Direct Current Resistivity Method Research Articles

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.

Groundwater Protection Assessment using Frequency Domain Electromagnetic Method and Direct Current Electrical Resistivity Method in Papalanto South-West Nigeria

The aim of this work is to assess the extent of protection of the subsurface hydrogeological structures. Fieldworks were performed integrated geophysical techniques namely Frequency Domain Electromagnetic Method (FDEM) using Geonics-EM-34 to determine the vertical and lateral variations of subsurface conductivity probing depths of 20m, 40m and 60m, while subsurface profiles were obtained using Direct Current Resistivity (DCRE) with AGI Super-sting Earth Resistivity meter; current electrode spacing (AB) ranging from 1 to maximum of 100m and the potential electrodes (MN) were consequently changed from 0.25m to 5m respectively. 1141.92 mmho/m was recorded as the highest true conductivity value for the Horizontal Dipole in the second layer (Profile EMPAP5) while the highest true conductivity value for the Vertical Dipole in the first layer was 134.31 mmho/m (Profile EMPAP1). Four principal geoelectric layers inferred from the VES data where the Topsoil is partly lateritic and alluvium, Sandy Clay/Clay/Silt, Sand/Clay/Shale, and Limestone/Sandstone. Resistivity values for these layers vary from 9.78 to 1428, 1.46 to 1057, 1.46 to 451, and 15 to 10,000 Ω m with corresponding thickness of 0.5m to1.43m, 1.29m to 13m, 2.8m to 84.4m and infinity, respectively. The higher resistivity values at the surface and extremes of both edges were indication of little or no presence of leachates or contaminant plume accumulation in other area. Also, there was a noticeable general decrease of resistivity values of formation rock with depth in these investigated areas; this is an indication that the plumes must have infiltrated rapidly into the subsurface through the massive presence of weathered rock materials of average lateral distances of 15m to 167m of considerable depth and thickness of about 24.9m. The degree of leachate contamination range from 0.0007264 mho to 0.668 mho with the highest value in VESPAP2 followed by VESPAP13 and VESPAP19 while VESPAP22 exhibited the lowest conductance.

Research on numerical simulation method for 3D marine direct current resistivity

As one of the most important methods in marine electromagnetic exploration, the marine direct current (DC) resistivity method has been widely used in the exploration of marine minerals, oil and gas, as well as in large-scale engineered geological exploration and other fields. Efficient and high-precision forward algorithms are the foundation for an accurate quantitative interpretation of the marine DC resistivity method. We have implemented an efficient and high-precision forward modeling approach for 3D marine DC resistivity. First, the wave number domain anomalous potential control equations are obtained by performing a 2D Fourier transform along the horizontal direction based on the differential control equations satisfied by the marine DC anomalous potential. Instead of directly solving the 3D numerical simulation problem, we transform the 3D numerical simulation problem into multiple 1D numerical simulation problems in the wavenumber domain by dimensionality reduction for computational efficiency. Second, the boundary conditions of the governing equations are given to obtain the corresponding boundary value problems, and the anomalous potential is solved using the 1D finite element method in the wavenumber domain. Next, we perform a 2D inverse Fourier transform on the wave-number domain anomalous potential to obtain the spatial domain anomalous potential. Furthermore, compact operators are used to iteratively modify the potential and obtain high-precision numerical solutions. Finally, we demonstrate the correctness of the proposed algorithm’s solution strategy by using a hierarchical ocean model, and the efficiency of the proposed algorithm by using a spherical model.

Estimation of Depth to Water Table within a Tropical University Campus Using Direct Current Resistivity Method

Ensuring access to clean and potable water is a global challenge, especially in regions like Nigeria where it is a pressing concern. Understanding the hydrogeological conditions, particularly the depth of the water table, is crucial for sustainable water resource management. In this study, we employed the direct current (DC) resistivity method to investigate the depth of the water table at the University of Calabar, Nigeria. Our approach involved measuring the electrical resistivity of subsurface materials to delineate the water table depth. The DC resistivity method emerged as a reliable and efficient tool for estimating the water table depth in our study area. By constructing a resistivity profile of the university campus, we uncovered valuable information about the subsurface hydrogeological conditions. Utilizing a multi-electrode resistivity system, we collected data at various depths and locations within the campus. These measurements were then processed using inversion techniques to produce a 2D resistivity image of the subsurface. This image revealed intriguing variations in subsurface resistivity, indicative of changes in composition and saturation of underground materials. Most importantly, our findings shed light on the depth of the water table, which ranged between 5.5m and 34.5m below the mean sea level. This information not only enhances our understanding of the University of Calabar’s hydrogeology but also contributes to broader efforts in sustainable water management and development strategies.

Groundwater Potential Evaluation and Aquifer Characterization using Direct Current Resistivity Method in Wasinmi South-West Nigeria

The effectiveness in near-surface characterization makes geoelectrical resistivity techniques viable for groundwater exploration, geotechnical studies and environmental investigations. Geo-electric soundings were carried out in 25 different locations in Wasinmi, South-West Nigeria to acquire aquifer properties required for groundwater production of the study area using Direct Current Resistivity (DCRE) of Vertical Electrical Sounding (VES) utilizing AGI Super-sting Earth Resistivity meter with schlumberger configuration; current electrode spacing (AB) ranging from 1 to maximum of 100 m and the potential electrodes (MN) were consequently changed from 0.25 m to 5 m respectively. The simulated results of the 25 VES points reveal the presence of 3 to 4 geo-electric layers. The top layer comprises clay, sand, siltstone intercalations. Layers underneath the top soil are the Lithified Laterite, Clayey Sand, Clay/Shale, Sandy Clay and Limestone/Sandstone, Saturated, Sandstone Aquifer. The area is also characterized with relatively high depth to sandstone aquifer which varies from 20 m to 69.1 m. This can be attributed to the thick water saturated Shale/Clay and Clayey Sand in the area. However, at the extreme of North-Western part of the study area, depths to aquifer are far lower, with VES location VESWAS15 having a thickness of about 14.4 m. Aquifer thickness in the study area varied from 14.4m to 63.5m. VESWAS19 has the highest aquifer resistivity value (2473 Ωm) in the study area, with depth to aquifer of 69.1 m. The transmissivity varies between 0.17695×/s in VESWAS4 to 8.97654×/s in VESWAS13. This study further shows that aquifer resistivity values vary from 284 Ωm to 2473 Ωm with a range of 2189 with the resistivity values suggesting lithology in the suite of Sandy Clay, Sandstone and Karst Limestone found to be widespread in the study area with mean aquifer thickness value of 32.25 m and a variance of 124.63 m...

Fictitious Point Technique Based on Finite-Difference Method for 2.5D Direct-Current Resistivity Forward Problem

With the widespread application of the direct-current resistivity method, searching for accurate and fast-forward algorithms has become the focus of research for geophysicists and engineers. Three-dimensional forward modeling can be the best way to identify geo-electrical anomalies but are hampered by computational limitations because of the large amount of data. A practical compromise, or even alternative, is represented by 2.5D modeling characterized using a 3D source in a 2D medium. Thus, we develop a 2.5D direct-current resistivity forward modeling algorithm. The algorithm incorporates the finite-difference approximation and fictitious point technique that can improve the efficiency and accuracy of numerical simulation. Firstly, from the boundary value problem of the electric potential generated by the point source, the discrete expressions of the governing equation are derived from the finite-difference approach. The numerical solutions of the discrete electric potential are calculated after the approximate treatment of the boundary conditions with a finite-difference method based on a fictitious point scheme. Secondly, through the simulation of a homogeneous half-space model and a one-dimensional model, and compared with the analytical results, the correctness and stability of the finite-difference forward algorithm are verified. Lastly, through the numerical simulation for a two-dimensional model, 2.5D direct-current sounding responses are summarized, which can provide a qualitative interpretation of field data.

The Comprehensive Detection Technology for Embankment Leakage

Based on the study of geophysical characteristics of embankment leakage, this paper adopts Dual coil transient electromagnetic (Dual TEM) and parallel direct current resistivity method(PDC) to carry out comprehensive detection. Dual TEM can greatly reduce the shallow blind area of conventional transient electromagnetic and improve the resolution of induced signal, PDC method can efficiently collect signals of all electrical arrange and spontaneous potential signals, By using the cross-correlation processing technology between spontaneous potential and resistivity data. we quickly eliminate the false abnormal influence of low resistivity in embankment, it is a good application in the detection of Paihe embankment leakage in Hefei, Anhui Province in 2020.

Seepage identification of Sidoarjo mud embankment via 2D resistivity and self-potential methods

Assessment of embankment stability is one of the ways to discover the embankment condition. Several factors can affect the strength of the embankment body including seepage, leakage, deformation (vertical and horizontal), and overtopping. Hence, identification of seepage in the subsurface of the embankment is important to provide early information about the threat of embankment failures. Sidoarjo mud (LUSI) embankment has been collapsed several times since it built in 2006. Most of the failures are mainly caused by the existing water seepage in the subsurface of the embankment. To identify the seepage pathways of the embankment body, two non-destructive geo-electricity methods were applied in the LUSI embankment. Direct current resistivity (DCR) and self-potential (SP) methods were carried out to reconstruct subsurface conditions at lines P76-P79. Therefore, seepage interpretation was conducted to identify the presence of water flows through the embankment body. 2D tomography of resistivity data revealed the indication of water seepage in some measurement areas. This information was strengthened by the numerical interpretation of self-potential data, recognizing water seepage through the embankment body in each line.

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.

A feasibility study on time-lapse transient electromagnetics for monitoring groundwater dynamics

Time-lapse geophysical studies have been used as noninvasive tools to study subsurface processes. However, compared to direct current resistivity methods, the transient electromagnetic (TEM) method has not been explored in much detail for time-lapse investigations. Here, we introduce the use of a monitoring TEM (mTEM) system and methodology for long-term groundwater monitoring purposes. The system can run measurements automatically and the modeling approach uses a time-constrained inversion (TCI) scheme based on an existing laterally constrained inversion scheme. Instead of lateral constraints that traditionally ensure lateral coherency between measurements, temporal constraints are used to control the temporal coherency between measurements. Synthetic analysis demonstrates that very tight time constraints on resistivities and a time constraint on the depth to the water table fixed at a fraction of the expected annual water table variation is needed to track water table changes at the decimeter level. Furthermore, the synthetic analysis indicates that the mTEM method can track annual variations in the water table with amplitudes as low as 0.6 m with a mean absolute error of 0.2 at depths between 16 m and 30 m. A field example consisting of 233 1D TEM measurements acquired over 10 months using the mTEM instrument supports the synthetic results. The estimated water table depth from the TCI scheme reproduces the variation in the water table accurately, as confirmed by measurements from a water level data logger in a nearby well. The differences between the results from the TEM monitoring system and the diver measurements are in the range of ±0.1 m with an average absolute difference of 0.05 m. This study demonstrates the potential to monitor changes in the groundwater level noninvasively.

3-D forward modelling for DC resistivity method based on smooth multiscale finite-element algorithm

SUMMARY When the conventional finite-element method is used to simulate the 3-D direct-current (DC) resistivity response over a conductive earth with large complex structures, it requires finely discretized mesh to accurately represent the underground structures. Directly solving the current-conduction problem on the fine mesh will lead to a huge amount of calculation. In this paper, we develop a fast 3-D forward modelling method for DC resistivity method based on smooth multiscale finite-element algorithm. Instead of using the conventional polynomial basis functions, we construct the multiscale basis functions by solving the local boundary-value problems of partial differential equation in parallel on the multiscale meshes. The multiscale basis functions can capture the small-scale heterogeneous information in coarse cells and reflect it to the large scale by assembling macro matrix of coarse mesh. Thus, it enables us to quickly obtain the accurate solution by solving the original current-conduction problem with complex structures on coarse mesh. We further adopt the oversampling technology to improve the forward modelling accuracy. Besides, by combining with the gradient smoothing technology, we avoid establishing the continuous form of multiscale basis functions and their spatial derivative integral operation to rapidly assemble the macro matrix. Finally, the reliability of the proposed algorithm is verified by applying our code to the 3-D complex models and comparing it with the conventional finite-element method.

Combined Application of Hydrogeological and Geoelectrical Study in Groundwater Exploration in Karst-Granite Areas, Jiangxi Province

Drinking water shortage is a major concern in villages across southern Jiangxi, and this has impacted economic and social development. In order to address this challenge, groundwater prospecting was carried out in the villages under the support of Drinking Water Safety Project of China Geological Survey. In this study, we present two example sites in Ningdu County selected to demonstrate the combined hydrogeological survey, and the direct current electrical resistivity method was utilized for the present study for groundwater exploration in karst-granite distribution areas. First, a hydrogeological study was effectively used to delineate shallow severely weathered structural fissures as prospective target water-bearing beds. Then, a direct current electrical resistivity survey was used to confirm the distribution, thickness scale, and water-bearing features. The structural fractured zone whose distribution and trend were first established through hydrogeological surveys and whose development characteristics and water-richness were investigated by the direct current electrical resistivity method is the target layer for water exploration in the karst-granite rock areas. The water-bearing fracture zone shows a groove or strip-shape low resistivity anomaly and can be identified in its aquifer position according to its IP half decay time (Th), apparent polarizability (ηs), and apparent resistivity (ρs). The findings demonstrate that the above methods were successful in locating water potential areas, providing information for comparison and accurate borehole positioning. The results of the subsequent drilling and pumping tests supported the interpretation of the geophysical exploration data, and the water output from both boreholes met the objectives of this study. This groundwater search might serve as a guide for future exploration projects in similar areas.

Residual NAPL Morphology Effects on Electrical Resistivity: Insights From Micromodel Displacement Experiments and Pore Network Simulations

AbstractCharacterizing residual non‐aqueous phase liquids (NAPLs) in porous media is essential for designing contaminated site remediation strategies. The direct current resistivity method is increasingly being used at sites contaminated by NAPLs, which uses the Archie's second law to connect NAPL saturation with the resistivity of porous media. A power‐law relationship connecting the phase morphology measured by Euler characteristic with resistivity has also been observed at the pore‐scale. Because these relationships are limited for porous media with specific wettability, previous research works have demonstrated deviations from Archie's second law in both the laboratory and field experiments. To evaluate the effects of residual NAPL morphology with different wettability on bulk resistivity, we developed two 2D‐micromodels and measured their electrical resistivity and phase morphology during phase displacement under laboratory‐controlled conditions. Furthermore, pore network simulations of a variety of conditions were performed in absence of surface conduction. Results show that NAPL distributed in dead ends of the pore space has limited influence on bulk resistivity since they do not control the current path and voltage distribution. The correlations between resistivity index and Euler characteristic are determined by NAPL ganglia size and pore throat width. A power‐law relationship is found between the Archie's saturation exponent and the average size of the residual NAPL ganglia, indicating that this exponent can be interpreted as the rate of change of the pore water connectivity with saturation. These insights provide a physical framework connecting the morphology and wettability of the NAPL ganglia with the Archie's saturation exponent.

Detection of shallow and deep conductive zones using direct current resistivity and time-domain electromagnetic methods, west El-Minia, Egypt

Direct current (DC) resistivity and time-domain electromagnetic (TEM) methods were used to distinguish between saturated and dry zones and in an evaluation of groundwater resources in the western desert of Egypt. DC-resistivity method was used to evaluate the shallow section while TEM method was used for the shallow and deep aquifer sections. In the decay (voltage) curves, the last parts of the early stage and the intermediate stage refer to the shallow aquifer while the late stage indicates the deep aquifer. The effect of ramp-off time was studied. The shallow unrecorded depths of the high current diffusion speed and first and last diffusion depths were determined. The resistivity and thickness of surface deposits and loop side length are the prime influences on diffusion, investigation, and shallow unrecorded depths. By combining the two methods, the subsurface layers were classified into eight conductive and resistive zones. The third (15-75.5 O m), sixth (55-124 O m), and seventh (35-54 O m) are high conductively zones that corresponds to the shallow and deep aquifers, respectively. The TEM method delineated the sedimentary basin and the maximum penetration depth was ∼1300 m. The complementary of two methods confirmed that the resistivity method is sensitive to shallow conductive and resistive zones while the TEM method is sensitive to shallow and deep conductive and resistive zones. The TEM method assisted in identifying the shallow unrecorded depths, the effect of ramp-off time, diffusion depths, and the effect of shallow resistive depths on diffusion depths.

Geophysical Analyses on the Geomechanical Characteristics of the Soil for Choices of the Drilling Rig, in the Area of Târgu Ocna, Bacău County, Romania

Abstract As part of the company Geoscan Service S.R.L., I was contacted to investigate the possibility of using resistivity, refraction seismic data and MASW seismic to identify the stratification up to 15m deep so that the client could choose the type of drilling rig for installing the conductor in order to drill two water injection wells. The main problem in the choice of geophysical methods was the lack of detailed geological data for calibrating the obtained results, as the presence of groundwater, the thicknesses of the deluvial layer and the bedrock. The choice of geophysical methods and the work procedure are carried out according to the international standards in force, ASTM D6429-99 “Standard guide for Selecting Surface Geophysical Methods”, ASTM D5777-00 “Standard guide for Using the Seismic Refraction Method for Subsurface Investigation, “Standard Guide for Using the Direct Current Resistivity Method for Subsurface Site Characterization”, STAS 1242/7-84 “Geophysical research of the land by seismic methods”.

Saturation sensitivity and influencing factors of marine DC resistivity inversion to submarine gas hydrate

The submarine gas hydrate usually exists in the sediment on the continental slope. The bottom simulating reflector on the reflected seismic was identified as the bottom of the hydrate stability zone. However, many BSRs may not find the hydrate’s effective storage and its underlying free gas in many places. It is essential to identify the saturation of the hydrate. The resistivity can be used to evaluate the hydrate’s porosity and saturation. The hydrate boasts a high resistance to the surrounding sediments. The sensitivity of the marine Direct Current resistivity method (DCR) to the high resistance of the sediment can be used to evaluate the saturation of the hydrate. We have assessed the sensitivity of various DCR array arrangements, towed depths, hydrate thicknesses, and saturation. These influencing factors for improving recognition ability were also systematically analyzed. We have compared the inversion results of various DCR array arrangements, as well as different depths, thicknesses, and hydrate saturation, and calculated the saturation. We suggest using the corrected saturation equation to analyze the DCR results, which can improve the ability of hydrate identification. Evaluating these parameters will help develop or select DCR instruments for detecting the submarine gas hydrate.

A new method of 3D direct current resistivity modelling using a long electrode source for forward probing in tunnels

ABSTRACTThe direct current resistivity method has been widely used for the prediction of water‐bearing structures in subway tunnels and mine tunnels. The traditional direct current resistivity uses point electrode sources in tunnels to excite the electric field; potential electrodes are arranged on the back of the tunnel face to measure the position of the anomaly using the apparent resistivity sounding curve. Due to the dimension limitations of the tunnel cavity, the maximum distance of potential electrodes is often restricted. Thus, the exploration depth often cannot cover the target appropriately. Additionally, owing to the inaccessibility of point electrode sources on the tunnel face, point electrode sources can only be set near the tunnel face, so the electric signal excited by point electrode sources cannot be coupled with the water‐bearing anomaly at a large depth. As such the traditional point electrode method for forward probing in tunnels has a shortcoming of small detection depth. To overcome this problem by increasing the detection depth, a horizontal drilling copper casing is first used as a new long electrode source array, which (as far as the authors are aware) has never been reported in forward probing in tunnels. We developed a new method of 3D direct current resistivity modelling with a long electrode source for forward probing in tunnels using the finite‐element method. The long electrode current source was used to replace the conventional point electrode current source, and the observed potential electrodes were respectively arranged in the tunnel floor, tunnel face and horizontal drilling. Theoretical formulas for the long electrode source for the whole‐space direct current method are first applied in forward probing in tunnels. An analytical test for a whole‐space model with the long electrode source has been used to validate the accuracy of the 3D algorithm. Three synthetic geological models for the long electrode source were used to examine the applicability by investigating the detection capability to predict the anomaly. The observed signal of apparent resistivity excited by the long electrode source is stronger than that of the point electrode source because the long electrode source is closer to the anomaly. This new method using the long electrode source greatly improves the resolution of the anomaly, which is of great significance for the safety of the tunnel construction.

Groundwater Detection Using the Pseudo-3D Resistivity Method: A History of Case Studies

With the rapid growth of the economy and population, the desire to use groundwater supplies is increasing. In order to detect groundwater, conducting a geophysics survey is a common way to map the subsurface. This method can describe the subsurface’s physical properties. For example, the direct current (DC) resistivity method provides a resistivity map of the subsurface, in which the groundwater is normally located in low resistivity anomaly zones. However, the DC method needs to overcome the challenges of the urban environment, with its infrastructure and background noise. In this paper, we propose a pseudo-3D resistivity surveying method to solve these problems, and it is applied to situations of groundwater detection within the city environment, dam leakage, and drinking water. From the pseudo-3D resistivity surveying, we detected the low-resistivity anomaly in the area, which is interpreted as groundwater through borehole verification.

Three-dimensional numerical modeling of direct current resistivity methods in mixed space-wavenumber domain

At present, in order to obtain highly accurate solution for complex (geo-electric) conditions, it is necessary to divide the model precisely in the numerical modeling of DC resistivity method, which results in greatly increases the amount of computation and memory. To solve this problem, we propose a 3D numerical simulation method in a mixed space-wavenumber domain. The method transforms the partial differential equation of DC abnormal potential into many independent 1D differential equations with different wavenumbers by performing a 2D Fourier transform along the horizontal direction. It decomposes a large-scale 3D numerical modeling problem into many 1D numerical modeling problems, which greatly reduces the computation and memory requirements of modeling, and each 1D differential equation is independent, so it has high parallelism. The vertical direction is reserved as the spatial domain, which is convenient for the subdivision, taking into account the calculation accuracy and efficiency. A finite-element algorithm combined with a chasing method is used to solve the 1D differential equations with different wavenumbers, and a contraction operator based on electromagnetic integral equation method is used to the iteration of the algorithm for the first time. Taking full advantage of the rapidity of Fourier transform, the high efficiency of solving 1D differential equations and the high parallelism of 1D problems with different wavenumbers, it can greatly reduce the amount of calculation and storage, thus greatly improves the efficiency of the algorithm. The accuracy and convergence of the algorithm are verified by using the model of a sphere in half space. Based on the model with five cubes in half space, the efficiency of the algorithm is verified by comparing with the academic Gimli package based on the finite element method. In addition, a parallel algorithm based on OpenMP is used to verify the parallelism of the proposed algorithm. The examples results show that, the 3D numerical modeling method of DC resistivity in the mixed space-wavenumber domain has the characteristics of high efficiency, high precision and highly parallel. This method provides a new way for 3D numerical simulation of DC resistivity method.

Prediction of Conductive Anomalies Ahead of the Tunnel by the 3D-Resitivity Forward Modeling in the Whole Space

Water inrush in tunneling poses serious harm to safe construction, causing economic losses and casualties. The prediction of water hazards before tunnel excavations becomes an urgent task for governments or enterprises to ensure security. The three-dimensional (3D) direct current (DC) resistivity method is widely used in the forward-probing of tunnels because of its low cost and highly sensitive response to water-bearing structures. However, the different sizes of the tunnel will distort the distribution of the potential field, which causes an inaccurate prediction of water-bearing structures in front of the tunnels. Some studies have pointed out that the tunnel effect must be considered in the quantitative interpretation of the data. However, there is rarely a predicted model considering the tunnel effect to be reported in geophysical literature. We developed a predicted model algorithm by considering the tunnel effect for forward-probing in tunnels. The algorithm is proven to be feasible using a slab analytic model. By simulating a large number of models with different tunnel sizes, we propose an equation, which considers the tunnel effect and can predict the water-bearing structures ahead of the tunnel face. The Monte Carlo method is used to evaluate the quality of the predicted model by simulating and comparing 10,000 random models. The results show that the proposed method is accurate to forecast the water-rich structures with small errors.