Time-domain Electromagnetic Field Research Articles

Comparative analysis of computational schemes for FEM modeling of 3D time-domain geoelectromagnetic fields excited by a horizontal grounded-wire source

Two mathematical formulations are considered for calculating the time-domain electromagnetic fields excited by a horizontal grounded-wire source in a 3D geological medium. The first of them is formulated for a vector potential (A-formulation), the second one is formulated for the electric field strength (E-formulation). Both formulations are also considered when using the primary-secondary field approach (PSFA), where the primary field is calculated in a horizontally layered medium. The calculation of 3D non-stationary fields is performed using the vector finite element method (FEM). For time discretization, both two-point and three-point implicit schemes are considered. As the initial field, we used the stationary field of the direct current, the corresponding mathematical formulations are also presented using the PSFA. To verify computational schemes, a comparison with the results of other authors is given. For the problems of marine electrical exploration, we present a comparison of two formulations, analyze the effectiveness of PSFA and the use of a three-point implicit scheme instead of a two-point one. The results of computational experiments have shown that when using both formulations, the use of PSFA and the three-point implicit scheme “with backward overstepping” (instead of the two-point implicit scheme) can reduce computational costs by more than an order. In this case, both formulations give solutions that are close to each other in accuracy and computational costs. However, the implementation of the E-formulation using the PSFA requires certain thoroughness and in some cases can lead to a sharp deterioration in the numerical solution accuracy at late times. This is due to the fact that when using the vector FEM, the numerical solution can lead to a nonzero constant field, which is the gradient of some scalar function.

Study on Time Domain Electromagnetic Remote Boundary Detection Method for Multi-component Well Logging

Borehole time-domain electromagnetic remote detection realizes reservoir scale formation boundary measurement. There is a strong correlation between the abnormal response signal of borehole time-domain electromagnetic pure quadratic field and the distance of formation boundary. The greater the boundary distance, the later the abnormal extreme point appears. The response characteristics of the secondary field of the coaxial and coplanar multi-component measurement modes are just "opposite" at different dip angles. Using borehole time-domain electromagnetic measurement information, the formation dip and remote borehole boundary detection can be directly calculated.

Pulsed electromagnetic field coupling to a transmission line with arbitrary loads—A unified methodology based on reciprocity

A unified description of the time-domain (TD) electromagnetic (EM) field coupling to a transmission line (TL) that is terminated by arbitrary linear time-invariant loads is presented. Closed-form expressions for the electric current induced in the loads are derived with the aid of the EM reciprocity theorem of the time-convolution type. The validity of the solution is demonstrated via illustrative numerical examples.

A general forward solver for 3D CSEMs with multitype sources and operating environments

To determine the electromagnetic (EM) fields of different three-dimensional (3D) controlled-source electromagnetic methods (CSEMs) using the same parameters of the forward solution, by explicitly considering the commonalities, we present a general 3D forward modeling solver for CSEMs with multitype sources and operating environments. The commonality of the solver is reflected in two aspects. First, the solver is based on a frequency-domain (FD) vector Helmholtz equation for determining the scattered electric field. The different types of sources are imposed on the right-hand term of the equation, expressed as background Green’s function. Second, sources of any CSEM can be composed of electric dipole (ED) or magnetic dipole (MD) superposition. Thus, the focus of the 3D forward modeling of CSEMs is reduced to determining the EM fields of ED or MD sources for the background medium. The quasi-minimal residual (QMR) method is used to solve the large sparse complex linear system. Once the FD EM fields have been calculated, the time-domain (TD) response can be obtained using the cosine/sine transformation. The numerical results show that the relative error is less than 5% between the 3D numerical and analytical solutions, which verifies the accuracy of the solver. We further study the difference between the real (bent) and theoretical (straight) wires. We suggest that the shape of the source must be considered for TD and FD CSEMs with a wire source during data processing and inversion. The last example investigated the characteristics of FD EM fields from a finite-length wire and TD EM fields from a rectangular fixed loop on the same conductive tilted disk model buried in resistive sediments. According to the numerical results, we recommend FD CSEMs with a wire source for detecting deep anomalies.

Effective Numerical Simulations of Multipactor by WBPAT Theory

We propose a fast electromagnetic particle-in-cell (EM-PIC) method to simulate multipactor in waveguide devices. First, complex amplitudes (amplitudes and phases) at multiple frequencies are quantitatively extracted by using the wideband power-to-amplitude transformation (WBPAT) algorithm in the finite-difference time-domain (FDTD) method. Then the charged particles are advanced one way from the time-domain (TD) electromagnetic (EM) fields transformed from the complex amplitudes without considering the space-charge effects. Therefore, the conventional FDTD iterations and interpolations to cell nodes are avoided at the iterative stage. As a result, the simulation efficiency can be greatly improved. The efficiency can be further promoted by using the time step magnification and local region simulation. The proposed method can also be utilized for analyzing the multicarrier multipactor. For the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{C}$</tex-math> </inline-formula> -band impedance transformer under the excitations by different multicarrier waveforms, the simulation speed of the proposed method can be improved by several orders of magnitude and the accuracy of the power threshold is comparable with the self-consistent simulation.

Synthesizing magnetotelluric time series based on forward modeling

The validity of magnetotelluric time-series processing methods has been lacking reasonable testing criteria. Since the time series synthesized by existing techniques are not fully derived from a given model, they are not reliable. In this paper, we present a novel approach to synthesize magnetotelluric time series based on forward modeling and the correspondence between frequency and time domain electromagnetic fields. In this approach, we obtain the electromagnetic response of two orthogonal polarization sources for a given model by magnetotelluric forward modeling, and simulate the randomness of the polarization of the natural field source by a linear combination of the two polarization sources. Based on the correspondence between the frequency and time domain electromagnetic fields, the electromagnetic fields obtained by forward modeling in the frequency domain are transformed into the time domain, and finally the time series are synthesized. The test results on 1D and 3D models validate the effectiveness of the proposed method and the correctness of the procedure. After adding noise to the synthesized time series, we can test the performance of each method by comparing the results of the time series processing methods with the response of the given model. Therefore, the method presented in this paper can be used to construct standard magnetotelluric time series, which can be used as a carrier to construct synthetic data satisfying various noise distributions, and for the study of related methods. This method can also be used to synthesize time series of other frequency-domain electromagnetic methods.

The impact of respiratory motion on electromagnetic fields and specific absorption rate in cardiac imaging at 7T.

To present electromagnetic simulation setups for detailed analyses of respiration's impact on and E-fields, local specific absorption rate (SAR) and associated safety-limits for 7T cardiac imaging. Finite-difference time-domain electromagnetic field simulations were performed at five respiratory states using a breathing body model and a 16-element 7T body transceiver RF-coil array. and SAR are analyzed for fixed and moving coil configurations. SAR variations are investigated using phase/amplitude shimming considering (i) a local SAR-controlled mode (here SAR calculations consider RF amplitudes and phases) and (ii) a channel-wise power-controlled mode (SAR boundary calculation is independent of the channels' phases, only dependent on the channels' maximum amplitude). Respiration-induced variations of both amplitude and phase are observed. The flip angle homogeneity depends on the respiratory state used for shimming; best results were achieved for shimming on inhale and exhale simultaneously ( ). The results reflect that respiration impacts position and amplitude of the local SAR maximum. With the local-SAR-control mode, a safety factor of up to 1.4 is needed to accommodate for respiratory variations while the power control mode appears respiration-robust when the coil moves with respiration (SAR peak decrease: 9% exhale→inhale). Instead, a spatially fixed coil setup yields higher SAR variations with respiration. Respiratory motion does not only affect the distribution and hence the image contrast, but also location and magnitude of the peak spatial SAR. Therefore, respiration effects may need to be included in safety analyses of RF coils applied to the human thorax.

Geometric 3-D inversion of airborne time-domain electromagnetic data with applications to kimberlite pipes prospecting in a complex medium

We consider an approach to solving 3-D inverse problems of airborne time-domain electromagnetic (TD-EM) survey in complex geoelectrical conditions, when the responses of target objects in the measured signal are relatively small and mixed with responses of rugged topography, 3-D inhomogeneities in overburden layers, and other interfering 3-D objects. For parameterization of the geoelectrical model of the geological medium, global and local structures are used. A block structure is a grid with large cells whose boundaries can move during the inversion process. Block structures are characterized by two types of parameters: geometric and physical. Geometric parameters include the coordinates of the boundaries of blocks in block structures, which are used for recovering local bodies or 3-D inhomogeneities within the layers, and physical parameters are the conductivities inside the blocks. In addition, the geometric parameters include displacements of control points, which are used for describing curved surfaces. The functional employed for inversion includes regularizing terms that allow controlling the self-crossing of geometric boundaries and extension of physical parameters beyond the boundaries of the allowed values range. Regularization coefficients are calculated adaptively at each iteration of the nonlinear 3-D inversion. In order to separate the responses of 3-D inhomogeneities located under the overburdens from those of 3-D inhomogeneities inside the overburdens, we propose to carry out 3-D inversion in two stages. At the first stage, over a shortened time range, we recover the conductivity distribution using global block structures and the shape of the boundaries of the overburden layers using control points. At the second stage, the entire time range is used. In those places where the significant residuals remained at late times, local block structures are employed to recover local objects (including target ones) under the overburden layers. This enables us to define quite accurately the position in plan, top border depth, and type of 3-D inhomogeneities, which are located under the overburdens, at the second stage of geometric inversion. To calculate 3-D time-domain electromagnetic fields, we use the vector finite element method implemented on optimized non-conforming hexahedral meshes with the possibility of adjoining the faces of several finite elements to the face of one finite element. The workability of the proposed approaches is demonstrated on synthetic airborne TD-EM data as well as on experimental airborne data, which are obtained as a result of methodical work over the kimberlite pipe deposit. The proposed geoelectrical model parameterization and the approach to 3-D inversion allow the discovery of relatively small 3-D target objects, when many non-target objects, including 3-D inhomogeneities in the overburdens, give several times greater responses in the measured signals.

Fast Time-Domain Solution of Dynamic Electromagnetic Problems Based on Sinc Interpolation

In time-domain electromagnetic field problems that have a fast time response with sharp field change or need a long time transient process to get the steady-state solution, a large number of time step iterations are required using the classical time-stepping method. A reduced model based on Sinc interpolation is proposed in this work. The accuracy of the proposed method does not depend on the traditional time-domain discretization step but only the number of sampling points. Two numerical examples, namely an electro-quasistatic (EQS) problem and a field-circuit coupled problem, are considered to illustrate the accuracy and performance of the proposed method. It is shown that only a few pre-computed samplings are sufficient to obtain a good performance while comparing with the traditional time-stepping method.

GSvit — An open source FDTD solver for realistic nanoscale optics simulations

Surface and volume imperfections can significantly affect the performance of nanoscale or microscale devices used in photonics, optoelectronics or scientific instrumentation. In this article we present an open source software package for Finite-Difference Time-Domain electromagnetic field calculations suitable for calculations on graphics cards. Its special features include handling realistic models of imperfect nanoscale objects, such as treatment of arbitrary geometries including addition of random roughness to any geometrical object. The method is compared to conventional optical approach represented by Rayleigh-Rice theory. Practical applicability is demonstrated using a calculation of variation of field enhancement at proximity of a rough nanoscale antenna and rough particle scattering. It is shown that such approach can be namely useful in the areas where many repeated calculations are necessary, e.g. when studying how the optical response of nanoscale objects can vary when they are rough. Program summaryProgram Title: GSvitCPC Library link to program files:https://doi.org/10.17632/k424zbsxnk.1Licensing provisions: GPLv2Programming language: CNature of problem: If we want to analyse impact of random imperfections, in particular surface roughness, on optical response of nanoscale and microscale objects, we need to run many calculations with different random realisations. GSvit is a general electromagnetic field solver optimized for running such calculations, via fast computing on graphics cards and algorithms for loading of arbitrary data and modification of their geometry to construct randomly rough surfaces and interfaces.Solution method: Finite-Difference Time-Domain method implemented on computer processor and on graphics card, with advanced pre-processing in order to add realistic roughness to 3D objects.Additional comments including restrictions and unusual features: The current version of software, including the documentation and downloadable examples can be found on http://gsvit.net/.

A Maxwell's Equations Based Deep Learning Method for Time Domain Electromagnetic Simulations

In this paper, we discuss an unsupervised deep learning (DL) method for solving time domain electromagnetic simulations. Compared to the conventional approach, our method encodes initial conditions, boundary conditions as well as Maxwell's equations as the constraints when training the network, turning an electromagnetic simulation problem into an optimization process. High prediction accuracy of the electromagnetic fields, without discretization or interpolation in space or in time, can be achieved with limited number of layers and neurons in each layer of the neural network. We study several numerical examples to demonstrate the effectiveness of this method for simulating time-domain electromagnetic fields. First, the accuracy of this method is validated by comparing with the analytical solution of a 1D cavity model filled with homogeneous media. Then, we combine the continuity condition to modify the loss function for handling medium discontinuities. Further, the computational efficiency of finite-difference and DL methods in conductive and nonlinear media is compared. Finally, we prove the effectiveness of this method in high-dimensional and multi-scale simulations.

Improvement of the Efficiency of Time-Domain Electromagnetic Measurement

The long-term sustainable development of mineral exploration under covers require effective deep detection techniques and methods. Start from enhancing the surface-borehole time-domain electromagnetic (TEM) technique, the present study established a new relationship between the pulse width (Δ), the target time constant (τ) and the measurement time (t). Under certain conditions, the new formula has been extended to all TEM systems that use square or trapezoidal waveforms. A series of numerical simulations illustrate the consistent behaviors of the surface-borehole, ground and airborne TEM fields. The new relationship allows us to evaluate optimal pulse widths for different off-times and to help TEM survey design.

Performance of Krylov subspace method with SOR preconditioner supported by Eisenstat’s technique for linear system derived from time-periodic FEM

PurposeThis paper aims to present the affinity of BiCGStab and BiCGStab2 with successive over-relaxation (SOR) preconditioner supported by Eisenstat’s technique for a linear system derived from the time-periodic finite element method (TP-FEM). To solve the time domain electromagnetic field problem with long transient state, TP-FEM is very useful from the perspective of rapidly achieving a steady state. Because TP-FEM solves all of the state variables at once, the linear system derived from TP-FEM becomes the large scale and nonsymmetric, whereas the detailed performance of some preconditioned Krylov subspace method is not reported.Design/methodology/approachIn this paper, BiCGStab and BiCGStab2 are used as the linear solver for a large-sparse nonsymmetric linear system derived from TP-FEM. In addition, incomplete LU (ILU) factorization is applied as a preconditioner to compare SOR supported by Eisenstat’s technique. As examples, the pot-type reactor and three-phase transformer is analyzed.FindingsIn the problem of the pot-type reactor, when SOR preconditioner supported by Eisenstat’s technique is applied to BiCGStab and BiCGStab2, the elapsed time can be reduced dramatically. However, in the problem of the three-phase transformer, the iterative process of the linear solvers with SOR preconditioner is not terminated, whereas the iterative process of linear solvers with ILU preconditioner is terminated. The preconditioner that can be supported by Eisenstat’s technique is not necessarily appropriate for the problem to derive from TP-FEM.Originality/valueIn this paper, the affinity of preconditioned linear solver supported by Eisenstat’s technique for the nonsymmetric linear system derived from TP-FEM is demonstrated.

Multistage topology optimization of induction heating apparatus in time domain electromagnetic field with magnetic nonlinearity

Purpose The purpose of this paper is to solve efficiently the topology optimization (TO) in time domain problem with magnetic nonlinearity requiring a large-scale finite element mesh. As an actual application model, the proposed method is applied to induction heating apparatus. Design/methodology/approach To achieve TO with efficient computation time, a multistage topology is proposed. This method can derive the optimum structure by repeatedly reducing the design domain and regenerating the finite element mesh. Findings It was clarified that the structure derived from proposed method can be similar to the structure derived from the conventional method, and that the computation time can be made more efficient by parameter tuning of the frequency and volume constraint value. In addition, as a time domain induction heating apparatus problem of an actual application model, an optimum topology considering magnetic nonlinearity was derived from the proposed method. Originality/value Whereas the entire design domain must be filled with small triangles in the conventional TO method, the proposed method requires finer mesh division of only the stepwise-reduced design domain. Therefore, the mesh scale is reduced, and there is a possibility that the computation time for TO can be shortened.

The Simulation of Transient Electromagnetic Based on Time-domain IP Model

When transient electromagnetic investigation methods are carried out in the field, the measured data often contain both the induced polarization (IP) effect and the electromagnetic effect. In order to study the IP effect in the transient electromagnetic response, many researchers first calculate the electromagnetic field which considers the IP effect by replacing traditional resistivity with complex resistivity of the Cole-Cole model in the frequency domain. After the forward modeling calculation of the electromagnetic field in the frequency domain that considers the IP effect, the transient electromagnetic field in time-domain is obtained by a time-frequency transform algorithm. In this paper, the resistivity is directly replaced by the time-variant resistivity expression of the Cole-Cole model by using digital filter algorithms when we simulate the transient electromagnetic fields in time- domain. The calculated result of the Cole-Cole model in time-domain and in frequency-domain are consistent with each other, as observed in the horizontal electric field and the vertical magnetic field comparisons, which indicates the correctness of the numerical computation method adopted in this paper. The research presented herein allows us to observe the influence of the IP effect on transient electromagnetic field as well as study the mechanisms of IP directly.

Multi-Objective Optimization of a Wireless Body Area Network for Varying Body Positions.

The purpose of this research was to improve the performance of a wireless body area sensor network, operating on a person in the seated and standing positions. Optimization-focused on both the on-body transmission channel and off-body link performance. The system consists of three nodes. One node (on the user’s head) is fixed, while the positions of the other two (one on the user’s trunk and the other on one leg) with respect to the body (local coordinates) are design variables. The objective function used in the design process is characterized by two components: the first controls the wireless channel for on-body data transmission between the three sensor nodes, while the second controls the off-body transmission between the nodes and a remote transceiver. The optimal design procedure exploits a low-cost Estra, which is an evolutionary strategy optimization algorithm linked with Remcom XFdtd, a full-wave Finite-Difference Time-Domain (FDTD) electromagnetic field analysis package. The Pareto-like approach applied in this study searches for a non-dominated solution that gives the best compromise between on-body and off-body performance.

Design considerations for a pulse line ion accelerator (PLIA)-based PET isotope generator.

Positron emission tomography (PET) imaging remains limited due to the cost associated with on-site production of short half-life, positron-emitting isotopes. In this work, we examine the use of a pulse line ion accelerator (PLIA) to accelerate protons for single-dose PET isotope production. Time-domain electromagnetic field and particle-in-cell (PIC) simulations were performed for a 1.5-m PLIA structure modeled in CST Microwave Studio and Particle Studio software. Scaled measurements from a kV ramp-pulse generator were incorporated into the simulations to accelerate a 1 A, 50 ns proton beam injected with initial kinetic energy of 100 keV. A uniform, 3 T, solenoidal magnetic field was used to provide external beam focusing. Electromagnetic fields and particle phase space were recorded with ns resolution for subsequent analysis. Applying a scaled 100 kV, 20 ns ramped voltage pulse to the PLIA input resulted in a travelling electric field wave inside the structure with accelerating gradient of 2.4 MV/m. The observed wave speed was 1.2 × 107 m/s and is in good agreement with theoretical predictions. Phase space monitors showed both acceleration and bunching of the proton beam, with a maximum kinetic energy of 2.5 MeV, observed at the exit of the single PLIA stage. Evaluation of beam position monitors at different locations in the accelerator showed bunch compression and minimal beam divergence, illustrating that the 3 T field is adequate to contain the beam over the length of the PLIA structure. Simulations performed in this work demonstrate the feasibility of using a PLIA structure to accelerate protons with MV/m level gradients. Combining several PLIA stages in series could allow for a low-cost accelerator suitable for dose-on-demand PET isotope production.

Study of the time-domain electromagnetic pulse standard field generation setup and its application.

In this paper, a time-domain electromagnetic pulse standard field generation setup was designed and manufactured for transient electromagnetic pulse sensor calibration. The calibration setup is based on the mono-cone structure. It can produce a calculated electromagnetic pulse field with the electric field intensity from 100 V/m to 600 V/m. The quantity of the electric field intensity is traced to the national primary standard of the pulse parameter, the S parameter, and the length quantity. The standard uncertainty of the produced electric field is 2.4%. The waveform and field distribution of the standard field were verified by experiment. Based on this facility, the calibration methods and uncertainty evaluation methods for two types of electromagnetic pulse sensors (TEM horn and D-dot sensor) were proposed. Finally, we obtained the calibration results of the sensors. The standard uncertainties of the calibration are 3.6% for the TEM horn and 3.0% for the D-dot sensor.

Use of time-domain electromagnetic (TDEM) method to investigate seawater intrusion in the Lebna coastal aquifer of eastern Cap Bon, Tunisia

A multi-method geophysical survey, using time-domain electromagnetic (TDEM) fields, is conducted on the north-eastern coastal aquifer of Cap Bon, Tunisia. The aim of the study is to investigate the inland extent saltwater intrusion, to estimate the fresh-saltwater transition zone, and to characterize the lithologic spatial variability of the underground layers. Moreover, the TDEM is used to determine both fluid resistivity and bulk resistivity which are required to calculate the porosity by applying the Archie’s equation. The survey of TDEM profiles is carried out along the left and right overbanks of the Lebna river from the coast until the Lebna dam. The interpretation and the analysis of these profiles allow us to better identify the flux exchanges between the river and the underlying aquifer. On the basis of the 1D and 2D longitudinal and transversal resistivity profiles as well as the existing boreholes data and groundwater quality, it seems that the freshwater-saltwater interface is moving forward inland. Furthermore, electromagnetic results combined to the Archie’s law show that the porosity values are at the ranges of 12–36 and 5–31% for the Quaternary outcropping and Pliocene formation, respectively.

Efficient Modeling of Time-domain AEM using Finite-volume Method

ABSTRACT We present an efficient three-dimensional (3D) time-domain airborne electromagnetic (EM) modeling based on finite-volume method, in combination with the merits of solving the secondary field, local mesh, and the direct solver. Taking the strategy of separating primary from secondary field for the calculation of time-domain EM field, we greatly reduce the number of grids in comparison to direct solution of the total field. The primary field is obtained by Hankel transform from the frequency-domain for a half-space or layered earth model. The techniques of local mesh and direct solver are adopted to further improve the modeling efficiency. We compare and discuss the characteristics of the method developed in this paper from time consumption and grid sizes. The EM responses for different transmitting waveforms are calculated via a convolution between step-wave responses and the transmitting current or its derivatives. All numerical experiments on models with multiple geological bodies and fracture z...