Finite-element Forward Modeling Research Articles

Three-dimensional finite-memory quasi-Newton inversion of the magnetotelluric based on unstructured grids

Abstract Simulation optimization of complex geological bodies is a necessary means to improve inversion accuracy and computational efficiency; thus, inversion of magnetotelluric (MT) based on unstructured grids has become a research hotspot in recent years. This article realizes the three-dimensional (3D) finite element forward modeling of MT based on the magnetic vector potential-electric scalar potential method, using unstructured grids as the forward modeling grid, which improves computational efficiency. The inversion uses the limited-memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) method, and in the process of calculating the objective function gradient, the quasi-forward method is used to avoid solving the Jacobian matrix, which has the advantages of requiring small storage space and fast computational efficiency. Finally, the 3D LBFGS inversion algorithm of MT based on unstructured grids was realized, and the inversion studies of classic and complex models verified the effectiveness and the reliability of the algorithm proposed in this article.

Fast iterative solver for 3D finite-element modeling of controlled-source electromagnetic responses with vector and scalar potentials

The controlled-source electromagnetic (CSEM) forward modeling with vector and scalar potentials could provide insights into the inductive and galvanic effects. We have developed a finite-element (FE) forward modeling algorithm for the CSEM with vector and scalar potentials. The first-order vector and nodal shape functions are used for the vector and scalar potentials, respectively. To mitigate the null space and thus the nonuniqueness of the potentials caused by the curl operator, we introduce a new preconditioner constructed from an incomplete Cholesky decomposition with zero fill-ins of the Laplacian approximation to the resulted matrix after the FE discretization. We implemented a preconditioned quasiminimal residual method to iteratively solve the resulting linear system with the new preconditioner. We first verified the accuracy of the algorithm through comparison against the analytic solutions obtained for a three-layered earth model. The new iterative modeling algorithm converges much faster compared with the modeling algorithm with the preconditioner constructed from the original stiffness matrix. The efficiency and accuracy are further illustrated by comparison with the modeling scheme based on coupled potentials with explicit enforcement of the Coulomb gauge condition for the vector potential by modeling three 3D models. In addition, the accuracy of our algorithm is demonstrated via a comparison of our numerical solution for a 3D model with the numerical solution obtained from the integral equation method. We also present the inductive and galvanic components of the horizontal secondary electric field for numerical solutions obtained with direct and iterative solvers. The numerical test demonstrated that, aside from the efficiency improved with the new iterative solver, the unstable and nonuniqueness problem for the potentials is eliminated by the new preconditioner with the Laplacian approximation involved.

A Study on Magnetotelluric Characteristics of Magmatic Geothermal Systems

The Magnetotelluric (MT) method is a widely used and effective method of exploring geothermal resources because it can reveal geological information at a great depth and is cost effective. In order to further improve the reliability and rationality of MT data interpretation, MT responses for a typical hydrothermal system and a hot dry rock (HDR) and partial melting system are investigated by a finite-element (FE) forward modeling approach based on unstructured tetrahedral grids that can handle with complex-shaped geothermal systems. These two geothermal models, designed by the 3ds Max software, are comprised of a clay cap, a reservoir, and a heat source, and are discretized into tetrahedral elements by TetGen software. The results show that the apparent resistivities at the broadband of frequencies are mainly affected by the shallow low-resistivity clay cap due to its strong shielding effects, and the induction arrows effectively reflect the boundary of the clay cap. The conductive heat-conducting path and heat source (1 S/m) considered in the models of the HDR and partial melting system could cause significant changes in the apparent resistivities and induction arrows at low frequencies. It suggests that in addition to the apparent resistivities, the induction arrows should be taken into consideration in MT data processing and inversion for better lateral resolution when exploring geothermal resources.

Application of electrical resistivity tomography (ERT) in uranium mining earth dam

Abstract Dams are built to contain water or mining tailings and provide several benefits to society. The safety and stability of these structures are essential since eventual accidents can generate catastrophic damage. The main cause of ruptures is associated with abnormal seepage, which can progress to an internal erosion process. To assess the stability and safety of dams, periodic inspections are carried out, which typically include visual inspections and geotechnical instrumentation. Some geophysical methods have the potential to assist conventional geotechnical instrumentation using non-destructive and rapid acquisition investigations. The present study applied a finite element forward modeling to evaluate the percolation conditions and water stability in an earth dam of a decommissioned uranium mine in Brazil. The dam is the final structure of the contention system of mine water treatment. The electrical resistivity data were acquired using electrical resistivity tomography (ERT) and Schlumberger array. The results were presented from the inversion of data in 3D models. The data were processed by open-source software (modeling and inversion of geophysical data). The results indicate the presence of water in the vertical filter located in the crest area. The different levels of investigation indicated water infiltration in the rock mass of the dam foundation. These results are supported by structural surveys carried out in the area that indicate a fracturing pattern in the rock mass of the mine area. The results of the study were satisfactory for the desired purposes and demonstrate that geophysical methods constitute an important complementary tool for the geotechnical monitoring dams.

A Fast Globally Convergent Particle Swarm Optimization for Defect Profile Inversion Using MFL Detector

For the problem of defect inversion in magnetic flux leakage technology, a fast, globally convergent particle swarm optimization algorithm based on the finite-element forward model is introduced as an inverse iterative algorithm in this paper. Two aspects of the traditional particle swarm optimization algorithm have been improved: self-adaptive inertia weight and speed updating strategy. For the inertia weight, it can be adaptively adjusted according to the particle position. The speed update strategy mainly uses the best experience positions of other particles in a randomly selected population to realize the algorithm’s learning. At the same time, the learning factor of the position variable is designed to change with the number of iteration steps. The particle with a good position is added to jump out of the local minimum and accelerate the optimization process. Through the comparison experiment, the improved particle swarm optimization algorithm has a faster convergence speed compared with other traditional particle swarm optimization algorithms. It is more difficult for it to fall into the local minimum value and it is more easily converted to a higher precision.

Comparison of terrain corrections based on the point source and line source DC methods

In the direct current (DC) exploration method, topographic relief distorts the apparent resistivity curve. To eliminate effects of terrain fluctuations, two undulating terrains comprising valleys and ridges were investigated in the present study. An unstructured triangular mesh method in which the wave number k and its coefficient g were obtained using the integral method and the point and line source surveys were conducted using comsol multiphysics. Current sources were evaluated using two-dimensional (2-D) finite element forward modeling, whereas terrain correction was performed using both the comparison and conformal transformation methods. The results reveal comparable theoretical curves for the line and point sources, but quantitative characteristics of the curves differ. The comparison method is suitable for both curves, whereas the conformal transformation method is only applicable to the line source. Even though electric fields associated with the line and point sources differ, the comparison method that is based on the electrical cross-section curve of the line source and the electric profile curve of the point source remains effective.

Calibration of a Finite Element Forward Model in Eddy Current Inspection

We report on the use of a novel constrained optimisation algorithm for calibrating the finite element model in an eddy current inspection application. An accurate finite element forward model is often important in such eddy current applications for training neural networks or as part of an iterative solver. However, the subject of calibration of the model has not received much attention in the literature to date. We consider a multi-frequency, eddy current depth profiling application, which is important for non-destructive testing in the nuclear industry. In the optimisation algorithm, we use a Levenberg-Marquardt algorithm and a bisection search to ensure constraints are satisfied, coupled with a truncated Gradient and Hessian method. We calibrate two types of finite element models, one using a filament representation for the coils and the other using a full 3D approach. The results show the feasibility of using the constrained non-linear optimisation algorithm for tuning the finite element model parameters. The mean signal-noise ratio after tuning on a truncated spectrum was 29.47 dB for the 3D model and 28.96 dB for the filament; in contrast the mean SNR using the measured coil parameters was 1.48 dB and 4.98 dB for the two uncalibrated models, respectively. The results show that a filament model is competitive with a 3D model of the coils (within the nuclear graphite application); therefore, a computationally faster filament model can be used with minimal effect on accuracy.

3D Finite-Element Forward Modeling of Airborne EM Systems in Frequency-Domain Using Octree Meshes

The 3-D airborne electromagnetic (AEM) inversions have been restricted by the modeling efficiency resulting from the complex geology in exploration areas and massive amount of data collected by AEM systems. In order to improve the modeling efficiency, we develop an algorithm that combines the hexahedral vector finite element (FE) with octree meshes, in which the boundary conditions are imposed via an algebraic constraint to ensure the continuity of the FE solution. This makes the division with hexahedral meshes more flexible for complex geology such as rugged topography or underground structures so that we can reduce the number of elements while maintaining the accuracy. After formulating the forward problem, we check the accuracy of our algorithm by taking a homogeneous half-space model and comparing the results of our octree method with the semianalytical solutions. Furthermore, we demonstrate the efficiency of our octree method by comparing with the traditional FE method using tetrahedral meshes. Finally, we subdivide a complex topography constructed using the 2-D Gaussian rough surface and calculate the EM responses with and without anomaly embedded. The results show that the EM responses are overwhelmed by the Earth topography. We carry out the topographic correction by taking a method based on the ratio of EM responses with and without anomaly. The experiments show that after topographic correction to AEM data, the response of anomaly becomes more distinguishable so that the anomaly can be clearly identified. Furthermore, we also calculate the EM response for a realistic model—the Ovoid Zone ore body located at Voisey’s Bay, Labrador, Canada, to verify the flexibility and practicality of our algorithm.

Numerical analysis of groundwater flow behaviour at a dam site in Karst area during its reservoir impoundment

The Jiangpinghe concrete-faced rockfill dam, with a maximum height of 219 m, is located in the karst area in western Hubei Province, China. The bedrocks at the dam site are highly dissolved, in which karst conduits, faults, fractures and weak interlayers are developed. Given the complex geological conditions, a large-scale grouting curtain covering an area of 376,000 m2 was built to control the seepage in the dam foundation. However, the piezometers in the middle section of the lowest grouting tunnel at the right bank manifest an abnormal rise of hydraulic head after reservoir impounding. The hydraulic head varies with a good correlation with the reservoir water level. This abnormal rise of hydraulic head can be attributed to higher permeability of strata where small-scale karst pipes and conduits are developed. In this study, an inverse modelling procedure combined orthogonal design, finite element forward modelling of transient groundwater flow, artificial neural network, and genetic algorithm was adopted to evaluate the permeability of the strata. The inverse results show that the permeability of shallow-buried rocks is one order of magnitude larger than that of deep-buried rocks in the right bank. The numerical simulations show good agreement with field measurements. Based on the inversed results, the groundwater flow behaviour at the dam site was analysed and the performance of the seepage control system was evaluated. It is demonstrated that the abnormal rise of hydraulic head is induced by the permeable structures developed along karst strata, and the seepage control system performs well in lowering the hydraulic head and limiting the amount of leakage through the dam foundation.

Quantitative evaluation of fracture porosity from dual laterlog based on deep learning method

Fracture porosity is one of the key parameters for characterizing fractured reservoirs. However, fracture porosity calculation is difficult with conventional logging data due to severe anisotropy of the reservoirs. To deal with the problem, the equivalent macroscopic anisotropic formation model based on dual laterolog (DLL) data is adopted to cyclically assign such parameters as bedrock resistivity (RB), fluid resistivity in fractures (RFL), fracture dip angle (FDA) and fracture thickness as well as fracture spacing, and to produce massive data for formation modeling. A large number of training data obtained through three dimensional finite element forward modeling and the functional relationship between DLL responses and fracture parameters that are trained and summarized by deep neural network, are combined to establish a new fast forward model for calculating DLL responses in fractured formations. A new fracture porosity inversion model for fractured reservoirs based on gradient optimization inversion algorithm combined with multi-initial inversion strategy is then proposed. While running the model, formation is divided into eight intervals according to bedrock resistivity and fracture dip angle from 0° to 90° is divided every 0.5° to improve the operation speed and efficiency. The results of numerical verification show that when bedrock resistivity is greater than 1000 Ω m, the mean absolute error (MAE) of fracture porosity inversion is 0.001658% for horizontal fractures, 0.00413% for intermediate fractures and 0.0027% for quasi-vertical fractures. When bedrock resistivity is between 100 Ω m and 1000 Ω m, MAE of fracture porosity inversion is 0.003% for horizontal fractures, 0.0034% for intermediate fractures and 0.00348% for quasi-vertical fractures. Fracture parameters determined by the fracture porosity inversion model with actual data are in good agreement with the results of micro resistivity imaging logging.

Direct current electrical resistivity forward modeling using comsol multiphysics

Forward modeling of direct current (DC) resistivity is very important for the inversion of the resistivity data to obtain the true resistivity of the subsurface. In this study, we demonstrated finite-element forward modeling of DC resistivity method with point electric source using COMSOL Multiphysics. We employed the AC/DC module in COMSOL which often provides comparatively easy implementation of models and permits exterior boundaries to be placed at infinity, a boundary condition often experienced in most geophysical problems. The validity and effectiveness of the results of numerical simulation using COMSOL Multiphysics were evaluated by comparing the output of the numerical simulations with the calculated analytic solutions. The result reveals that the numerical simulation is in agreement with the analytic solution. This study shows that COMSOL Multiphysics can be used to simulate the distribution of electrical potentials of point source in 3D space in real life and the information from this study can be used for further studies, such as DC resistivity inversions.

Magnetotelluric multiscale 3-D inversion reveals crustal and upper mantle structure beneath the Hangai and Gobi-Altai region in Mongolia

SUMMARY Central Mongolia is a prominent region of intracontinental surface deformation and intraplate volcanism. To study these processes, which are poorly understood, we collected magnetotelluric (MT) data in the Hangai and Gobi-Altai region in central Mongolia and derived the first 3-D resistivity model of the crustal and upper mantle structure in this region. The geological and tectonic history of this region is complex, resulting in features over a wide range of spatial scales, which that are coupled through a variety of geodynamic processes. Many Earth properties that are critical for the understanding of these processes, such as temperature as well as fluid and melt properties, affect the electrical conductivity in the subsurface. 3-D imaging using MT can resolve the distribution of electrical conductivity within the Earth at scales ranging from tens of metres to hundreds of kilometres, thereby providing constraints on possible geodynamic scenarios. We present an approach to survey design, data acquisition, and inversion that aims to bridge various spatial scales while keeping the required field work and computational cost of the subsequent 3-D inversion feasible. MT transfer functions were estimated for a 650 × 400 km2 grid, which included measurements on an array with regular 50 × 50 km2 spacing and along several profiles with a denser 5–15 km spacing. The use of telluric-only data loggers on these profiles allowed for an efficient data acquisition with a high spatial resolution. A 3-D finite element forward modelling and inversion code was used to obtain the resistivity model. Locally refined unstructured hexahedral meshes allow for a multiscale model parametrization and accurate topography representation. The inversion process was carried out over four stages, whereby the result from each stage was used as input for the following stage that included a finer model parametrization and/or additional data (i.e. more stations, wider frequency range). The final model reveals a detailed resistivity structure and fits the observed data well, across all periods and site locations, offering new insights into the subsurface structure of central Mongolia. A prominent feature is a large low-resistivity zone detected in the upper mantle. This feature suggests a non-uniform lithosphere-asthenosphere boundary that contains localized upwellings that shallow to a depth of 70 km, consistent with previous studies. The 3-D model reveals the complex geometry of the feature, which appears rooted below the Eastern Hangai Dome with a second smaller feature slightly south of the Hangai Dome. Within the highly resistive upper crust, several conductive anomalies are observed. These may be explained by late Cenozoic volcanic zones and modern geothermal areas, which appear linked to mantle structures, as well as by major fault systems, which mark terrane boundaries and mineralized zones. Well resolved, heterogeneous low-resistivity zones that permeate the lower crust may be explained by fluid-rich domains.

The three-dimensional finite element forward modelling of complex excitation source NMR

Abstract Traditional nuclear magnetic resonance (NMR) is mainly applied to horizontal ground and one-dimensional electrical structures. However, calculations of the excitation fields rarely consider the three-dimensional electrical changes of the subsurface medium and undulating terrain, or the deformations caused by emission sources. Therefore, to analyse the influences of terrain fluctuations, emission source deformations and three-dimensional electrical changes on NMR, three-dimensional finite element forward modelling of undulating terrain NMR was conducted in this study. First, based on a scalar finite element method, the direct calculations of the excited magnetic fields of a three-dimensional electrical medium were realised, which improved calculation accuracy by avoiding the finite element calculations of magnetic vector potential and vector on the magnetic field. During the source loading process, the equivalent thin wire source of the pseudo δ function was used to load the source function directly into the equation for the purpose of achieving total field calculations. This was completed to enable the calculations to be applied to any shape of the transmitting loop and undulating terrain. Then, the components of the excitation magnetic fields perpendicular to the geomagnetic fields were calculated using the rotation matrix. Finally, the NMR sensitivity function and 3D responses were calculated. The calculations of the excitation magnetic fields were verified using a uniform half-space model. The overall algorithm was tested by the nuclear magnetic responses of the layered medium. Also, a typical undulating terrain model was adopted and the complex excitation source NMR was simulated using the algorithm proposed in this study. The algorithm provided a three-dimensional forward basis for the NMR inversion in the cases of determining the electrical medium for the subsequent undulating terrain.

Determination of thermal properties of materials by Monte Carlo inversion of pulsed needle probe data

Needle probe measurements are used in a wide variety of fields for measuring the thermal conductivity of materials. It is most common to extract the thermal conductivity from the temperature rise data using the asymptotic solution to the heat equation. With special reference to, but not limited to Earth materials, this study presents an inversion procedure using pulsed needle probe data to determine both thermal conductivity and thermal diffusivity. The measured temperature response data are interpreted using a finite element forward model and a Markov Chain Monte Carlo inversion algorithm. The thermal properties of the needle probe are part of the forward model and determined by measurements on calibration standards. We examine several factors by synthetic modelling and quantify their effects by Monte Carlo inversions. This include (1) the heat production rate of the probe in order to produce similar temperature increases in materials of different thermal properties, (2) the contact resistance between needle probe and sample, (3) the limitations imposed by sample diameter and the thermal properties of the surrounding medium, and (4) the duration of heating period required to obtain good results. Laboratory test measurements on selected materials (water, glycerol, ceramic standard, clay) demonstrate good agreement with expected values obtained from literature. We demonstrate that the combination of numerical forward modelling and Monte Carlo inversion, applied to the pulsed needle, is a flexible and powerful methodology for accurate laboratory measurements of material thermal properties and with well-defined estimates of uncertainty. With the given equipment and laboratory setup, thermal conductivity is measured to within few percent, while thermal diffusivity generally has a somewhat higher degree of uncertainty, up to about five percent.

Application of 3D marine controlled-source electromagnetic finite-element forward modeling to hydrocarbon exploration in the Flemish Pass Basin offshore Newfoundland, Canada

In recent years, marine controlled-source electromagnetic (CSEM) surveying has become an effective supplemental interpretation tool to the seismic reflection method to help mitigate risk in an offshore exploration setting. Interpretation of marine CSEM data is commonly achieved via finite-difference inversions on rectilinear meshes, which has its merits, but the results are typically of very low resolution. The alternative is forward modeling, which requires a model to be known a priori, but the detail of the model can be created to reflect realistic geologic conditions. What is typically seen in the literature are applications of EM forward modeling codes to synthetic, and sometimes complex synthetic, models. However, what the literature is missing is an application that overcomes the challenges of applying a 3D forward modeling method to real models constructed from real information. We have developed an application of a 3D marine CSEM finite-element forward modeling method to the Bay du Nord prospect in the Flemish Pass Basin offshore Newfoundland. The 3D resistivity model, composed of four topographical layers and the Bay du Nord reservoir body, was built using 2D seismic data, one well log, and a marine CSEM inversion. Although other mesh representations have their merits, we chose to discretize our 3D model into an unstructured tetrahedral mesh because its flexibility enabled the accurate representation of complex structures while minimizing the number of unknowns. The availability of measured marine CSEM data allowed for the resistivities of each layer in the 3D model to be refined, and it also allowed for the simulated data to be assessed in the context of the real noise levels. A subsequent sensitivity analysis of the forward modeling results provided insights regarding the detectability of the Bay du Nord reservoir.

2-D magnetotelluric modeling using finite element method incorporating unstructured quadrilateral elements

In this research, the finite element (FE) method incorporating quadrilateral elements for solving 2-D MT modeling was presented. The finite element software was developed, employing a paving algorithm to generate the unstructured quadrilateral mesh. The accuracy, efficiency, reliability, and flexibility of our FE forward modeling are presented, compared and discussed. The numerical results indicate that our FE codes using an unstructured quadrilateral mesh provide good accuracy when the local mesh refinement is applied around sites and in the area of interest, with superior results when compared to other FE methods. The reliability of the developed codes was also confirmed when comparing both analytical solutions and COMMEMI2D model. Furthermore, our developed FE codes incorporating an unstructured quadrilateral mesh showed useful and powerful features such as handling irregular and complex subregions and providing local refinement of the mesh for a 2-D domain as closely as unstructured triangular mesh but it requires less number of elements in a mesh.

3D finite-difference modeling algorithm and anomaly features of ZTEM

The Z-Axis tipper electromagnetic (ZTEM) technique is based on a frequency-domain airborne electromagnetic system that measures the natural magnetic field. A survey area was divided into several blocks by using the Maxwell’s equations, and the magnetic components at the center of each edge of the grid cell are evaluated by applying the staggered-grid finite-difference method. The tipper and its divergence are derived to complete the 3D ZTEM forward modeling algorithm. A synthetic model is then used to compare the responses with those of 2D finite-element forward modeling to verify the accuracy of the algorithm. ZTEM offers high horizontal resolution to both simple and complex distributions of conductivity. This work is the theoretical foundation for the interpretation of ZTEM data and the study of 3D ZTEM inversion.

Seafloor bathymetry in deep and shallow water marine CSEM responses of Nigerian Niger Delta oil field: Effects and corrections

Topography distortions in bathymetrically acquired marine Controlled-Source Electromagnetic (mCSEM) responses are capable of misleading interpretation to the presence or absence of the target if not corrected for. For this reason, the effects and correction of bathymetry distortions on the deep and shallow seafloor mCSEM responses of the Niger Delta Oil province were examined in this paper. Marine CSEM response of the Niger Delta geological structure was modelled by using a 2.5D adaptive finite element forward modelling code. In both the deep water and shallow water cases, the bathymetry distortions in the electric field amplitude and phase were found to get smaller with increasing Tx–Rx offsets and contain short-wavelength components in the amplitude curves which persist at all Tx–Rx offsets. In the deep water, topographic effects on the reservoir signatures are not significant, but as water depth reduces, bathymetric distortions become more significant as a result of the airwave effects, masking the target signatures. The correction technique produces a good agreement between the flat-seafloor reservoir model and its equivalent bathymetric model in deep water at 0.25Hz, while in shallow water, the corrected response only shows good agreement at shorter offsets but becomes complicated at longer offsets due to airwave effects. Transmission frequency was extended above and below 0.25Hz in the frequency spectrum and the correction method applied. The bathymetry correction at higher frequency (1.75Hz) is not effective in removing the topographic effects in either deep or shallow water. At 0.05Hz for both seafloor scenarios, we obtained the best corrected amplitude profiles, removing completely the distortions from both topographic undulation and airwave effects in the shallow water model. Overall, the work shows that the correction technique is effective in reducing bathymetric effects in deep water at medium frequency and in both deep and shallow waters at a low frequency of 0.05Hz.

Evaluation of Groundwater Leakage into a Drainage Tunnel in Jinping-I Arch Dam Foundation in Southwestern China: A Case Study

The Jinping-I double-curvature arch dam, located in the middle reach of Yalong River and with a maximum height of 305 m, is the world’s highest dam of this type that has been completed. Since the second stage of reservoir impounding, after which the reservoir water level was gradually raised by about 232 m, a significant amount of leakage was observed from the drainage holes drilled in the lowest drainage tunnel at the left bank abutment at an elevation of 1595 m a.s.l. (above sea level), with an observed maximum pressure of about 0.3 MPa. A number of investigations, including water quality analysis, digital borehole imaging, tunnel geological mapping, and in situ groundwater monitoring, were performed to examine the source of leaking, the groundwater flow paths, and the performance of the grouting curtains. By defining two objective functions using the in situ time series measurements of flow rate and hydraulic head, respectively, a multiobjective inverse modeling procedure was proposed to evaluate the permeability of the foundation rocks that was underestimated in the design stage. This procedure takes advantage of the orthogonal design, finite element forward modeling of the transient groundwater flow, artificial neural network, and non-dominated sorting genetic algorithm, hence significantly reducing the computational cost and improving the reliability of the inversed results. The geological structures that lead to the leakage were identified and the seepage flow behaviors in the dam foundation and the left bank abutment were assessed. Based on the field measurements and the inverse modeling results, the effects of the engineering treatments of the leakage event on the dam safety were analyzed. It has been demonstrated that the seepage control system is effective in lowering the groundwater level and limiting the amount of seepage in the dam foundation, and the leakage event does not pose a threat to the safety of the dam.

A study on Parallel Computation Based on Finite Element Forward Modeling of 2D Magnetotelluric

Magnetotelluric sounding method based on the difference of the rock’s resistivity is an exploration method about doing research in earth’s resistivity and phase using the native electromagnetic field. The paper adopts 2D finite element method as the magnetotelluric forward method and calculates the total field by primary field (also named background field) plus secondary field. We can get more accurate forward result through the finite element method and we can get the result effected by the dense degree of grid slightly by the total field. But the method is not effective enough when the model is divided into relative big grid. When the frequency changes, program solves relevant equation separately. According to the feature of the algorithm, we apply MPI parallel method in the algorithm. Every process solves relevant equation. The account of frequency that a process needs to solve in parallel computation is less than the account that the process needs to solve in serial algorithm. We can see that the forward result is the same with the serial algorithm and proves the correctness of algorithm. We do statistics about the efficiency of the parallel algorithm. When the account of processes is from 2 to 8, the speedup is from 1.63 to 2.64. It proves the effectiveness of the parallel algorithm.