Time-domain Electromagnetic Modeling Research Articles

Improved convergence speed using hybrid AI for TD EM modeling in power electronics

This paper presents a time-domain (TD) approach based on hybrid artificial intelligence (AI) to speed up convergence of radiating sources characterization in power electronics. To obtain a representative equivalent model of device under test, a dedicated optimization framework has been developed in TD using a particle swarm optimization (PSO) toolbox. In addition, for elementary feature extraction, a pseudo-Zernike moment invariant (PZMI) descriptor has been defined. Finally, with the aim of identifying remaining dipole parameters and classification problems, artificial neural networks (ANN) have been implemented. A coupling of TD electromagnetic (EM) inverse method based on a PSO algorithm along with PZMI and ANN application has been investigated and applied to a real test case. Experimental measurements have been conducted using the near-field scanning technique above an alternating current (AC)/direct current (DC) converter. Obtained results are discussed based on a comparison between measured and estimated EM field distributions using both the hybrid AI method and a conventional TD inverse method based on genetic algorithms (GA) only. This study confirms that, compared with those given by non-hybrid method, the proposed algorithm further improves the convergence speed while maintaining high accuracy. Hence, the present work offers an impressive perspective for radiated emissions characterization using hybrid AI algorithms.

A new technique inversion Time-Domain electromagnetic data

Time-Domain Electromagnetic (TDEM) data modeling, especially for central-loop configurations, is often achieved through 1D inversion models. This study aims to enhance the accuracy and efficiency of TDEM data inversion by employing the Born Approximation method to address calculation and convergence speed issues. We also utilize the modified Symbiotic Organism Search (mSOS), a global optimization algorithm capable of handling multi-minimum problems in non-linear objective functions, to optimize the inversion process. Our research includes the assessment of the accuracy and performance of this approach through inversion modeling on both synthetic and field data. The accuracy of the synthetic data was evaluated based on the algorithm's capability to retrieve the values of the synthetic data, as indicated by the small relative error between the synthetic model parameters and the calculated model. In the case of field data modeling, the accuracy relied on the consistency achieved when modeling the data with different numbers of layers. Additionally, we considered the time required to perform the inversion as an evaluation metric for inversion performance. For the synthetic data case, the algorithm produced relatively accurate models with misfit values of approximately 0 % and low relative error values. In the field data case, the inversion models demonstrated consistency and reduced misfit values when the data was modeled with different numbers of layers, specifically 8.72 % for the 2-layer model, 3.92 % for the 3-layer model, and 2.61 % for the 4- and 5-layer models. Both datasets required less than 19 min for 10,000 iterations. These findings highlight the innovative nature of the mSOS algorithm and its potential for practical applications in TDEM inversion studies.

Implicit finite-difference time-domain schemes for TDEM modeling in three dimensions

Geophysical exploration methods that use controlled electromagnetic sources in time domain are becoming ubiquitous because of their ease of deployment and data coverage capabilities. Although these prospecting methodologies have evolved significantly, most computational numerical modeling techniques have been developed in the frequency domain. Given this evolution, it is pertinent to ask whether some known advantages of implicit finite-difference (FD) modeling techniques, which are common among other disciplines, apply to the time-domain electromagnetic (TDEM) problem in geophysics. To explore the potential advantages of 3D time-domain modeling for TDEM, we have analyzed the differences between two implicit FD formulations: a single-order backward Euler scheme and a second-order Crank-Nicolson scheme. To validate our algorithms, we tested them with existing analytical solutions for simple geometries and performed detectability tests for various electromagnetic sources. The results find an acceptable match of both numerical schemes to the analytical solutions and higher accuracy of the second-order discrete operator without a significant difference in computing time.

3-D time-domain electromagnetic modeling based on multi-resolution grid with application to geomagnetically induced currents

Time-domain electromagnetic modeling in 3-D requires the solution of partial differential equations discretized on a grid. The finer grid resolution is usually required to describe rapid variations of the electromagnetic field in the near-surface, where the source and small-scale anomalies present. Since the electromagnetic field diffuses in the lossy medium, its variations become smoother with depth. The conventional finite-difference modeling approach using the staggered grid extends the fine grid resolution (needed for shallow layers) to all depths. It results in over-discretization of the problem and redundant computational costs. Here, we apply the multi-resolution (MR) grid approach to the time-domain electromagnetic modeling (TDEM). The MR grid allows us to decrease the grid resolution with depth and consequently reduce the number of degrees of freedom without compromising the accuracy of the solution. We implement a way of treating the loop source in TDEM modeling such that the definition of the source term is based on the Biot-Savart law; this allows separation of the loop source from the grid, making the source simulation more flexible.To verify our new TDEM modeling, we perform several synthetic tests. We also apply the algorithm to model the geomagnetically induced electric field (GIE). Such modeling is an essential part of estimating hazards caused by geomagnetically induced currents (GIC). In contrast to frequency-domain modeling primarily used in previous studies, the time-domain GIE modeling allows us to consider the time variability of the source in the ionosphere in real-time.For more realistic simulations, we use a large-scale 3-D resistivity model of Fennoscandia. An example of the MR grid GIE modeling highlights the areas of high GIE contrasts and shows that the real inhomogeneous 3-D resistivity distribution and realistic source geometry are necessary for a better estimation of GIC.

3D finite-volume time-domain modeling of geophysical electromagnetic data on unstructured grids using potentials

Unstructured grids are capable of faithfully representing real-life geologic models and topography with relatively few mesh cells. We have developed a finite-volume solution to the 3D time-domain electromagnetic forward modeling problems using unstructured Delaunay-Voronoï dual meshes. We consider the Helmholtz equation for the electric field and a combination of the Helmholtz equation and the conservation of charge equation for the magnetic vector (A) and electric scalar ([Formula: see text]) potentials. The [Formula: see text] formulation requires initial values for A that can be obtained by solving the magnetostatic problem. We use backward Euler time stepping to advance the electric field and the potentials in the time domain. When using the potential method, the electric and magnetic fields are calculated from [Formula: see text] solutions. To obtain consistent potential solutions at different time steps, we enforce the Coulomb gauge condition, using implicit and explicit methods. We validate the proposed method with a simple 3D conductive block model and with a comparison with other numerical methods. By using [Formula: see text] potentials, it is possible to decompose the electric field into galvanic and inductive parts, which is helpful in understanding the physics behind the behavior of the electromagnetic fields in the ground. We use vector plots to visualize the decomposed electric fields for horizontal and vertical thin conductor models with inductive loop sources. This allows the interplay between inductive and galvanic parts as the electric field and current density develop with time to be visualized.

Higher-Order Convolution PML (CPML) for FDTD Electromagnetic Modeling

A new simple formulation for incorporating a higher-order perfectly matched layer (PML) stretching function within a convolution PML (CPML) implementation in finite-difference time-domain (FDTD) electromagnetic modeling codes is developed. Obtaining in closed form the corresponding time domain impulse response of the inverse of a number of higher-order PML stretching functions enables the efficient and simple implementation of such higher-order PMLs using recursive convolution, in the same way as it was introduced initially for the complex frequency shifted (CFS) PML. This new higher-order CPML exhibits excellent performance that is comparable to the performance shown by other higher-order PML formulations whilst it retains the advantage of a relatively simpler implementation.

3-D Full-Time TEM Modeling Using Shift-and-Invert Krylov Subspace Method

The 3-D time-domain electromagnetic (TEM) modeling is computationally expensive. Shift-and-invert (SAI) Krylov subspace technique has proved efficient for the modeling of OFF-time TEM data. However, the ON-time data, which also involves useful Earth conductivity information, have not been well treated. In this article, we extend the SAI Krylov subspace method to deal with the ON-time data and obtain a complete algorithm for modeling of the full-time data. To deal with the ON-time problem, while retaining the whole framework of an SAI-style method, we have developed a new time integration method, based on the exponential trapezoidal rule, to help discrete the integral terms into matrix exponential function. Next, the solution of this matrix exponential function is obtained by constructing a new type of SAI Krylov subspaces. Numerical results for typical transmitting waveforms, such as half-sine, versatile-time-domain-electromagnetic (VTEM), and MULTIPULSE, demonstrate that the novel algorithm is accuracy for full-time TEM modeling.

Application of perfectly matched layers in 3D transient controlled-source electromagnetic modeling by the rapid expansion method

I have developed an extension of the rapid expansion method (REM) for 3D time-domain controlled-source electromagnetic modeling that includes perfectly matched layers (PMLs) as the absorbing boundary. The REM solves the time-domain electric field by a weighted summation of the Chebyshev polynomials. The results are free of temporal dispersion and accurate to the Nyquist frequency, yet the domain of Chebyshev polynomials lacks an accurate absorbing boundary. I find that by introducing a fictitious magnetic field in the Chebyshev domain, the recursion of the Chebyshev polynomials obeys a discrete coupled wave equation, which shares a similarity with the propagation of EM waves in a lossless medium. The time and frequency components in the Chebyshev domain are derived based on the eigenvalues of the propagation matrix, and the PML theory designed for EM waves can be extended to the Chebyshev domain in a straightforward way. Numerical tests against analytical solution and spectral methods show an excellent agreement after PML solves the boundary problem in the Chebyshev domain, which demonstrates the accuracy of the REM algorithm and the usefulness of the PML absorbing boundary.

Time evolution of the electric field using the rapid expansion method with pseudospectral evaluation of spatial derivatives — Part 2: Inclusion of anisotropy and the earth-air interface

We have evaluated an extension of the 3D 3C rapid-expansion method for time-domain electromagnetic modeling with pseudospectral evaluation of spatial derivatives that includes anisotropic conductivity and the earth-air interface. We found that transverse isotropic anisotropy can be included in the modeling with the manipulation of the conductivity tensor. We model the response of the earth-air interface by using the upward continuation of the time derivative of the magnetic induction. All three electric field components are collocated with the electric conductivities and are modeled independently and simultaneously with spectral accuracy in space and time. Numerical tests against the analytical solution for a half-space and spectral methods for 1D anisotropic layered earth models demonstrate the excellent accuracy of this approach.

Power Flow in a Multi-Frequency HVac and HVdc System: Formulation, Solution, and Validation

This paper proposes a novel power flow formulation and solution algorithm for a generalized large-scale interconnected transmission system encompassing multi-frequency HVac and HVdc grids having arbitrary numbers of buses, topologies, and operating frequencies. Back-to-back and ac/dc voltage-source converters are employed to interconnect and control the voltage and power interchange between two power grids operating at different frequencies. The power Flow formulation is based on a steady-state model of back-to-back and ac/dc converters operated in centralized and distributed droop control strategies. Each power grid is represented by a set of nonlinear power balance equations. These equations are solved simultaneously using a unified power flow algorithm, taking into account generator and converter limits. It is shown that the solution convergence is achieved rapidly despite the system size, topology, and converter control strategies. The efficacy and accuracy of the proposed steady-state solution algorithm are demonstrated by comparing the numerical solution to the one obtained by time-domain electromagnetic models of multi-frequency HVac and HVdc transmission systems with fully controllable back-to-back and ac/dc converters. The results obtained by using the proposed algorithm and the time-domain simulation are practically identical.

Weighted Goal-oriented Adaptive Finite-element for 3D Transient EM Modeling

The unstructured finite-element method has been widely used in 3D time-domain electromagnetic (EM) modeling due to its flexibility for modeling rugged topography and complex underground structures. However, how to generate high-quality grids becomes the key to high-accuracy EM responses. We have developed a weighted goal-oriented adaptive finite-element method based on hybrid posterior error estimation in combination with unstructured vector finite-element method and Backward Euler scheme to create an effective mesh. By introducing a weighting factor and adjusting the relative weights of the hybrid posterior errors, the numerical accuracy and convergence rate are greatly improved. To handle the huge difference of EM responses at different time channels, we introduce another weighting factor defined by the exponential power of time to achieve a synchronous refinement of shallow and deep meshes. The numerical experiments on a homogenous half-space model show that our algorithm performs better than the traditional adaptive method both from the accuracy and convergence. Further, we also test the effectiveness of our algorithm for modeling different abnormal bodies under a topographic earth.

Modeling L-Band Reflection and Emission From Seawater, Foam, and Whitecaps Using the Finite-Difference Time-Domain Method

Reflection and emission from flat and rough seas with embedded whitecaps (WCs) are investigated at L-band using a custom finite-difference time-domain electromagnetic model. The model is applied to multiple layers, with vertically inhomogeneous dielectric profiles representing foam and spray overlying a homogeneous seawater layer. The foam and spray layers are adapted from an L-band radiative transfer model, and the rough sea surface is a statistical realization of the Kudryavtsev wave spectrum model. The 1-D and 2-D model versions are validated for a flat sea with optional foam cover, and the emissivity effects of WCs embedded in flat and rough seas are investigated. An overlying spray layer is found to markedly reduce WC detectability. Possible applications are the stochastic simulation of WC cover and its effect on emissivity at various wind speeds, and the effects of wave and WC shape on emissivity.

Ground-source Airborne Time-domain ElectroMagnetic (GATEM) modelling and interpretation method for a rough medium based on fractional diffusion

Ground-source Airborne Time-domain ElectroMagnetic (GATEM) modelling and interpretation method for a rough medium based on fractional diffusion

Coupled simulation of electromagnetic induction and induced polarization effects using stretched exponential relaxation

We have developed a new algorithm for 3D time-domain electromagnetic (EM) modeling, taking full account of induced polarization (IP) and the coupling between EM and IP effects. The algorithm can be used to model grounded source IP surveys that indicate EM induction effects and airborne time-domain EM surveys that exhibit IP effects. IP effects are most often approximated as static or modeled in the frequency domain, using frequency-dependent electrical conductivity. It is difficult to translate the frequency-dependent conductivity approach directly to the time domain in a computationally efficient manner. We take an alternative approach in which we model IP relaxations in time using the stretched exponential (SE) function. We incorporate this IP model into a direct time-stepping discretization of the quasistatic time-domain Maxwell equations. We found that modeling of IP effects with this SE approach is asymptotically equivalent to the commonly used Cole-Cole model of IP transformed to the time domain. We have implemented our algorithm using efficient numerical methods that allow it to tackle large-scale problems and are amenable to use in inversion. In particular, we have developed a parallel time-stepping technique that allows us to compute transient electric fields at multiple time steps simultaneously. We demonstrate the behavior of the SE model of IP decay and the efficiency of our algorithm by applying it to synthetic numerical examples that simulate a grounded source IP survey with significant EM effects and a concentric-loop airborne EM sounding over a chargeable body.

Adaptive finite element for 3D time-domain airborne electromagnetic modeling based on hybrid posterior error estimation

Airborne electromagnetic (AEM) forward modeling has been extensively developed in past years. However, not much attention has been paid to the adaptive numerical algorithms for time-domain electromagnetic modeling. We have created an adaptive method that can generate an effective mesh for time-domain 3D AEM full-wave modeling using an unstructured finite-element method and a backward Euler scheme. For the estimation of the posterior error in the adaptive process, we use a hybrid technique based on the continuity of the normal current density for modeling the off-time channels, and on the continuity of the tangential magnetic field for the on-time channels. To improve the stability of the forward modeling and control the number of grids in the adaptive process, a random grid-selection technique is applied. We check the modeling accuracy of the algorithm by comparing our adaptive results with the semianalytical solution for a time-domain AEM system over a homogeneous half-space. Furthermore, we test the effectiveness of our algorithm for multiple-source time-domain AEM systems by analyzing the meshes generated by the adaptive method and the model results. Finally, we study the topographic effect by calculating time-domain AEM responses over a hill model with an abnormal body embedded.

Time domain electromagnetic‐induced polarisation: extracting more induced polarisation information from grounded source time domain electromagnetic data

ABSTRACTElectrical induced polarisation surveys are used to detect chargeable materials in the earth. For interpretation of time domain electrical‐induced polarisation data a common procedure is to first invert the direct current data (electric current on time) to recover conductivity and then invert the induced polarisation data (current off‐time) to recover chargeability. This direct current‐induced polarisation inversion procedure assumes that the off time data are free of secondary electromagnetic induction effects. To comply with this, early time data are often discarded or not recorded. For mid‐time data, an electromagnetic decoupling technique, which removes electromagnetic induction in the observations, needs to be implemented. Usually, responses from a half‐space or a layered earth are subtracted. Recent capability in three‐dimensional time domain electromagnetic forward modelling and inversion allows to revisit these procedures. In a Time domain electromagnetic‐induced polarisation survey, a high sampling rate allows early time channels of the electromagnetic data to be recorded. The recovery of chargeability then follows a three‐step workflow: (i) invert early time channel time domain electromagnetic data to recover the three‐dimensional conductivity; (ii) use that conductivity to compute the time domain electromagnetic response at later time channels and subtract this fundamental response from the observations to extract the induced polarisation responses, and (iii) invert the induced polarisation responses to recover a three‐dimensional chargeability. This workflow effectively removes electromagnetic induction effects in the observations and produces better chargeability and conductivity models compared with conventional approaches. In a synthetic example involving a gradient array, we show that the conductivity structure obtained from the early time channel data, which are usually discarded, is superior to that obtained from the steady state direct current voltages. This adds a further reason to collect these electromagnetic data.

Preliminary Study of 2-D Time Domain Electromagnetic (TDEM) Modeling to Analyze Subsurface Resistivity Distribution and its Application to the Geothermal Systems

2-D Time Domain Electromagnetic (TDEM) has been successfully conducted to illustrate the value of Electric field distribution under the Earth surface. Electric field compared by magnetic field is used to analyze resistivity and resistivity is one of physical properties which very important to determine the reservoir potential area of geothermal systems as one of renewable energy. In this modeling we used Time Domain Electromagnetic method because it can solve EM field interaction problem with complex geometry and to analyze transient problems. TDEM methods used to model the value of electric and magnetic fields as a function of the time combined with the function of distance and depth. The result of this modeling is Electric field intensity value which is capable to describe the structure of the Earth’s subsurface. The result of this modeling can be applied to describe the Earths subsurface resistivity values to determine the reservoir potential of geothermal systems.

Three-Dimensional Modeling of TDEM Study for Carbon Capture Storage

TDEM (Time Domain Electromagnetic) method is a sounding geophysical method using electromagnetic wave generated by the electrical current source to image cross section of earth’s subsurface. TDEM using galvanic source (grounded wire) is one of TDEM acquisition technique which has flexible properties for the complex topography of measurement area. Three-dimensional forward and inversion modeling technique of TDEM with galvanic source still develops until now. Three-dimensional modeling is required because three-dimentional structure can influence TDEM signal which has a dimension of z-axis direction only. In this paper, We have been developing a 3D forward modeling program applying finite difference time domain method for 3D subsurface models. We can assess a distribution of TDEM synthetic data affected by 3D model. Using this 3D TDEM modeling program synthetic data has been generated as the function of transmitter and receiver position in 3D model space. Furthermore, this program can be used to simulate a conductivity change of reservoir model as consideration of reservoir monitoring implementation.

Effective Permittivity of 3-D Periodic Composites With Regular and Irregular Inclusions

This paper explores the effective temporal surface-illuminated properties of two-component composites consisting of inclusions of regularly-and irregularly-shaped crystals in a matrix. Time-domain electromagnetic modeling using the finite integration technique is used to calculate scattering (S-) parameters, and from these, the effective relative permittivities are calculated. It is shown that the orientation of inclusions with high permittivity contrast affects the effective electrical permittivity of a composite mixture. For both low and high contrast inclusions, fields localize at edges and corners of the irregular inclusion in a manner not dependent on boundary conditions used in simulation.

Modelling investigations of DBRs and cavities with photonic crystal holes for application in VCSELs

We investigate the reflection spectra of distributed Bragg reflectors (DBRs) and DBR cavities with and without photonic crystal holes fabricated within them. A finite-difference time domain (FDTD) electromagnetic model which is considered to provide the exact solution of Maxwell equations is used as a reference model. Two simplified modelling approaches are compared to the FDTD results: an effective index model where the individual DBR constituent layers penetrated by holes possess an effective index and a spatial loss model where optical losses are introduced spatially where the holes are fabricated. Results of the FDTD and the spatial loss model show that optical loss determines the properties of an etched DBR and DBR cavity when the lattice constant of the holes of exceeds 1 μm and the hole depth is small. The spatial loss model compares well to the FDTD results for holes with a lattice period exceeding 1 μm. We also consider the realistic effect of angling the sides of the etched holes.