameters on grounding parameters

AbstractCalculated parameters (soil layer resistivity, soil layer thickness, and the number of soil layers) of horizontally layered soil are usually obtained based on the measured apparent resistivity under different measurement distances, which are significant for the design, operation, and maintenance of grounding grids. Most existing calculation methods of soil parameters are just trying to make the calculation results approach the measurement data, ignoring the relationship among measurement data, the calculated soil parameters, and grounding parameters, which would increase the workload of the measurement. To better balance the distance range of the measurement data and the influence of the calculated horizontally layered soil on grounding parameters, this paper systematically studies the relationship among measured apparent soil resistivity, calculated horizontally layered soil parameters, and grounding parameters. The basic theories of apparent resistivity measurement, soil parameter calculation, and grounding parameter calculation are given, the influence of soil layer thickness on the measured apparent resistivity is studied, and the influence of the calculated soil parameters on the grounding resistance of different grounding models is analysed. Based on different scales of grounding grids, the results give a corresponding reference distance range of measured apparent soil resistivity. Therefore, this paper can help decrease the workload of soil resistivity measurement during grounding parameters analysis, which has far‐reaching engineering significance.

Extraction of the stable component of electrical surveys of soils and the consequence on the mapping of their thicknesses

Knowledge of the spatial variability of soil thickness (ST) in agricultural fields is useful for improving crop management. Spatial patterns of ST can be characterized using temporal stability analysis of high spatial density and temporal frequency data, associated with sparse and difficult to obtain data on the target variable. Apparent electrical resistivity measurements of soil at high spatial density have been widely used to infer the spatial variability of soil properties. However, electrical resistivity measurements are sensitive to many factors (e.g. soil water content). Thus, it remains difficult to interpret them according to a characteristic of the soil such as its thickness. The objective of this study was to present a geostatistical approach called automatic factorial cokriging (AFACK), which allows capturing the time-invariant part between the spatio-temporal measurements of a signal, called stable component in the sequel. The stable component achieved by AFACK was then used as a covariate in a multivariate estimation algorithm to map a static soil property pattern. The underlying idea was to highlight that the spatial estimates of a static soil property pattern is well achieved by integrating, in a multivariate estimation algorithm, the stable component over the time of a covariate instead of its single acquisitions. The latter generally show weak and inconsistent relationships with the static properties of the soil such as its thickness. These inconsistent relationships are mainly generated by the temporal variability of the signal measurements carried out under various conditions. Through three surveys of soil resistivity measurements carried out on three dates on the soil of an agricultural plot, results revealed that AFACK allows: (i) reproducing an initial signal deliberately corrupted by a noise, (ii) extracting the time-stable component of two or more soil electrical resistivity surveys. Cluster analysis results also revealed that the time-stable component of the signal exhibits well homogeneous areas in space conversely to surveys considered separately. Results also showed that the time-stable component of the electrical signal is better linked to the thickness of soil (ST). In addition, the mapping of ST by collocated cokriging (CC), using any stable component between two or more electrical resistivity surveys carried out by AFACK, leaded to an invariable map of ST, unlike the maps achieved by CC using, as covariate, soil electrical surveys considered individually. Statistical indicators resulting from leave-one-out cross-validation (LOOCV) showed that CC using any invariant part of the signal outperforms CC using the single acquisitions. Correlation coefficient (r), mean absolute error (MAE) and root mean square error (RMSE) values range between 0.93 and 0.94; 4.33 and 5.03; 0.75 and 0.88, respectively, for estimates using as a covariate an invariant part of the signal. While values of these statistical indicators range between 0.64 and 0.74; 7.20 and 8.69; 1.25 and 1.52, respectively, for estimates by CC using single acquisitions. Values of these indicators are almost invariant regardless of the invariant part used in CC, unlike the scenario using the surveys individually.

Application of vertical electrical sounding resistivity technique to explore groundwater in the Errachidia basin, Morocco

The resistivity technique involving Vertical Electrical Sounding (VES) was carried out North of Ain Al Atti area, in Zaouia Jdida locality, with the aim of delineating zones not contaminated by the extension of the salinity and determining the potentiality of the existing aquifers. The measurements of apparent resistivity were collected using MolisanaApparecchiatureElettroniche (MAE) advanced geophysics instruments and were taken in twenty two VES points, along four profiles oriented N-S. The VES profiles were implanted using the Schlumberger configuration. VES Interpretation results shows that the potential aquifer horizon consists of the infracenomanian sand. The isopach map shows that the thickness of this geological formation varies between 20 m and 170 m. The sand layer is more thick (>80 m) along the profiles P3 and P4, with a maximum of about 170 m at 2P4 and 3P4 VES points. The isohypse map indicates that the sand formation is shallow (<10 m) in the East, and the depth of the roof of the infracenomanian sand increases gradually towards the West of the prospect area (>30 m). The transverse resistance (Tr) map shows that the identified aquifer has high values of Tr (Tr > 50000 Ω m2) in the western part, corresponding to zones with relatively high thickness and may have high transmissivity. The longitudinal conductance anomaly (Sl > 0.6 Ω-1) indicates that the area delimited by 1P2, 4P2, 1P4 and 3P4 VES points may have an important underground hydraulic potential. The interpretation of the acquired data also shows the presence of small depressions that could be implicated in the storage of the infracenomanian groundwater. Furthermore, the resistivity results reveal the presence of electrical discontinuities interpreted as faults and fracture zones. These could be the preferential axes of the groundwater circulation.

Exploring the regolith with electrical resistivity tomography in large-scale surveys: electrode spacing-related issues and possibility

Abstract. Within the critical zone, regolith plays a key role in the fundamental hydrological functions of water collection, storage, mixing and release. Electrical resistivity tomography (ERT) is recognized as a remarkable tool for characterizing the geometry and properties of the regolith, overcoming limitations inherent to conventional borehole-based investigations. For exploring shallow layers, a small electrode spacing (ES) will provide a denser set of apparent resistivity measurements of the subsurface. As this option is cumbersome and time-consuming, larger ES – albeit offering poorer shallow apparent resistivity data – is often preferred for large horizontal ERT surveys. To investigate the negative trade-off between larger ES and reduced accuracy of the inverted ERT images for shallow layers, we use a set of synthetic “conductive–resistive–conductive” three-layered soil–saprock/saprolite–bedrock models in combination with a reference field dataset. Our results suggest that an increase in ES causes a deterioration of the accuracy of the inverted ERT images in terms of both resistivity distribution and interface delineation and, most importantly, that this degradation increases sharply when the ES exceeds the thickness of the top subsurface layer. This finding, which is obvious for the characterization of shallow layers, is also relevant even when solely aiming for the characterization of deeper layers. We show that an oversized ES leads to overestimations of depth to bedrock and that this overestimation is even more important for subsurface structures with high resistivity contrast. To overcome this limitation, we propose adding interpolated levels of surficial apparent resistivity relying on a limited number of ERT profiles with a smaller ES. We demonstrate that our protocol significantly improves the accuracy of ERT profiles when using large ES, provided that the top layer has a rather constant thickness and resistivity. For the specific case of large-scale ERT surveys the proposed upgrading procedure is cost-effective in comparison to protocols based on small ES.

Analysis on Deep-Well Apparent Resistivity Measurement at Dabaishe Seismic Station

We interpret the horizontally layered homogeneous medium model of Dabaishe station according to the electric sounding data. The measurement array at the station is the fixed Schlumberger arrays. The deep-well measurement has two set of arrays. One is horizontally placed under 100 meters, and the other is vertically arranged. Under the layered model, we analyze the sensitivity coefficient variations of deep-well apparent resistivity measurement versus the different electrode depth and the spacing of current electrodes. The results show that the horizontal deep-well measurement has well ability on inhibiting disturbances from surface. However, its current electrodes spacing is relatively short, only 60 meters, thus the measurement data cannot effectively reflect the resistivity variations from deep mediums. Electrodes of the vertical deep-well measurement array locate within the layer where underground water level changes. Therefore, its measurement data suffers great affection from the water level variations and it is very difficult to distinguish the resistivity variations of deep mediums from the data. In order to better detect information associated with earthquakes, the spacing of horizontal arrays of AB/2 should be set as 250-350m, and the bury depth exceeds 150m. A Horizontal array along NS direction is also recommended.

Functionally Graded Multilayered Soil Models, an Alternative to Modeling the Soil Electrical Resistivity for Computing the Grounding Resistance

Alternative models of the electrical resistivity of the soil to the well-known constant piecewise multilayer model are presented in this paper. By their special features, the proposed models lead to reasonably simple semi-analytical expressions for the electric potential. The parameters associated with these models are obtained from apparent resistivity measurements using an optimization procedure. The proposed models allow obtaining a continuous piecewise resistivity profile as a function of depth from the soil surface. From the full definition of the models, the grounding resistance of several electrodes is calculated and compared with that obtained from the classic multilayer model. Finally some application examples including data from field measurements are considered in this paper.

Guidelines for precise lime management based on high-resolution soil pH, texture and SOM maps generated from proximal soil sensing data

Soil acidification is caused by natural paedogenetic processes and anthropogenic impacts but can be counteracted by regular lime application. Although sensors and applicators for variable-rate liming (VRL) exist, there are no established strategies for using these tools or helping to implement VRL in practice. Therefore, this study aimed to provide guidelines for site-specific liming based on proximal soil sensing. First, high-resolution soil maps of the liming-relevant indicators (pH, soil texture and soil organic matter content) were generated using on-the-go sensors. The soil acidity was predicted by two ion-selective antimony electrodes (RMSEpH: 0.37); the soil texture was predicted by a combination of apparent electrical resistivity measurements and natural soil-borne gamma emissions (RMSEclay: 0.046 kg kg−1); and the soil organic matter (SOM) status was predicted by a combination of red (660 nm) and near-infrared (NIR, 970 nm) optical reflection measurements (RMSESOM: 6.4 g kg−1). Second, to address the high within-field soil variability (pH varied by 2.9 units, clay content by 0.44 kg kg−1 and SOM by 5.5 g kg−1), a well-established empirical lime recommendation algorithm that represents the best management practices for liming in Germany was adapted, and the lime requirements (LRs) were determined. The generated workflow was applied to a 25.6 ha test field in north-eastern Germany, and the variable LR was compared to the conventional uniform LR. The comparison showed that under the uniform liming approach, 63% of the field would be over-fertilized by approximately 12 t of lime, 6% would receive approximately 6 t too little lime and 31% would still be adequately limed.

Evaluation of spectral induced polarization field measurements in time and frequency domain

Spectral induced polarization (SIP) measurements have been demonstrated to correlate with important parameters in hydrogeological and environmental investigations. Although SIP measurements were often collected in the frequency domain (FDIP), recent developments have demonstrated the capabilities to solve for the frequency-dependence of the complex conductivity through measurements collected in the time domain (TDIP). Therefore, the aim of our field investigations is a comparison of the measured frequency-dependence at a broad frequency range resolved through FDIP and TDIP. In contrast to previous studies, we conducted measurements with different instruments and measuring technologies for both FDIP and TDIP. This allows for investigating the robustness of different measurements and assessing various sources of errors, for the assessment of the advantages and drawbacks from different measuring techniques. Our results demonstrate that data collected through different instruments are consistent. Apparent resistivity measurements as well as the inversion results revealed quantitatively the same values for all instruments. The measurements of the IP effect are also comparable, particularly FDIP readings in the low frequencies (< 10 Hz) revealed to be quantitatively the same for different instruments. TDIP measurements are consistent for data collected with both devices. As expected, the spatial distribution of the values is also consistent for low frequency data (in FDIP) and late times measurements in TDIP (> 0.1 s). However, data quality for higher frequencies in FDIP (i.e., early times in TDIP) show larger variations, which reflects the differences between the instruments to deal with the electromagnetic contamination of the IP data. Concluded in general, the different instruments and measuring techniques can provide consistent responses for varying signal-to-noise ratio and measuring configurations.

The influence of angled survey lines on 2D ERT surveys using the Wenner (α) array with implications for groundwater exploration in Karoo rocks

Two-dimensional (2D) electrical resistivity tomography (ERT) surveying systems typically use standard protocols that assume straight survey lines and collinear electrodes. However, due to the presence of infrastructures and other surface constraints, it is not always possible to conduct 2D ERT surveys along straight lines. When survey lines are angled, the apparent resistivity data are affected for measurements where electrodes occur on either side of the position of the angle, since the assumed distances between some of the electrodes are larger than the true distances. This study investigates the impact of angled survey lines on 2D ERT data and inverse resistivity models for the Wenner (α) array. Theoretical considerations show that measurements along angled survey line are sensitive to resistivity changes at position laterally displaced from the survey line, while both the calculated apparent resistivities and the depths of investigation are affected when electrodes straddle the angle. The resulting errors are, however, small. Even for a large angle of 45°, the errors are smaller than 6.5% for the affected apparent resistivity measurements, and smaller than 3.8% for the median depths. Since the apparent resistivity data and the pseudo-depths are affected by angles in the survey lines, the inverse resistivity models are also affected. Numerical modelling shows that even small input errors may be propagated (both in magnitude and spatially) during inversion, thereby distorting the resulting resistivity models. The distorted inverse resistivity models could lead to the incorrect interpretation of the locations, geometries and orientations of subsurface structures, which could lead to poorly sited production boreholes. The results of field surveys show that apparent resistivity data sets recorded along angled lines may be partially corrected by calculating the true geometric factors and by adjusting the apparent resistivity data accordingly. Significantly improved inverse resistivity models are found for corrected data sets.

Can Soil Electrical Resistivity Measurements Aid the Identification of Forest Areas Prone to Windthrow Disturbance?

This study investigates how certain forest soil properties influence the propensity of beech forests to windthrow disturbances. The field measurements of soil electrical resistivity were carried out in an old-growth natural beech forest where the soil has developed from Cainozoic sedimentary rock with mudstone–claystone stratigraphy. In 2014, the forest was hit by a severe windstorm, and dispersed windthrow occurred at certain plots. Apparent electrical resistivity measurements were performed to investigate whether some soil properties could influence the forest trees’ predisposition to windthrow. The increases in the clay content and soil bulk density below 30 cm were associated with weathered claystone and mudstone, which created a physiological barrier for deeper root penetration. The result of the χ 2 test suggested that the windthrown spots were not distributed evenly over the entire study area. They were mainly concentrated over approximately 50% of the area, and their positions coincided with low resistivity values, indicating low soil skeleton content, high clay content and soil moisture. Therefore, electrical resistivity tomography could be considered a useful predictive tool for reducing the risk of natural disturbances by preventive forest management.

Wenner Soundings for Apparent Resistivity Measurements at Small Depths Using a Set of Unequal Bare Electrodes: Selected Case Studies

The possibility of using a set of unequal electrodes, within limits, in a Wenner arrangement for the measurement of apparent resistivity at small depths is explored in this paper. A procedure in which only a simple preliminary calibration is necessary to obtain the best measurements of the apparent resistivity is proposed. On the basis of some case studies, a comparison with the usual procedures to obtain the apparent resistivity from resistance measurements is carried out. The results showed that when an unequal set of electrodes was used, the procedure proposed here was the only one that guaranteed the best apparent resistivity values for any value of electrode separation in the Wenner arrangement, especially for those associated with small depths.

Inadequacy of 1D, 2D and 3D Resistivity Inverse Modelling in the Presence of Electrical Anisotropy

Universal property of matter is the variation of a certain physical characteristic in different direction. The Substances that do not display this property are an exception. Anisotropy, as this property is named, is also notable in electrical conductivity of minerals, ores, rocks and geological formations. In order to properly define a geological model of an investigated area, it is necessary to account for electrical anisotropy and lateral effects of different origin that are almost always present phenomena. The degree of knowledge of these phenomena determines the quality of interpretation. The effects of electrical anisotropy on 1D, 2D and 3D inversion of apparent resistivity data were examined and the way to detect, quantify and analyse electrical anisotropy in 3D case is proposed. The results of this analysis showed that electrically anisotropic models have led to the totally erroneous results of 3D inversion while the effects of electrical anisotropy on 1D and 2D inversion were less pronounced. Among several existing ways of collecting 3D apparent resistivity data the complete Pole-pole array data set is the only one suitable for detection of electrical anisotropy. Pole-pole resistivity data enable calculating of corresponding resistance or apparent resistivity values for all other collinear or square arrays. This fact makes possible to use standard grid of electrodes in performing 3D Pole-pole apparent resistivity measurements for calculating square array apparent resistivity data. In the special case of vertical stratification (fracturing, schistosity..) this calculated square array data were used for electrical anisotropy analysis thus determining values of coefficient of anisotropy () and mean geometric resistivity (_m). The simple two and three layer 1D synthetic anisotropic models, were used to determine parameters of electrical anisotropy by using 3D forward modelling to calculate Pole-pole and then square array apparent resistivity values. The mean geometric resistivity data obtained by using square array, which are orientation-independent, were used for 1D inversion leading to more realistic results. In the case of oblique stratification (lamination, fracturing, schistosity or karstification) crossed square resistivity data can be reconstructed from 3D Pole-pole data set and then can be used to get parameters of electrical anisotropy, namely apparent coefficient of anisotropy (n), mean geometric resistivity (_m) and apparent electrical strike (). These parameters provide an indication that investigations of electrical anisotropy should be conducted (by using square and crossed square array) in order to avoid erroneous results of 3D inversion.

Hierarchical Multiple Linear Regression for Fast Estimation of Subsurface Resistivity from Apparent Resistivity Measurements Based on Dipole-Dipole Array

Multiple linear regression (MLR) models for fast estimation of true subsurface resistivity from apparent resistivity field measurements are developed and assessed in this study, based on Dipole-dipole array. The parameters that have been investigated are apparent resistivity (ρa) horizontal location (X) and depth (Z) of measurement as the independent variables; and true resistivity (ρt) as dependent variable. To achieve linearity in both resistivities, datasets were first transformed into logarithmic domain following diagnostic checks of normality of the dependent variable and heteroscedasticity to ensure accurate models. Four MLR models namely; DD1, DD2, DD3 and DD4 were developed based on hierarchical combination of the independent variables. The generated MLR coefficients were applied to another dataset to estimate ρt values for validation. The accuracy of the models was assessed using coefficient of determination (R2), standard error (SE) and weighted mean absolute percentage error (wMAPE). It is concluded that the MLR models can estimate ρt for the Dipole-dipole array with high level of accuracy, with the DD4 model being the best.

Method for Constructing a Model of a Geoelectric Section Taking into Account Seasonal Variations Based on Data from Long-Term Vertical Electric Sounding Monitoring in Search of Earthquake Precursors

The study analyzes data from high-precision measurements of the apparent resistivity by a stationary multielectrode vertical electric sounding (VES) system including 12 current and 4 potential lines spaced 2–650 m apart. Observations had been being carried out at the Garm test area on a daily basis for 12 years in an earthquake prediction experiment. The use of special technical methods during measurements ensured an instrumental error of about 0.01%. The virtual error of each individual measurement of apparent resistivity (taking into account all possible noise) was 0.1–0.2%. The availability of more than 3000 VES curves measured in different seasons allows us to propose a new approach to constructing a geoelectric section model. To solve the inverse VES problem, a set of 36 averaged 10-day VES curves was analyzed, each of which was obtained by averaging approximately 100 individual VES curves accumulated in the same 10-day period of the annual (seasonal) cycle in different years. Comparative analysis of these curves made it possible to calculate and include corrections for stationary geological noise in the model. As a result, it was possible to substantially reduce (by an order of magnitude) the discrepancies in fitting the curves and dramatically narrow the equivalence domain. Based on the results of our analysis, we have constructed a model of a four-layer horizontally layered geoelectric section of the Khazor-Chashma depression to adequately describe not only the averaged section, but also its seasonal variations throughout the year. The stability in estimating the model parameters is studied. To further reduce the equivalence domain, we propose that the layer thicknesses be fixed. This model can be used not only to study the aforementioned characteristics of the section, but also to monitor time variations of resistivity in individual layers of the section. This will significantly improve the resolving power of systems for detecting time variations in geoelectric sections, including when searching for earthquake precursors.

Linear regression models for estimating true subsurface resistivity from apparent resistivity data

Simple linear regression (SLR) models for rapid estimation of true subsurface resistivity from apparent resistivity measurements are developed and assessed in this study. The objective is to minimize the processing time and computer memory required to carry out inversion with conventional algorithms. The arrays considered are Wenner, Wenner–Schlumberger and dipole–dipole. The parameters investigated are apparent resistivity (\(\rho _a \)) and true resistivity (\(\rho _t\)) as independent and dependent variables, respectively. For the fact that subsurface resistivity is nonlinear, the datasets were first transformed into logarithmic scale to satisfy the basic regression assumptions. Three models, one each for the three array types, are thus developed based on simple linear relationships between the dependent and independent variables. The generated SLR coefficients were used to estimate \(\rho _t\) for different \(\rho _a\) datasets for validation. Accuracy of the models was assessed using coefficient of determination (\(R^{2})\), F-test, standard error (SE) and weighted mean absolute percentage error (wMAPE). The model calibration \(R^{2}\) and F-value are obtained as 0.75 and 2286, 0.63 and 1097, and 0.47 and 446 for the Wenner, Wenner–Schlumberger and dipole–dipole array models, respectively. The SE for calibration and validation are obtained as 0.12 and 0.13, 0.16 and 0.25, and 0.21 and 0.24 for the Wenner, Wenner–Schlumberger and dipole–dipole array models, respectively. Similarly, the wMAPE for calibration and validation are estimated as 3.27 and 3.49%, 3.88 and 5.72%, and 5.35 and 6.07% for the three array models, respectively. When compared with standard constraint least-squares (SCLS) inversion and Incomplete Gauss–Newton (IGN) algorithms, the SLR models were found to reduce about 80–96.5% of the processing time and memory space required to carry out the inversion with the SCLS algorithm. It is concluded that the SLR models can rapidly estimate \(\rho _t\) for the various arrays accurately.

Unidimensional Vertical Electrical Soundings involving uneven soil surfaces: improving the apparent resistivity measurements for soil modelling

The influence of a non-flat uneven soil surface on the soil apparent resistivity measurements in unidimensional Vertical Electrical Sounding is analysed. The sounding in a real uneven soil surface is simulated by using a soil model, which allows the semi-analytical expressions valid for perfectly plane soils to be used. In addition, real Wenner electrodes properly calibrated are used, and the differences with a sounding in an equivalent soil with a flat surface are highlighted. Due to the loss of symmetry around the centre of the Wenner array, measurements along different directions are needed and the mean value of the distributions of the measures is assigned to the value of the apparent resistivity. Furthermore, for the purpose of reducing the width of such distribution, the use of electrodes of increasing length is suggested within limits. Finally, the proposal of a multi-layered soil model with an uneven surface based on the Wenner measurements is discussed.