Controlled-source Electromagnetic Method Research Articles

Discriminating seismic amplitude pitfall by low saturation gas using controlled-source electromagnetic technology

One of false positives in seismic amplitude associates with the presence of low saturation gas. The amplitude response is ambiguous prominently in shallow subsurface due to similar amplitude of fizz gas to highly saturated gas reservoir. This pitfall is demonstrated in Gassmann’s fluid substitution modelling which drastic velocity reduction is modeled by 5% of gas. The strong reduction induces anomalous bright spot in seismic similarly manifested by a highly gas reservoir. In pore fluid characterization, seismic amplitude of a brine reservoir is well distinguished from gas by change of response polarity from negative to positive amplitude due to higher brine modulus than gas. To a lesser extent, the negative amplitude of gas sand almost identical between commercial and non-commercial gas trap and difficult to distinguish in seismic. The similar negative amplitude of the gas cases caused by a very low gas modulus resulting to sudden drop of rock bulk modulus despite with the presence of low gas percentage. Thus, seismic velocity slows down when travels through a gas sand medium. Integration of controlled-source electromagnetic (CSEM) method in hydrocarbon prediction reduces exploration risk by only detecting commercial hydrocarbon. It exploits resistivity contrast between overburden and hydrocarbon reservoir which highly controlled by hydrocarbon saturation. CSEM normalized response exceeds the cut off response by a minimum saturation of 70% of gas. Less than 70% of gas, CSEM response is below the cut off response which considered as insignificant anomaly in CSEM measurement. It becomes a key strength as this method reduces amplitude uncertainty in seismic due to low saturation gas and potentially improves the chances of economic discovery in hydrocarbon exploration.

Identification of fresh submarine groundwater off the coast of San Diego, USA, using electromagnetic methods

Climate change has a pronounced effect on water resources in many semiarid climates, causing populated areas such as San Diego County (USA), to become more vulnerable to water shortages in the coming decades. To prepare for decreased water supply, San Diego County is adopting policies to decrease water use and to develop additional local sources of water. One new local source of freshwater is produced by a desalination facility that purifies brackish groundwater from the coastal San Diego Formation. This formation has been studied extensively onshore, but little is known about the geology or groundwater quality offshore in the adjacent continental shelf. Because most groundwater systems are interconnected and complex, further analysis is needed to identify offshore geology, possible sequestration of freshwater in the shelf, and potential pathways for saltwater intrusion. This comprehensive understanding is important because seawater intrusion may limit use of the San Diego Formation and longevity of desalination facilities. Controlled-source electromagnetic methods are uniquely suited to detecting offshore groundwater as they are sensitive to changes in pore fluids such as the transition from fresh to brackish groundwater. This paper describes results from surface-towed electromagnetic surveys that mapped the pore-fluid salinity and possible fluid pathways in the continental shelf off the coast of San Diego. The results indicate a considerable volume of fresh-to-brackish groundwater sequestered in the shelf, both in continuous lenses and isolated pockets, that appear influenced by fault systems and shallow stratigraphy.

Do metal infrastructure effects cancel out in time-lapse electromagnetic measurements?

Controlled-source electromagnetic methods have the potential to be used in reservoir monitoring problems due to their sensitivity to subsurface resistivity distribution. For example, time-lapse electromagnetic (EM) measurements can help to determine reservoir changes during enhanced oil recovery processes, such as water/steam injection or CO2 sequestration. Although metal infrastructure, such as pipelines and casings, can strongly influence EM data and mask the underlying geologic response, these effects have not previously been quantified for time-lapse surveys. We have analyzed the effects of well casings on time-lapse surface-to-surface EM measurements using 1D and 3D modeling. First, using a synthetic example of an onshore 1D hydrocarbon reservoir, we quantified the effect of single and multiple casings at several source and receiver locations. We found that time-lapse responses are significantly distorted when a source or receiver is located near a casing. Next, we approximated a hydrocarbon reservoir as a thin bounded resistive sheet. We developed a method of moments algorithm to calculate the respective secondary currents and charges on a well casing and resistive sheet combination and validated the electric fields these secondary sources generate against finite-element modeling. Finally, we calculated and explicitly demonstrated time-lapse amplitude changes in the well casing-thin-sheet interaction matrix, secondary currents, charges, and surface electric fields. Our 3D modeling results indicated that the conductive casing reduces the ability of the resistive sheet to impede current flow and distorts time-lapse responses. Therefore, one cannot fully eliminate casing effects by subtraction of time-lapse data and must fully incorporate such infrastructure into forward models for time-lapse EM inversion.

HPC Geophysical Electromagnetics: A Synthetic VTI Model with Complex Bathymetry

We introduce a new synthetic marine model for 3D controlled-source electromagnetic method (CSEM) surveys. The proposed model includes relevant features for the electromagnetic geophysical community such as large conductivity contrast with vertical transverse isotropy and a complex bathymetry profile. In this paper, we present the experimental setup and several 3D CSEM simulations in the presence of a resistivity unit denoting a hydrocarbon reservoir. We employ a parallel and high-order vector finite element routine to perform the CSEM simulations. By using tailored meshes, several scenarios are simulated to assess the influence of the reservoir unit presence on the electromagnetic responses. Our numerical assessment confirms that resistivity unit strongly influences the amplitude and phase of the electromagnetic measurements. We investigate the code performance for the solution of fundamental frequencies on high-performance computing architectures. Here, excellent performance ratios are obtained. Our benchmark model and its modeling results are developed under an open-source scheme that promotes easy access to data and reproducible solutions.

An Effective Algorithm for 2D Marine CSEM Modeling in Anisotropic Media Using a Wavelet Galerkin Method

The marine controlled-source electromagnetic method (MCSEM) has attracted considerable attention as an approach to explore marine oil and gas resources and geological structures. This study presents a new wavelet Galerkin method (WGM) to solve the forward modeling problem of 2D MCSEM data incorporating conductivity anisotropy. The method uses Daubechies wavelets that may be differentiated based on the need to solve the governing field equations of MCSEM. A quasi-minimal residual method was adopted by combining an incomplete LU preconditioner to solve the WGM equations. The numerical results were compared with the analytical solution and those obtained by the finite difference and element methods. The results show that the proposed WGM is superior to the finite element and difference methods in terms of computing time and memory requirements. This algorithm can be applied to solve the forward modeling problem of MCSEM. The conductivity anisotropy of the background medium affects the MCSEM response more than the reservoir anisotropy. The match between the modeled results and measured data for the simplified real model demonstrates the necessity for using the anisotropic model to interpret data. Although this study used the proposed algorithm for 2D models, it may also be used for 3D models.

2-D joint inversion of semi-airborne CSEM and LOTEM data in eastern Thuringia, Germany

SUMMARY Various electromagnetic (EM) techniques have been developed for exploring natural resources. The novel frequency-domain semi-airborne controlled source electromagnetic (semi-AEM) method takes advantages of both ground and airborne techniques. It combines ground-based high-power electrical dipole sources with large-scale and spatially densely covered magnetic fields measured via airborne receivers. The method can survey the subsurface down to approximately 1000 m and is particularly sensitive towards conductive bodies (e.g. mineralized bodies) in a more resistive host environment. However, the signal-to-noise ratio of semi-AEM is lower than that of ground-based methods such as long-offset transient electromagnetics (LOTEM), mainly due to the limited stacking time and motion-induced noise. As a result, the semi-AEM often has reduced depth of investigation in comparison to LOTEM. One solution to overcome these flaws is to analyse and interpret semi-AEM data together with information from other EM methods using a joint inversion. Since our study shows that LOTEM and semi-AEM data have complementary subsurface resolution capabilities, we present a 2-D joint inversion algorithm to simultaneously interpret frequency-domain semi-AEM data and transient electric fields using extended dipole sources. The algorithm has been applied to the field data acquired in a former mining area in eastern Thuringia, Germany. The 2-D joint inversion combines the complementary information and provides a meaningful 2-D resistivity model. Nevertheless, obvious discrepancies appear between the individual and joint inversion results. Consequent synthetic modelling studies illustrate that the discrepancies occur because of (i) differences in lateral and depth resolution between the semi-AEM and LOTEM data caused by different measuring configurations, (ii) different measured EM components and (iii) differences in the error weighting of the individual data sets. Additionally, our synthetic study suggests that more flexible land-based configurations with sparse receiver locations are possible in combination with semi-AEM without a significant loss of target resolution, which is promising for accelerating data acquisition and for survey planning and logistics, particularly when measuring in inaccessible areas.

3-D Inversion of CSEM Data With Hexahedral Mesh in the Multinary Model Space

The controlled-source electromagnetic (CSEM) method is a crucial tool for near-surface investigations and hydrocarbon exploration because of its economic benefits. Limited resolution is one of the inherent defects of the CSEM method, and to obtain high contrast results a multinary transform function was introduced to CSEM 3-D inversion. The multinary transform function was constituted by superposing several error functions, and the transform function transformed the model parameters from continuously distributed space into a semistep distributed multinary space. To deal with complex geometries, the edge-based finite element (FE) method with an irregular hexahedral grid was applied to the modeling and inverse problem. We used the Gauss-Newton optimization method to minimize the Tikhonov parametric function. The complex chessboard model and the marine CSEM model with complex geometry were used to validate the ability of the new method in improving the resolution of the CSEM method. By comparing the results of conventional, focusing, and multinary inversion methods, the effectiveness of the multinary inversion method in depicting sharp boundaries of different physical properties was proved. Additionally, the comparisons proved that multinary inversion method can, to some extent, overcome the insensitivity to low conductors of the CSEM method.

Accelerating the Frequency Domain Controlled-Source Electromagnetic Data Inversion Using Rational Krylov Subspace Algorithm

Controlled-source electromagnetic (CSEM) method is crucial for detecting and locating underground anomalies and structures. However, it is challenging to interpret the field data with multi-frequency via 3D CSEM inversion. To fully excavate and utilize the valuable information of CSEM data at different frequencies, we propose an efficient algorithm for 3D multi-frequency CSEM (MFCSEM) inversion based on rational Krylov (RK) subspace. Within the framework of our algorithm, we first use the three-term Lanczos recursion to construct the RK basis matrix quickly; thus, the fast MFCSEM forward modeling can be realized via the RK approximation. Subsequently, we present a novel cyclic projection and correction (CPC) algorithm to solve the MFCSEM adjoint forward problems. Finally, the nonlinear conjugate gradient (NLCG) method is adopted to seek a solution to this nonlinear inverse problem. We demonstrate the excellent performance of our algorithm by synthetic and field data sets. The inversion results show that our algorithm is computationally efficient, resulting in considerable speedup compared with the conventional method. Our algorithm provides a new idea that would significantly improve the efficiency of MFCSEM inversion.

Goal-Oriented 3-D Time-Domain Marine CSEM Modeling With Anisotropy and Topography

We have proposed a goal-oriented iteration algorithm with adaptive error estimation for the 3-D modeling of the time-domain marine controlled-source electromagnetic (CSEM) method. The algorithm is based on finite-element time-domain (FETD) formulations, and it updates both the time step and the mesh size in a staggered manner. With this scheme, the computational error is well suppressed, and the efficiency of the FETD simulation is guaranteed by adaptive time-stepping within each iteration. The verification results of an electric dipole radiation model and a synthetic 1-D marine CSEM model have shown that the proposed algorithm achieves a fine balance between computational accuracy and efficiency. Through numerical examples incorporated with stratum anisotropy and seafloor topography, we further conclude that both background anisotropy and topography impede the identification of submarine high-resistivity bodies with the electric field response. Contrarily, the time derivative of the magnetic field is sensitive to high-resistivity reservoirs over an extensive period of time in both anisotropic and topographic models. Based on this, we suggest that the magnetic field should be collected along with the electric field over the whole target area to reveal the anisotropic structure of submarine sediments and the existence of oil and gas reservoirs.

Sensitivity and Resolution of Controlled-Source Electromagnetic Method for Gas Hydrate Stable Zone

Natural gas hydrate is one of the most important clean energies and part of carbon cycle, due to the least carbon content. Natural gas hydrates depend on high pressure and low temperatures, located under seabed or permafrost. Small changes in temperature and pressure may lead gas hydrates to separate into water and gas, commonly as methane. As a powerful greenhouse gas, methane is much stronger than carbon dioxide. Therefore, it is necessary to detect the gas hydrates stable zone (GHSZ) before the methane gas escapes from GHSZ. Marine controlled source electromagnetic method (CSEM) is a useful tool to detect gas hydrate in offshore. The results from 3D CSEM method are a resistivity cube to describe the distribution of gas hydrates. In order to study the detectability of CSEM method, we simulate the sensitivity and resolution of marine CSEM synthetic data. By using the sensitivity and resolution, a simple statement may be quickly judged on the existence and occurrence range of the natural gas hydrate. In this paper, we compare the resolution of marine CSEM method with various transverse resistance. This information may help researchers find out whether the GHSZ exists or not.

Offshore-onshore resistivity imaging of freshwater using a controlled-source electromagnetic method: A feasibility study

Coastal freshwater provides a water source for more than one billion people living in coastal regions. For sustainable groundwater management in coastal areas, an understanding of freshwater distribution is necessary. Freshwater distribution in a coastal area can extend across the shoreline and into the offshore region. Offshore-onshore mapping of freshwater helps us to gain a comprehensive understanding of the freshwater distribution in coastal areas. Resistivity imaging using electromagnetic methods has been used to reveal the freshwater distribution in coastal areas because electrical resistivity in these settings is primarily controlled by porosity and porewater salinity. We have considered a controlled-source electromagnetic (CSEM) method for offshore-onshore resistivity imaging of freshwater at a depth range of 0–500 m below the seafloor. Our CSEM method is novel in considering an array of onshore-offshore electromagnetic receivers with onshore electric dipole transmitters. We have conducted a feasibility study to investigate the ability of the CSEM method for offshore-onshore resistivity imaging of freshwater in a coastal area. The test results indicate that the method could image the resistivity distribution of freshwater located at a depth of 500 m below the seafloor. Our model study also indicates that the offshore-onshore CSEM method can detect offshore aquifers up to 5 km from the shoreline. These numerical test results imply that our CSEM method is a promising technique for offshore-onshore resistivity imaging of freshwater in coastal areas.

Solution of large-scale 3D controlled-source electromagnetic modeling problem using efficient iterative solvers

With geophysical surveys evolving from traditional 2D to 3D models, the large volume of data adds challenges to inversion, especially when aiming to resolve complex 3D structures. An iterative forward solver for the controlled-source electromagnetic (CSEM) method requires less memory than that for a direct solver; however, it is not easy to iteratively solve an ill-conditioned linear system of equations arising from finite-element discretization of Maxwell’s equations. To solve this problem, we have developed efficient and robust iterative solvers for frequency- and time-domain CSEM modeling problems. For the frequency-domain problem, we first transform the linear system into its equivalent real-number format, and then introduce an optimal block-diagonal preconditioner. Because the condition number of the preconditioned linear equation system has an upper bound of [Formula: see text], we can achieve fast solution convergence when applying a flexible generalized minimum residual solver. Applying the block preconditioner further results in solving two smaller linear systems with the same coefficient matrix. For the time-domain problem, we first discretize the partial differential equation for the electric field in time using an unconditionally stable backward Euler scheme. We then solve the resulting linear equation system iteratively at each time step. After the spatial discretization in the frequency domain, or space-time discretization in the time domain, we exploit the conjugate-gradient solver with auxiliary-space preconditioners derived from the Hiptmair-Xu decomposition to solve these real linear systems. Finally, we check the efficiency and effectiveness of our iterative methods by simulating complex CSEM models. The most significant advantage of our approach is that the iterative solvers we adopt have almost the same accuracy and robustness as direct solvers but require much less memory, rendering them more suitable for large-scale 3D CSEM forward modeling and inversion.

Application of powerline noise cancellation method in correlation identification of controlled source electromagnetic method

Abstract Powerline interference in the controlled source electromagnetic method has traditionally been one of the biggest conundrums plaguing geophysicists, and its conventional denoising methods primarily include filtering and noise estimation. The filter method leaches noise at specific frequency points, which might also filter useful signals; the noise estimation method significantly eliminates interference, whereas the premise is that the noise is stable after a short time and a recorder is necessary in the field. In the present study, using the periodicity and symmetry of powerline noise, we propose a subtraction and an addition method for cancellation of the powerline noise. First, the transmitted signal is optimized so that the equivalent transmitted signal is an m sequence; then the response signal is processed by using the cancellation method; subsequently, the correlation identification is applied and finally, we solve the earth impulse response by means of the Wiener filter deconvolution method. Simulation experiments and field data tests demonstrate that the powerline noise can be well suppressed by the cancellation method proposed in the present study, so that the system identification accuracy is greatly improved. The method is simple in principle and effective in removing powerline noise, which presents a novel perspective on noise elimination for system identification.

A New Method To Estimate Resistivity Distribution Of Shaly Sand Reservoirs Using New Seismic Attributes

A subsurface resistivity model is important in hydrocarbon exploration primarily in the controlled-source electromagnetic (CSEM) method. CSEM forward modelling workflow uses resistivity model as the main input in feasibility studies and inversion process. The task of building a shaly sand resistivity model becomes more complex than clean sand due to the presence of a shale matrix. In this paper, a new approach is introduced to model a robust resistivity property of shaly sand reservoirs. A volume of seismic data and three wells located in the K-field of offshore Sarawak is provided for this study. Two new seismic attributes derived from seismic attenuation property called SQp and SQs are used as main inputs to predict the volume of shale, effective porosity, and water saturation before resistivity estimation. SQp attribute has a similar response to gamma-ray indicating the lithological variation and SQs attribute is identical to resistivity as an indicator to reservoir fluids. The petrophysical predictions are performed by solving the mathematical step-wise regression between the seismic multi-attributes and predicted petrophysical properties at the well locations. Subsequently, resistivity values are estimated using the Poupon-Leveaux (Indonesia) equation, an improvised model from Archie’s to derive the mathematical relationship of shaly sand’s resistivity to the volume and resistivity of clay matrix in shaly sand reservoirs. The resistivity modeled from the predicted petrophysical properties distributed consistently with sand distribution delineated from SQp attribute mainly in southeast, northeast, and west regions. The gas distribution of the net sand modeled by 5% and 90% of gas saturation scenarios also changed correspondingly to SQs attribute anomaly indicating the consistent fluid distribution between the modeled resistivity and SQs attribute.

Source modification for efficiency enhancement of marine controlled-source electromagnetic method

Abstract Controlled-source electromagnetics is a strongly efficient technique to explore deep-water marine hydrocarbon reservoirs. However, the shallow-water unsolved limitations of electromagnetic shooting methods still exist. In this regard, this work aims to alter the existing conventional electromagnetic source such that it can converge the down-going electromagnetic wave while simultaneously dispersing the up-going electromagnetic energy to minimise the airwave in shallow water. This work presents computed electric current distribution inside a modified transmitter, using a method of moments. Simulation and an experiment-based methodology are applied to this work. Finite element simulation of the response of the modified transmitter displayed the capability of the new transmitter in dispersing the airwave, by 15%. The experimental setup confirmed a better performance of the new transmitter, showing hydrocarbon delineation of up to 48%, compared to the existing conventional transmitter, with 25% oil delineation at the same depths in the same environment. Modification of the electromagnetic source to unbalance the up-down signals may have the potential to enhance the delineation magnitude of the target signal and, as a result, significantly improve oil detection capability.

A new borehole electromagnetic receiver developed for controlled-source electromagnetic methods

Abstract. Conventional surface electromagnetic methods have limitations of a shallow detection depth and low resolution. To increase the detection depth and resolution, borehole–surface electromagnetic methods for electromagnetic three-dimensional observations of the ground, tunnels, and boreholes have been developed. Current borehole receivers only measure a single parameter of the magnetic field component, which does not meet the special requirements of controlled-source electromagnetic (CSEM) methods. This study proposes a borehole electromagnetic receiver that realizes synchronous acquisition of the vertical electric field component in the borehole and the three-axis orthogonal magnetic field components. This receiver uses Ti electrodes and fluxgate magnetometers (fluxgates) as sensors to acquire electric and magnetic field components. Multi-component comprehensive observation methods that add the electric field component can effectively support the CSEM method, improve detection accuracy, and exhibit a strong potential for detecting deep ore bodies. We conducted laboratory and field experiments to verify the performance of our new borehole electromagnetic receiver. The receiver achieved a magnetic field noise of less than 6 pTHz-1/2 at 1 kHz, and the electric field noise floor was approximately 20 nVm-1Hz-1/2 at 1 kHz. The −3 dB electric field bandwidth can reach DC −10 kHz. The results of our experiments prove that high-quality CSEM signals can be obtained using this new borehole electromagnetic receiver and that the electric field component exhibits sufficient advantages for measuring the vertical component of the electric field.

The latest development of Marine controllable source electromagnetic transmitter

Marine Controlled-Source Electromagnetic (MCSEM) methods have been recognized as an important and effective tool in accurate analysis of shallow electrically resistive structures such as oil, gas and gas hydrate. However, the MCSEM performance in the deep ocean is strongly affected by the hardware design, especially the transmitter system. We have developed a series of deep-towed MCSEM transmitter systems. The design of the transmitter system meets serious challenges such as long-distance and high-voltage transmission, water sealing under high-pressure, the real-time monitoring of seafloor status information 4 km below the sea-surface. In this paper, we present the latest research and development of the MCSEM transmitter systems by presenting key technologies in hardware development and implementation details. The deep tow transmitter system consists of three parts: the deck unit, the deep tow cable and the deep tow unit, which can transmit the high frequency and high power to the seawater, maintaining a high-speed data communication with control center which in the ship’s lab. We conducted several experiments in the South China Sea from August of 2010, to November of 2019. The results showed that the development of the transmitter is successful and it can be used for oil, gas and gas hydrate exploration as an effective source.

Theoretical and Methodological Substantiation of Transient Electromagnetic Sounding from the Arctic Drift Ice

Abstract —Marine geoelectromagnetic sounding with artificial sources is strongly hindered by the influence of a conductive seawater layer. There is only one known wide successful application of electrical prospecting in this field – Controlled Source Electromagnetic Method (CSEM). However, this method has unfortunate limitations: the need to submerge an electromagnetic probe to the bottom of a deep (more than 1000 m) sea and the great rafting (~15 km). The method is not applicable in an ice-covered sea. Deep sounding from the sea surface and, hence, from the ice surface is possible if the TM polarization field is used. This field is generated by a vertical electric line (VEL) or a circular electric dipole (CED). The former has drawbacks even when it is used at sea. At the same time, a CED is efficient in one-dimensional and three-dimensional media in frequency and time modes. We have developed a three-dimensional mathematical tool for the CED field in the Born approximation, which is quite adequate in a conductive section with deep local inhomogeneities. The research is carried out within the framework of a geophysical project using the Arctic drift ices.

Time-lapse CSEM: how important is survey repeatability?

SUMMARYAn important concern for time-lapse studies using the controlled-source electromagnetic (CSEM) method is repeatability of acquisition parameters for the base and monitoring surveys. We consider a challenging case when variations in source and receiver positions, conductivity of seawater, etc. will lead to differences in the recorded EM fields that exceed EM response due to production-induced changes in the reservoir resistivity. We show that even in that case, 4-D response can often be clearly resolved if the base and monitor EM data sets are inverted to produce 3-D resistivity distributions. More precisely, for a synthetic model of the Snøhvit gas field, changes in the inverted resistivity maps caused by such non-repeatability will be at least 10 times smaller than the time-lapse differences in the reservoir resistivity. By contrast, measurement errors and poor knowledge of background resistivity may reduce the resolution of 4-D CSEM to a much stronger degree. Analysis of field CSEM data from the Wisting oil field supports our conclusion about strongly relaxed repeatability requirements when 4-D effects are established by examining inverted resistivity volumes rather than by looking at raw EM data.

Fast forward modeling of the 3D land controlled-source electromagnetic method based on model reduction

The main bottleneck of fast forward modeling of 3-D land controlled-source electromagnetics based on the finite element method lies in solving multi-frequency large-scale sparse equations.In this paper,a Krylov subspace projection algorithm based on model reduction is introduced,a model reduction form of the finite element stiffness matrix is derived,and a frequency domain transfer function is constructed.A standard orthogonal vector sequence is used to construct a matrix that is much smaller than the finite element stiffness matrix,which is unrelated to frequency.Through model reduction,it is possible to quickly solve these multiple frequency finite element equations.The variational equation based on the electric field is used,and divergence correction conditions are added to eliminate spurious solutions.The pseudo-delta function is introduced to eliminate the singularity of the source point,which can be applied to 3D finite element numerical simulation of complex models.Such an algorithm may be regarded as the basic principle for a solution to the problem of multiple sources.Using the analytical solution of the layered medium model as the standard,comparison shows that the averaged percentage computing error of the proposed method is 1.72%.Compared with the 3DFEM algorithm using the Pardiso direct solver,the CPU time consumption of the proposed method is reduced by 1/10 of the original one.Therefore,with a required accuracy,it is possible to achieve highly efficient 3-D finite element numerical solutions.In the numerical simulation,with the horizontal and vertical high-low resistance models,we analyze the changes of the electric field and the Cagniard apparent resistivity from the near to the far region,the performance characteristics of false extremes,and the effects of shadow effects,which verify the correctness of the proposed algorithm.Finally,we apply the proposed algorithm to simulation of a stratum collapse column model.The results show that the apparent resistivity cross section looks like a“sag”above the collapse column,which is consistent with the model design,and further indicates that the proposed algorithm can be applied to real complex geoelectric structure.