Direct Current Resistivity Data Research Articles

Enhancing DC resistivity data two-dimensional inversion result by using U-net based Deep learning- algorithm: Examples from archaegeophysical surveys

In this study, we suggested using a convolutional neural network (CNN) based algorithm to enhance two-dimensional (2D) Direct Current Resistivity (DCR) data inversion results. We developed U-net based CNN algorithm, named DCR2D_Net_Archaeo. We generated 1080 sets of 2D resistivity models that simulate buried archaeological remains. We calculated synthetic data for those models for different electrode arrays. We added 2% random noise to apparent resistivity data sets and inverted those data sets. We used the 2D inversion results as input and the corresponding real resistivity model as output. By using those 1080 input and output data sets we developed the DCR2D_Net_Archaeo algorithm. First, we tested this algorithm by using synthetic data. We showed that the developed algorithm improved the 2D classical smoothing regularization inversion and the buried body’'s geometry and depth can be found very close to the real model. Afterward, we also tested the developed algorithm with real data collected from two different archaeological sites. We showed that the buried wall cross-section location and depth are better found by the DCR2D_Net_Archaeo algorithm than by using the conventional inversion codes for the inversion of DCR data if we compare it with the excavated wall structure.

Forward and inversion approach for direct current resistivity based on an unstructured mesh and its application to tunnel engineering

AbstractThe accurate identification of water‐bearing structures is urgently required for the safe construction of tunnel engineering. Currently, the direct current resistivity method is an effective method for detecting water‐bearing structures in tunnels. In the advanced detection of the direct current resistivity based on the finite element method, the traditional hexahedron mesh performs poorly for the discretization of models of complex tunnel structure sections such as horseshoe‐shaped and round sections. Therefore, this study adopts unstructured grid generation technology combining tetrahedra and hexahedra to achieve more accurate modelling of complex structures, such as round and horseshoe‐shaped sections, and establishes a forward modelling method of the direct current resistivity in tunnels based on an unstructured mesh. The maximum error between the numerical simulation and theoretical results for an infinite tabular body in full space is less than 0.8%. It is more complicated to calculate the sensitivity matrix and model constraint term for the inversion region containing two types of grid than for one. For this purpose, the sensitivity matrix of different types of grid areas is calculated, a model constraint term based on the dual constraints of volume and distance is constructed, and finally, a partitioned domain‐weighted least‐squares inversion method based on an unstructured mesh is proposed. Synthetic examples of typical water‐bearing structures are analysed, and the results show that the proposed forward and inverse methods of the direct current resistivity in tunnels based on an unstructured mesh can effectively capture the position and morphology of the water‐bearing structure. Finally, an on‐site application was conducted in the Yellow River Diversion Project in central Shanxi. The proposed method could effectively identify the water body in front of the tunnel face and guide the on‐site construction of the project. These results can improve the interpretation of the direct current resistivity data in tunnels and play a positive role in promoting the use of the direct current resistivity method to prevent and control water‐inrush disasters in tunnels with complex structures.

Characterization of DNAPL source zones in clay-sand media via joint inversion of DC resistivity, induced polarization and borehole data

Toxic organic contaminants in groundwater are pervasive at many industrial sites worldwide. These contaminants, such as chlorinated solvents, often appear as dense non-aqueous phase liquids (DNAPLs). To design efficient remediation strategies, detailed characterization of DNAPL Source Zone Architecture (SZA) is required. Since invasive borehole-based investigations suffer from limited spatial coverage, a non-intrusive geophysical method, direct current (DC) resistivity, has been applied to image the DNAPL distribution; however, in clay-sand environments, the ability of DC resistivity for DNAPLs imaging is limited since it cannot separate between DNAPLs and surrounding clay-sand soils. Moreover, the simplified parameterization of conventional inversion approaches cannot preserve physically realistic patterns of SZAs, and tends to smooth out any sharp spatial variations. In this paper, the induced polarization (IP) technique is combined with DC resistivity (DCIP) to provide plausible DNAPL characterization in clay-sand environments. Using petrophysical models, the DCIP data is utilized to provide tomograms of the DNAPL saturation (SN) and hydraulic conductivity (K). The DCIP-estimated K/SN tomograms are then integrated with borehole measurements in a deep learning-based joint inversion framework to accurately parameterize the highly irregular SZA and provide a refined DNAPL image. To evaluate the performance of the proposed approach, we conducted numerical experiments in a heterogeneous clay-sand aquifer with a complex SZA. Results demonstrate the standalone DC resistivity method fails to infer the DNAPL in complex clay-sand environments. In contrast, the combined DCIP technique provides the necessary information to reconstruct the large-scale features of K/SN fields, while integrating DCIP data with sparse but accurate borehole data results in a high resolution characterization of the SZA.

Forward modeling of direct-current resistivity data on unstructured grids using an adaptive mimetic finite-difference method

An effective solver for the direct-current (DC) resistivity forward-modeling problem should be capable of accommodating arbitrary electrode layouts, adapting the mesh to topography and complex geologic structures, and adaptively refining the mesh to ensure high solution accuracy. We use the capability of the mimetic finite-difference method in naturally accommodating meshes with nonconforming elements to develop adaptive and parallel cell-based (CB) and vertex-based (VB) mimetic schemes for the forward modeling of DC resistivity data on unstructured meshes. A diffusion problem in mixed form and Poisson’s problem are solved in the CB and VB schemes, respectively. The mesh adaptivity involves an iterative h-refinement conducted by a regular subdivision of the marked elements together with a 2-irregularity condition. Goal-oriented residual- and gradient-based error estimators are used to mark the elements for refinement in the CB and VB schemes, respectively. To evaluate the accuracy and efficiency of the mimetic schemes, we use two benchmark models with analytical solutions and standard linear and quadratic finite-element solutions. The numerical results for apparent resistivity from both mimetic schemes accurately approximate the reference analytical and numerical values. Furthermore, on similar meshes, the VB mimetic scheme is found to be less demanding than the CB method in terms of computational resource requirement. We also develop a grid-based mesh generation technique based on the body-centered cubic lattice to generate high-quality initial meshes. Using benchmark examples, we validate this mesh generation method and demonstrate its versatility by discretizing a model of a thin dike where a standard Delaunay mesh generator fails to generate a mesh. Moreover, we display the effectiveness of the presented mimetic approach and the grid-based mesh generation technique using a realistic example with topography and parallelization over a large number of sources.

Testing Different Stochastic Methods to Model Direct Current Resistivity and Seismic Refraction Geophysical Data Using a Combined Local and Global Optimization Algorithm

Testing Different Stochastic Methods to Model Direct Current Resistivity and Seismic Refraction Geophysical Data Using a Combined Local and Global Optimization Algorithm

Application of Combined Local and Global Optimization Algorithms in Joint Interpretation of Direct Current Resistivity and Seismic Refraction Data: A Case Study of Dammam Dome, Eastern Saudi Arabia

The main geological structures in the Dammam Dome are defined by integrating geophysical measurements and applying new methodological approaches. Dammam Dome is characterized by a well-developed fracture/joints system; thus, high complexity of the subsurface is expected. Direct Current Resistivity (DCR) and Seismic Refraction (SR) geophysical survey aimed to map the Dammam Dome's near-surface features. The geophysical data were acquired along two profiles in the northern part of Dammam Dome. To maximize the results from conducting DCR and SR measurements over a complex area, a combined local and global optimization algorithm was used to obtain high-resolution near-surface images in resistivity and velocity models. The local optimization technique involves individual and joint inversion of the DCR and SR data incorporating appropriate regularization parameters, while the global optimization uses single and multi-objective genetic algorithms in model parameter estimation. The combined algorithm uses the output from the local optimization method to define a search space for the global optimization algorithm. The results show that the local optimization produces satisfactory inverted models, and that the global optimization algorithm improves the local optimization results. The joint inversion and processing of the acquired data identified two major faults and a deformed zone with an almost N-S direction that corresponds with an outcrop were mapped in profile one, while profile two shows similar anomalies in both the resistivity and velocity models with the main E-W direction. This study not only demonstrates the capability of using the combined local and global optimization multi-objectives techniques to estimate model parameters of large datasets (i.e., 2D DCR and SR data), but also provides high-resolution subsurface images that can be used to study structural features of the Dammam Dome.

A Comprehensive Study of Local, Global, and Combined Optimization Methods on Synthetic Seismic Refraction and Direct Current Resistivity Data

Most geophysical inversions face the problem of non-uniqueness, which poses a challenge in the mapping and delineation of the subsurface anomalies. To tackle this challenge, a combined local and global optimization approach is considered for jointly inverting two-dimensional direct current resistivity (DCR) and seismic refraction (SR) data that aim to estimate the corresponding physical model parameters. In this combined approach, the output of the local optimization method is used to determine the search space and tuning parameters for the global optimization algorithm. The multi-objective genetic algorithm (non-dominated sorting genetic algorithm) was utilized to jointly optimize the objective functions of two different methods. Because the genetic algorithm is a population-based optimization method, it requires numerous forward calculations. To deal with the expected high computational cost associated with this approach, parallel computing was utilized for the forward function evaluations to reduce the run time of the entire process. The proposed approach was tested using synthetic two-dimensional resistivity and velocity models that had three different types of anomalies (dyke, positive, and combined positive and negative). The results showed an improvement in the anomaly delineation in the output of the combined local and global optimization method compared with the local optimization method. Additionally, similar synthetic models were tested using only the single objective global optimization algorithm (conventional global optimization), which showed promising anomaly delineation.

Groundwater budgeting of Nari and Gaj formations and groundwater mapping of Karachi, Pakistan

Groundwater depletion is an emerging problem worldwide due to changes in climate and an increase in urbanization. Two significant water-bearing formations, the Oligocene-aged Nari and the Miocene-aged Gaj, were utilized as a case study exposed near Karachi, Pakistan. Groundwater budgeting was performed through a classical equation. The inflow of groundwater in the formations was calculated by thermo-pluviometric data and water loss of Hub Dam. The potential of evapotranspiration (PET) was calculated by the Thornthwaite method. The groundwater inflow from Hub Dam was estimated by using 20 years of annual water loss data by removing PET. The total mean annual inflow of groundwater in the formations was 2414.12 US Gallons per Second (gps). The annual mean outflow was estimated by calculation of groundwater usage for industries and domestic purposes and the mean annual groundwater outflow was 5562.61 US gps and an annual deficit of groundwater was 3148.5 US gps. The research is composed of validating the groundwater budget. Direct Current Electrical Resistivity (DCER) and static water level data from existing industrial wells were used for groundwater maps. The DCER data indicates A-Type and K-Type sub-surface with high resistivity in the three-layer model. The average water table of residential areas in 2019 was 60 m and in industrial areas was 130 m. The oscillation of the groundwater table over the last 20 years and the deficit of the groundwater budget shows an alarming condition for the future. If the same scenario persists, then by 2025, the water table will decline up to 140 m.

Analysis of direct current resistivity data using continuous wavelet transform

We have developed a new method for the direct current resistivity interpretation, based on the continuous wavelet transform (CWT) of electric potential-difference data. It exploits the main properties of the CWT, such as stability versus noise, and does not require a starting model or other a priori information such as a model weighting function or constraints. Because the approximate integral equation of the resistivity problem has the same form as the forward problem for potential fields, the authors analyze geoelectric data (with dipole-dipole configuration) using the wavelets belonging to the Poisson kernel semigroup. They find that the CWT analysis of the measured electric potential difference is able to identify buried bodies, defining their depth, position, and extent. Such parameters are estimated with no prior knowledge of the resistivity contrast between the bodies and the background. We consider several synthetic models, such as dikes, compact bodies, and contacts. In general, the depth and the lateral thickness of the buried bodies are estimated with good accuracy, using a diagram relating the singular point estimations to the different values of the dipole separation factor n. Thanks to the good results obtained from synthetic data, we test the method with data generated during laboratory experiments. In two laboratory-scale models, our method displays a better precision compared with smoothness-constrained least-squares inversion in identifying the exact position of the edges of a buried body. Finally, we find that combining CWT and inversion is advantageous: after constraining the inverse problem with a priori information from the CWT analysis, we obtain an improved inverse model.

Geoelectrical properties of saline permafrost soil in the Adventdalen valley of Svalbard (Norway), constrained with in-situ well data

Direct Current (DC) Resistivity and Induced Polarization (IP) response of six profiles were measured using the Gradient electrode configuration in Adventdalen, Svalbard, to characterise the near-surface stratigraphy of the soil and to account for geotechnical and environmental aspects of global warming in the arctic region. In addition, Wenner array data was collected for the selected profiles to examine its effectiveness as compared to the Gradient array, given the characteristics of the study site. Two commercial inversion software programs, Res2DINV and AarhusINV, were used for the inversion of the DC resistivity and IP data, to compare the software. Physical soil properties, including porosity, water saturation, water salinity, freezing temperature and grain size distribution, previously measured from samples retrieved from wells along the studied profiles, were integrated in this study to investigate the correlation with geoelectrical properties of the sediments inferred from the DC resistivity and IP data.Results from processing of the Wenner array DC resistivity data provided higher resolution as compared to the Gradient array data, especially from deeper parts of the models, due to its higher signal-to-noise ratio. The Wenner array data also indicated better inversion result for the IP data as distinctive anomalies were better indicated in data from Wenner array survey. The Wenner array data also provided a realistic trend for the anomalies, thanks to the symmetrical geometry of the electrodes during the survey, although at the cost of time and higher expenses. Inversion results proved that AarhusINV resolved the geometry of the subsurface layers with higher resolution compared with the Res2DINV. However, the two inversion algorithms use slightly different parameters for the processing and for presenting the results, thus only allowing qualitative comparison. Based on the interpretations of the DC resistivity and IP data, four distinctive zones were identified from the surface to the maximum depth of 26 m, consisting of (i) unfrozen active-layer-(silts and sands), with intermediate resistivity values 200–300 Ω·m; (ii) frozen soil with 3–10 m thickness and resistivity values between 2500 and 5000 Ω·m; (iii) unfrozen soil (cryopeg) with high salinity and low resistivity of 40 Ω·m; and finally (iv) clayey-unfrozen soil sediments with low resistivity ranging 10–20 Ω·m, at depths between 13 and 26 m. The IP data allowed for the delineation of a low chargeability zone near the surface and a high chargeability zone at greater depth which denote the active layer, lower parts of unfrozen soil sediments and cryopeg respectively, within the top 10 m of the subsurface.The 3D subsurface model of the study area was created based on interpretations of the DC resistivity and IP data and was constrained by the description of the subsurface stratigraphy from nearby wells, which provided detailed information about the vertical stratigraphy of the study area. In addition, a good correlation was observed between the studied physical properties of the sediments and the DC resistivity data for the intersecting profile SVAER04, as the interface between high and low resistivity data at ca. 10 m depth coincided the sedimentary formation with intermediate-fine grain size, high porosity, high water saturation and high salt content. Our findings show that joint application of the geoelectrical surveys and laboratory analysis of soil samples are an efficient complement to each other. These methods can be used as an alternative to each other to investigate larger areas where achieving high resolution data is not necessary.Our study results underline the importance of choosing the right survey design for collecting the DC resistivity and IP data. Contribution of the IP data in this study mostly concerns the shallow parts of the subsurface due to the low signal-to-noise ratio at greater depths, and frozen ground which limited the ion mobility and hence the IP response. An appropriate inversion program coupled with integration of the physical properties of the sediments, can be successfully applied to characterise the near-surface morphology of the sedimentary formations to address the geotechnical and environmental challenges related to the permafrost in the Arctic.

Integrated geophysical study in the cemetery of Marquis of Haihun

AbstractA group of Han dynasty tombs were found in a small town in central eastern China. It is difficult to infer the underground structures of the cemetery based on surface information. Geophysical methods are nonintrusive technology that can be used in archaeological excavations to provide important underground information. Multiple geophysical methods including total magnetic field (TMF), self‐potential (SP), direct‐current resistivity (DCR) and ground‐penetrating radar (GPR) were used to investigate the structure of ancient tombs. Total magnetic anomaly (TMA) and SP data can be used to obtain the projections of anomalous bodies on earth surface. DCR and GPR data can be used to gauge and further determine the spatial locations and depths of the anomalies. The results of the integrated geophysical interpretation were used to optimize the excavation plans and were verified by the subsequent works, such as coffin chambers, dromoi, ancient building foundations and funeral pit. Integrated geophysical survey can effectively reduce the uncertainly of a single method and obtain the targets more accurately.

Three-dimensional inversion of DCR data incorporating structural similarity constraint

The three-dimensional inversion of direct current resistivity data is an ill-posed problem, which should to be regularized to obtain a physically meaningful parameter distribution. This is usually realized by introducing additional stabilizing model objective functionals to the optimization problem or constraining the model parameters. The constraints may be defined relative to a reference model which prevents the divergence of parameters from the given reference model. A half-space of homogeneous resistivity, results of a previous survey (i.e. time lapse) or simply a vector of zeros may be assigned as the reference model. The reference model must be defined in accordance with the physical parameter, subject to the study (resistivity in our case). However, high-resolution geophysical images of subsurface, provided by a different method (e.g. ground penetrating radar) could also be used to define a reference model using appropriate tools. In this study, a method is proposed to carry out a three-dimensional constrained inversion of direct current resistivity data using a reference model derived from ground penetrating radar method. We have converted depth slices of radar data volume and the three-dimensional resistivity model into grayscale images to make them comparable on a common basis. An image quality assessment tool, namely the structural similarity index is used to evaluate the similarity/difference of the calculated model parameters with respect to the radar slices belonging to same depth. The method is tested on two different data sets acquired during archaeogeophysical investigations. The constrained inversion of direct current resistivity data revealed the buried anthropogenic structures more clearly, which verifies the use of the proposed methodology.

Transdimensional Markov Chain Monte Carlo joint inversion of direct current resistivity and transient electromagnetic data

SUMMARYJoint inversion of multiple geophysical data sets with complementary information content can significantly reduce the non-uniqueness inherent to each individual data set and, therefore, can improve subsurface characterization. Gradient-based joint inversion methods depend on the choice of model regularization and usually produce one single optimal model, and rely on linearization to estimate model parameter uncertainty. However, a quantitative evaluation of the parameter uncertainty of the derived model parameters is crucial for reliable data interpretation. In this study, we present a transdimensional Markov Chain Monte Carlo (MCMC) method for the joint inversion of direct current resistivity and transient electromagnetic data, which provides a rigorous assessment of the uncertainty associated with the derived model. The transdimensional property of the algorithm allows the number of unknown model parameters to be determined adaptively by the data. This usually favours models with fewer parameters through the parsimony criterion of the Bayesian method by choosing suitable prior distributions. In this paper, we demonstrate that the transdimensional MCMC method combines complementary information contained in each data set and reduces the overall uncertainty using synthetic examples. Furthermore, we successfully applied the new joint inversion scheme to field data from Azraq, Jordan. The transdimensional MCMC inversion results are in good agreement with the results obtained by deterministic inversion techniques. From the MCMC inversion results we identified the thickness of a basalt formation and a conductive zone, which were uncertain and not interpreted in prior studies, adding to the geological interpretation.

Efficient Probabilistic Joint Inversion of Direct Current Resistivity and Small-Loop Electromagnetic Data

Often, multiple geophysical measurements are sensitive to the same subsurface parameters. In this case, joint inversions are mostly preferred over two (or more) separate inversions of the geophysical data sets due to the expected reduction of the non-uniqueness in the joint inverse solution. This reduction can be quantified using Bayesian inversions. However, standard Markov chain Monte Carlo (MCMC) approaches are computationally expensive for most geophysical inverse problems. We present the Kalman ensemble generator (KEG) method as an efficient alternative to the standard MCMC inversion approaches. As proof of concept, we provide two synthetic studies of joint inversion of frequency domain electromagnetic (FDEM) and direct current (DC) resistivity data for a parameter model with vertical variation in electrical conductivity. For both studies, joint results show a considerable improvement for the joint framework over the separate inversions. This improvement consists of (1) an uncertainty reduction in the posterior probability density function and (2) an ensemble mean that is closer to the synthetic true electrical conductivities. Finally, we apply the KEG joint inversion to FDEM and DC resistivity field data. Joint field data inversions improve in the same way seen for the synthetic studies.

Geotechnical assessment of fractured limestone bedrock using DC resistivity method: a case study at New Minia City, Egypt

ABSTRACT The new urban development is an important priority in Egypt to face a rapid increase in the population during the last few decades. As a case study, the geotechnical assessment of the New Minia City is studied applying direct current (DC) resistivity technique. In the presented study, the DC resistivity data are interpreted to (i) characterize the subsurface layer distributions, (ii) deduce the subsurface structures considering the surface geological and structural setting and borehole information and (iii) predict geotechnical parameters of the bedrock based on empirical relationships. The inversion results of DC resistivity data indicate that a lens of clay is locally capping the fractured limestone in different parts of the area. The constructed geoelectrical cross-sections show that the limestone bedrock is highly fractured regarding many normal faults trending in the NW and NE directions. In an attempt to derive empirical relationships for predicting the geotechnical parameters, the inverted resistivity values of the fractured limestone were correlated with different geotechnical parameters, Rock Quality Designation (RQD) and Unconfined Compressive Strength (UCS). It is noticed that there are good correlations between the limestone resistivity values and geotechnical parameters obtained from borehole data applying linear relations. Accordingly, the results indicate that the DC resistivity method constitutes a valuable technique to introduce a preliminary geotechnical assessment for new urban areas.

Two dimensional joint inversion of direct current resistivity and radiomagnetotelluric data based on unstructured mesh

Using the unstructured mesh, a new two-dimensional joint inversion algorithm has been developed for Radiomagnetotelluric and Direct current resistivity data. The unstructured mesh is generated with triangular cells, whose vertical and lateral lengths increase towards the depths. The Finite Element Method (FEM) has been used in the forward modelling part of the developed joint inversion algorithm. In the previous studies, structured grid-based joint inversion algorithms have been developed using the Finite Difference Method (FDM). In the structured grid-based algorithms, when the mesh is being generated with rectangular cells, the vertical lengths of the cells get bigger towards the depths while the lateral lengths remain constant. With the structured mesh, the undulated surface topography cannot be represented well enough. Also, because of the incompatible aspect ratio of model cell sizes in deeper model sections, the resolution of the model parameters will get smaller and cannot be resolved well with the structured grids. Imaging of surface topography and underground resistivity structures by the new algorithm requires fewer elements than those using structured grids. Therefore, the developed algorithm is faster than traditional 2D inversion algorithms. Furthermore, the resolution of the deeper model parameters has been increased by using the definition of the unstructured grid. A regularized inversion scheme with a smoothness-constrained stabilizer has been employed to invert the data. First, we have tested the developed joint inversion algorithm using synthetic data simplified from archaeological and mine site scenario and the results have been compared with the conventional algorithms using structured grids. We have also tested our algorithm with the real data which were collected from mineral investigation site at approximately 10 km east of the Elbistan district of Kahramanmaraş province, in the west of the Taurus Mountains, Turkey. The results show that the developed joint inversion algorithm is a powerful tool to detect both resistive and conductive targets.

Characterization of the bridge pillar foundations using 3d focusing inversion of DC resistivity data

We investigated the effectiveness of a focusing regularization technique for the inversion of direct current (DC) resistivity data for a typical engineering problem. A smoothing stabilizer (Laplacian of model parameters) is generally preferred in the inversion (OCCAM's inversion) of DC resistivity data. Smooth reconstructions may be produced with this stabilizer, but some specific problems might require more focused images for adequate interpretations. For this reason, we investigated the capabilities of the minimum gradient support (MGS) stabilizer for providing shaper results. This stabilizer allows the a sharper reconstruction because its main effect is to minimize the area where strong differences occur between adjacent model parameters. We also analyze the effects of the focusing parameter, which is the parameter in the MGS expression controlling the level of sharpness of the final result. Our strategy for the selection of the optimal focusing parameter allows the resolution of distinct resistivity contrasts. Moreover, some artifacts that may arise in the use of the a very small focusing parameter disappear while using the normalized focusing parameter. We demonstrate these results by using both synthetic and field data examples. In the field data test, the subsurface image reconstructed using the proposed MGS approach matches well with the lithology inferred from borehole drillings.

A framework for petrophysically and geologically guided geophysical inversion using a dynamic Gaussian mixture model prior

SUMMARYWe propose a new framework for incorporating petrophysical and geological information into voxel-based geophysical inversion. By developing the geophysical inverse problem from a probabilistic perspective, we redesign the objective function and the iteration steps as a suite of cyclic optimization problems in which three separate MAP optimization problems are solved using geophysical, petrophysical and geological data, respectively. By quantitatively linking these data into a single framework, we recover a final inverted model that reproduces the observed, or desired, petrophysical and geological features while fitting the geophysical data. To achieve our goal we replace the Gaussian prior, used in the Tikhonov inversion approach, by a Gaussian mixture model. After each geophysical model update, the mixture parameters (means, variances and proportions) are determined by the geophysical model and the expected characteristics of the lithologies through another optimization process using the expectation–maximization algorithm. We then classify the model cells into rock units according to the petrophysical and geological information. These two additional steps over the petrophysical and geological data result in a dynamic update of the reference model and associated weights and guide the inversion towards reproducing the expected petrophysical and geological characteristics. The resulting geophysical objective function does not require extra terms to include the additional petrophysical and geological information; this is an important distinction between our work and previous frameworks that carry out joint geophysical and petrophysical data inversion. We highlight different capabilities of our methodology by inverting magnetotelluric and direct-current resistivity data in 1-D and 2-D, respectively. Finally, we apply our framework to inverting airborne frequency domain data, acquired in Australia, for the detection and characterization of saline contamination of freshwater.

Hydrogeologic Characterization of a Fault-Related Dome Using Outcrop, Borehole and Electrical Resistivity Data

Geological structures introduce heterogeneity along deformed strata, which in turn exert a strong control on regional groundwater occurrences and water flow. We developed and applied procedures of structural, borehole and direct current resistivity (DCR) data to (1) figure out a reliable structural model of a fault-related dome, (2) visualize the relationship between structural complexity and aquifers geometry and (3) characterize the fault damage zones and its related sealing potentialities. The present approach was applied at the northern Eastern Desert, Egypt, considering its complex deformation history. To alleviate the uncertainties and artifacts in solving the DCR inverse problem, advanced and non-conventional inversion schemes were applied. Moreover, fault seal potentialities were assessed by applying the shale gouge ratio (SGR) estimation to predict the groundwater pathway flow. The main findings include: (a) The DCR measurements can be considered as a complementary tool to visualize the relationship between subsurface structures and aquifers geometry at highly deformed areas; (b) detailed surface structural data analysis combined with sophisticated inversion algorithms application can increase the reliability of the constructed geo-electrical cross sections for deep and large-scale geological surveys; and (c) the structural modeling of geological units and faults distribution contributes to clarify hydrogeological settings and aquifers connectivity. The approach can be readily applied elsewhere, as long as detailed structural analysis, geometric parameters and high-resolution DCR resistivity data are available.

A user-driven feedback approach for 2D direct current resistivity inversion based on particle swarm optimization

We have developed an inversion approach based on particle swarm optimization (PSO) for 2D direct current resistivity data. Once the PSO algorithm is implemented, cost-function changes on constraints and misfit criteria can be easily performed and an approximate invariance of the Lagrange multipliers is obtained if each term of the cost function is properly normalized. More importantly, the interpreter can divide the mesh into partitions and apply a different constraint or combination of constraints in each partition. We explore several restrictions on the log-resistivity variation, either in single or in joint versions, including spatial continuity constraints in the [Formula: see text]-and [Formula: see text]-norms, total variation, sparsity constraints using the discrete cosine transform and Daubechies bases, and minimum moment of inertia constraints to impose concentration of resistive or conductive materials along target axes. In the latter case, the earth surface might be used also as a target axis. In addition, the final state of the PSO algorithm, once a stopping condition has been reached, contains not only the best solution but also a cluster of good suboptimal solutions that can be used for uncertainty analysis. As a result, the interpreter has the flexibility to perform an interpretation process based on a feedback trial-and-error inversion approach, in a similar manner that he/she has when using a friendly forward modeling software. The interpreter can then drive the tentative solutions obtained along the inversion process to incorporate their conceptions about the geologic environment, besides appraising misfit and stability of the solutions. We evaluate synthetic and field data examples. In the first case, we determine how the interpreter can drive the inversion process in a karst environment to image dissolution features. In the second case, we explore a similar situation aiming to optimize borehole locations in fracture zones in crystalline rocks.