Low-frequency Electromagnetics Research Articles

The effectiveness of very low-frequency electromagnetics (VLF-EM) method in detecting buried targets at a controlled site

The ever-increasing anthropogenic activities that pose a significant threat to environmental security and sustainability have spurred geophysicists to review enhance geophysical techniques for shallow geophysical investigations, especially in identifying illegal buried materials. This article applied very low-frequency electromagnetic (VLF-EM) at an experimental geophysical site (EGS) to examine the geophysical response over various buried targets. The VLF-EM data acquired on the site with and without buried targets demonstrate the nature of the anomalies and the characteristic signals of the buried targets. There are significant variations in the anomalies source-bodied between the site with and without buried targets. The result of the pre-burial investigation shows no major contrast in the equivalent current density values across the site without targets. Minors and major anomalies were encountered after burying the targets corresponding to the buried targets. Some signals become stronger over a large buried target. However, there were a few undetected targets and some cases of unsatisfied results, which were also discussed. The performance of the VLF-EM method in terms of depth estimation was also examined. A significant variation was noted due to the presence of the buried targets and it was noted that the current density seems to always emerge maximally and minimally around the conductor targets and non-conductive targets, respectively. The failure of the VLF-EM to detect the buried pipes in various orientations was examined. The VLF-EM method is more consistent at small spacing and it can be very useful for identifying underground metallic and non-metallic targets. The study successfully provides useful information to complement the complexity of the use of geophysical methods while enhancing the subsurface information and understanding of VLF-EM anomalies or responses generated by various targets such as subsurface geological structures, buried waste contaminants and underground utilities to boost environmental studies and engineering investigations.

Comparison of reduced basis construction methods for Model Order Reduction, with application to non-linear low frequency electromagnetics

Numerical simulation is more and more used during the design stage of a manufactured product in order to optimize its performances. However, it is often too time consuming, particularly when it is used to solve optimization problems, preventing an intensive usage. A-posteriori Model Order Reduction methods can be very effective to shorten the computational time. An approximated solution is then sought in a space of small dimension defined by a reduced basis. The accuracy of such methods is highly dependent on the choice of the reduced basis, extracted from preliminary numerical simulation. The method usually applied to construct such reduced basis is based on the Singular Value Decomposition (SVD), which can be time consuming, and is not adapted when a large collection of preliminary numerical simulations must be used to construct the basis. An alternative to this approach has been proposed recently with the Maximum Entropy Snapshot Sampling (MESS) method. In this paper, we propose to compare these methods with other approaches usually used for clustering or data classification based on vectors distance calculation, like the Centroidal Voronoi Tessellation (CVT), Density Based Spatial Clustering of Applications with Noise (DBSCAN), and Clustering Using Representatives (CURE). The methods are compared on a complex and realistic nonlinear problem in low frequency electromagnetics. The quality of the reduced bases obtained by the different methods are compared. Then, field distributions and global quantities, like eddy current losses and magnetic energy, are computed from the reconstructed results, to further analyze the quality of the reduced bases.

EFFECT OF LOW-FREQUENCY ELECTROMAGNETICS (LFE) ON MUSCLE SATELLITE CELLS DIFFERENTIATION AND IMMUNE SYSTEM IN RAT

Spinal cord injury (SCI) is a severe neurological disease. Although surgery within 8[Formula: see text]h after SCI can substantially reduce paraplegia, most patients still suffer from hypomusculariasis after neuron recovery, which results in insufficient lower limb muscles to support bodyweight. Currently, there is no effective method to prevent muscle atrophy. Previous studies have shown that low-frequency electromagnetics (LFE) can stimulate the differentiation, proliferation and fusion of muscle satellite cells, however, the optimal electromagnetic strength and effects on the immune system have not been established. Here, we investigated the influence of LFE at different electromagnetic strengths on muscle cell recovery and assessed the impact of chronic LFE on the immune system of SCI rats. The rat immune system was rapidly activated after SCI. High-energy LFE provoked intensive immune responses, while low-energy LFE did not affect immune responses. Simultaneously, LFE effectively prevented myotube reduction and atrophy in SCI rats. The mRNA and protein levels of Pax7 and MyoD were increased after LFE at both high and low electromagnetic strengths, with the latter leading to more robust increases. Indeed, LFE remarkably induced muscle cell fusion. Together, our results demonstrated that LFE activates muscle satellite cells via stimulating myogenic factors. Chronic low-energy LFE is a safe therapy with no adverse impact on the immune system of SCI rats. LFE with 1.5 mT energy should be considered as an optimal therapeutic strategy.

One-dimensional stacking miniaturized low-frequency metamaterial bulk for near-field applications

Metamaterials (MTMs) are very promising in engineering applications because they can be used to easily manipulate the spatial and temporal distributions of electromagnetic fields and waves. Nevertheless, studies on MTMs have been directed primarily toward high-frequency electromagnetics and optics. Consequently, the development and applications for MTMs in low-frequency electromagnetics still face some bottleneck problems and challenges. For example, deteriorated resonance strength and large unit dimensions are inevitable for low-frequency MTM unit cells. Moreover, the existing analytical, computational, and experimental methodologies for MTMs are not applicable for low-frequency cases. To address these problems, one-dimensional compact stacking miniaturized MTM bulk in the kHz frequency band, which is the lowest resonance frequency for passive MTMs reported to date in the literature, is proposed and fabricated. This work develops a miniaturized and high performance low-frequency MTM unit cell using a unit topology that consists of two spiral structures connected with a via and a lumped chip capacitor. A numerical model is proposed for performance simulations of the MTM unit cell, and a quality factor equivalence-based method is introduced. An experimental–numerical methodology is developed to extract the complex permeability of the MTM bulk. Comprehensive numerical computations and experimental studies significantly impact the investigation of the extraordinary performance of MTM-based near-field electromagnetic devices. Both numerical and experimental results have confirmed the feasibility and applicability of the presented work, which reveals the extraordinary physical properties of novel MTM-based electromagnetic devices.

An Efficient Parallel Computing Method for the Steady-State Analysis of Low-Frequency Electromagnetics Using an Anti-Periodic Condition

In this article, an efficient parallel computing method is described based on the message passing interface (MPI) for the steady-state analysis of low-frequency electromagnetics. Two frames of reference (the Eulerian frame and the Lagrangian frame) are used to account for the magnetic field behaviors with rigid-body motions, and an anti-periodic condition is exploited to reduce simulation time. The performance of the algorithm is demonstrated by two application examples.

Utilizing 2D Electrical Resistivity Tomography and Very Low Frequency Electromagnetics to Investigate the Hydrogeology of Natural Cold Springs Near Virginia City, Southwest Montana

Virginia City, Montana, is located in the northern Rocky Mountains of the United States. Two natural springs supply the city’s water; however, the source of that water is poorly understood. The springs are located on the east side of the city, on the edge of an area affected by landslides. 2D electric resistivity tomography (ERT) and very low frequency electromagnetics (VLF-EM) were used to explore the springs and landslides. Two intersecting 2D resistivity profiles were measured at each spring, and two VLF profiles were measured in a landslide zone. The inverted 2D resistivity profiles at the springs reveal high resistivity basalt flows juxtaposed with low resistivity volcanic ash. The VLF profiles within the landslide show a series of fracture zones in the basalt, which are interpreted to be a series of landslide scarps. Results show a strong correlation between the inferred scarps and local topography. This study provides valuable geological information to help understand the source of water to the springs. The contact between the fractured basalt and the ash provides a sharp contrast in permeability, which causes water to flow along the contact and discharge at outcrop. The fracture zones along the scarps in the landslide deposits provide conduits of high secondary permeability to transmit water to the springs. The fracture zones near the scarps may also provide targets for municipal supply wells.

Lean Cohomology Computation for Electromagnetic Modeling

Solving eddy current problems formulated by using a magnetic scalar potential in the insulator requires a topological pre-processing to find the so-called first cohomology basis of the insulating region, which may be very time-consuming for challenging industrially driven problems. The physics-inspired Dlotko–Specogna (DS) algorithm was shown to be superior to alternatives in performing such a topological pre-processing. Yet, the DS algorithm is particularly fast when it produces as output not a regular cohomology basis but a so-called lazy one, which contains the regular one but it keeps also some additional redundant elements. Having a regular basis may be advantageous over the lazy basis if a technique to produce it would take about the same time as the computation of a lazy basis. In the literature, such a technique is missing. This paper covers this gap by introducing modifications to the DS algorithm to compute a regular basis of the first cohomology group in practically the same time as the generation of a lazy cohomology basis. The speedup of this modified DS algorithm with respect to the best alternative reaches more than two orders of magnitudes on challenging benchmark problems. This demonstrates the potential impact of the proposed contribution in the low-frequency computational electromagnetics community and beyond.

Spectral Element Method and Domain Decomposition for Low-Frequency Subsurface EM Simulation

Low-frequency subsurface electromagnetic measurements are important tools for characterizing natural resources and environmental wastes. Rapid simulations of low-frequency subsurface electromagnetic measurements are still a challenge because of the large computational domain and low-frequency breakdown phenomenon. We develop an effective method to simulate these low-frequency subsurface electromagnetic measurements by using the spectral element method together with a domain decomposition method (DDM). A specific mesh has been designed based on the traveling wave nature in the air and the diffusion field nature in the underground space to greatly reduce the number of unknowns. The frequency-domain version of the Riemann solver (upwind flux) is used as an effective transmission condition to simulate the interactions between neighboring subdomains in DDM. Several numerical examples demonstrate the efficiency of the proposed approach in low-frequency subsurface electromagnetics simulations.

A telluric method for natural field induced polarization studies

Natural field induced polarization (NFIP) is a branch of low-frequency electromagnetics designed for detection of buried polarizable objects from magnetotelluric (MT) data. The conventional approach to the method deals with normalized MT apparent resistivity. We show that it is more favorable to extract the IP effect from solely electric (telluric) transfer functions instead. For lateral localization of polarizable bodies it is convenient to work with the telluric tensor determinant, which does not depend on the rotation of the receiving electric dipoles.Applicability of the new method was verified in the course of a large-scale field research. The field work was conducted in a well-explored area in East Kazakhstan known for the presence of various IP sources such as graphite, magnetite, and sulfide mineralization. A new multichannel processing approach allowed the determination of the telluric tensor components with very good accuracy. This holds out a hope that in some cases NFIP data may be used not only for detection of polarizable objects, but also for a rough estimation of their spectral IP characteristics.

A multidisciplinary study of “Benetutti” thermal waters (Tirso Valley, Sardinia)

We report a multidisciplinary study of Benetutti thermal waters based on hydrochemistry, isotopic techniques, structural geology and geophysical surveys. Seven thermal waters and two cold spring waters have been studied. Thermal waters show temperature values ranging between 28 °C and 42 °C, a medium mineralization and a sodium-chloride chemical hydrofacies. Isotopes of the water molecule allowed verifying that these waters have not been affected by isotopic exchange phenomena with the Sardinian granite complex aquifer. VLF-EM (Very Low Frequency-Electromagnetics) surveys were undertaken for a rapid assessment of the distribution of thermal waters over vast areas. A northeast-southwest trend of high conductivity anomalies was revealed. This trend can be correlated to the occurrence of sub-parallel discontinuities along which thermal waters uprise.

Interference effects of aircraft on earth's electromagnetic response at very low frequency and low frequency

ABSTRACTOver the last few decades, very low frequency electromagnetics has been widely and successfully applied in mineral exploration and groundwater exploration. Many radio transmitters with strong signal‐to‐noise ratios are scattered in the very low frequency band and low frequency band. Based on experiences gained from ground measurements with the radio‐magnetotelluric technique operating in the frequency interval 1–250 kHz, broadband magnetometers have been used to cover both very low frequency (3–30 kHz) and low frequency (30–300 kHz) bands to increase the resolution of the near‐surface structure. The metallic aircraft as a conductive body will distort the magnetic signal to some extent, and thus it is important to investigate aircraft interference on the electromagnetic signal. We studied noise caused by rotation of an aircraft and the aircraft itself as a metallic conductive body with three methods: 3D wave polarization, determination of transmitter direction and full tipper estimation. Both very low frequency and low frequency bands were investigated. The results show that the magnetic field is independent of the aircraft at low frequencies in the very low frequency band and part of the low frequency band (below 100 kHz). At high frequencies (above 100 kHz), the signals are more greatly influenced by the aircraft, and the wave polarization directions are more scattered, as observed when the aircraft turned. Some aircraft generated noise mixed with radio transmitter signals, detected as ‘dummy’ signals by the 3D wave polarization method. The estimated scalar magnetic transfer functions are dependent on the aircraft flight directions at high frequencies, because of aircraft interference. The aircraft eigenresponse in the transfer functions (tippers) between vertical and horizontal magnetic field components was compensated for in the real part of the estimated tippers, but some unknown effect was still observed in the imaginary parts.

An assessment of the performance of the geophysical methods as a tool for the detection of zones of potential subsidence in the area southwest of Nakuru town, Kenya

The area to the southwest of Nakuru town in Kenya located within the Kenya Rift Valley is prone to incidences of ground subsidence especially toward the end of the heavy rain season. The zones affected by subsidence are typically linear, trending approximately north–south conforming to the structural trend of the Kenya Rift Valley. These ground subsidence incidences have in the past led to collapse of houses and damage to roads that happen to be located above the affected linear zones. This study set out to investigate the potential of geophysical methods to delineate these linear zones. Two profiles of lengths 2,430 and 2,850 m, respectively, were selected for this purpose. The study was conducted immediately after one major incidence of subsidence when the zones affected were still fresh and observable. Magnetics, very low-frequency electromagnetics (VLF-EM), and gravity methods were used in the study. The choice of these methods was dictated by their widely known applicability in the detection of linear structures, especially faults. The results of the study have shown that the linear zones affected yield good response to magnetic and VLF-EM methods. Anomalies similar to those detected across fresh subsidence zones were also detected at locations where there was no surface expression of subsidence, suggesting that the latter locations are potential zones of future subsidence. Further, there were locations along the profile that were without any anomalies. The relatively low sensitivity of the zones to the gravity method is attributed to the very narrow nature of these zone and hence limited low-density material to generate appreciable negative gravity anomalies. It is concluded from this study that geophysics permits identifying the potential areas to develop surficial collapse and to identify sectors that are potentially dangerous because they present similar signatures as the sectors with surficial evidence and sectors without anomalies. The sectors without anomalies are interpreted as having a different subsoil structure to that with sinkholes.

Determining a relationship between a newly forming sinkhole and a former dry stream using electric resistivity tomography and very low-frequency electromagnetics in an urban karst setting

Sinkhole formation is an ongoing hazard for urban karst settings, compromising construction foundations, and accelerating groundwater pollution. In Springfield, Missouri, the uppermost exposed unit is the Burlington limestone, a carbonate bedrock which is susceptible to karst formation, including caves and sinkholes. This study site concerns a detention basin near a major highway interchange, in which a new sinkhole is forming. Electric resistivity, very low-frequency electromagnetics, and dye-tracing surveys were performed at this sinkhole to determine its subsurface extent and any relation to surface features. The low resistivity associated with the sinkhole and thin soil contrasts with the high resistivity of the underlying Burlington limestone. This contrast highlights a curvilinear trough of thicker soil, which correlates with a former intermittent stream and represents a stream channel, which was graded and filled during construction of the highway and basin. The newly formed sinkhole lies entirely within this former stream channel. This relationship between the sinkhole and stream provides useful insights into the effects of urbanization on sinkhole formation. Knowledge of these relationships allows urban managers to better understand the risk this sinkhole poses to major highways and public buildings in the area.

Physics inspired algorithms for (co)homology computations of three-dimensional combinatorial manifolds with boundary

The issue of computing (co)homology generators of a cell complex is gaining a pivotal role in various branches of science. While this issue may be rigorously solved in polynomial time, it is still overly demanding for large scale problems. Drawing inspiration from low-frequency electrodynamics, this paper presents a physics inspired algorithm for first cohomology group computations on three-dimensional complexes. The algorithm is general and exhibits orders of magnitude speed up with respect to competing ones, allowing to handle problems not addressable before. In particular, when generators are employed in the physical modeling of magneto-quasistatic problems, this algorithm solves one of the most long-lasting problems in low-frequency computational electromagnetics. In this case, the effectiveness of the algorithm and its ease of implementation may be even improved by introducing the novel concept of lazy cohomology generators.

Using VLF-EM to delineate a fracture zone in basement granites for uranium exploration

This article describes a survey using low-frequency electromagnetics (VLF-EM) over an unconformity-related uranium mineralization in the northern part of India's Cuddapah Basin. The uranium occurs in granite close to the contact between basement granite and Srisailam sediments. The uranium mineralization is controlled by the basement fractures containing rich concentrations of coffinite and pitchblende. The basement granite is Palaeoproterozoic age.

Edge Elements and Current Diffusion

Current flow in the neighborhood of sharp conducting edges and corners is encountered in many applications of computational electromagnetics. Some examples include resonant cavities and waveguides of rectangular shape, cracks in metal components in nondestructive testing, and the edges and corners of the rail–armature contact in an electromagnetic launcher. Although the number of analytical solutions to such problems is small, it is generally believed that such solutions often involve singularities, high gradients, or discontinuities in one or more field components near the edge or corner. It has been demonstrated that the so-called edge elements can provide much more accurate predictions of global quantities (like resonant frequencies and scattering parameters) in the case of full-wave electromagnetics when field discontinuities or singularities are present. They have also been shown to better represent field discontinuities at material interfaces in magnetostatics and reentrant corners in low-frequency electromagnetics. This feature of edge elements is due to their ability to allow necessary jumps in field components at geometric or material discontinuities, as opposed to nodal elements, with the Coulomb gauge enforced, which can overconstrain the fields in certain situations. The main question of interest in this paper is whether edge elements give a similar advantage in the representation of current diffusion around a sharp edge. Both edge- and node-based formulations are considered, and the results are discussed.

Iterative Solvers for Singular Symmetric Linear Systems in Low Frequency Electromagnetics

In this paper, several methods based on Krylov methods are proposed to solve the singular linear systems from finite element method. Indeed, in the magnetostatic case, for A-formulation the system to solve is singular but it is auto-gauged by Krylov methods. However, due to the computation of residual vector all the methods (CG, MRTR, SQMR, MINRES) do not present the same behavior. Moreover, these methods are applied to eddy current problem. The numerical behavior are compared and analyzed.

Unified framework for an a posteriori error analysis of non-standard finite element approximations of H(curl)-elliptic problems

Recently, a unified framework for a residual-based a posteriori error analysis of standard conforming finite element methods as well as non-standard techniques such as nonconforming and mixed methods has been developed. This paper provides such a framework for an a posteriori error control of nonconforming finite element discretizations of H(curl)-elliptic problems as they arise from low-frequency electromagnetics. These nonconforming approximations include, among others, the interior penalty discontinuous Galerkin (IPDG) approach.

Integration of surface geophysical methods for fracture detection in crystalline bedrocks of southwestern Nigeria

The application of electrical imaging and very low frequency (VLF) electromagnetics was investigated for the purpose of delineating basement fracture zones, and to show how incorporating a priori information in numerical modelling would facilitate the location of fractured zones within a basement rock more precisely. To this end, direct current (DC) dipole–dipole resistivity and VLF modelling and inversion experiments were carried out to evaluate the efficacy of the methods in detecting low-resistivity fracture zones in a typical crystalline basement rock that is favourable for groundwater accumulation. Most wells drilled in such an environment usually have low yields. Results of the numerical experiment generally indicate that fractures covered by moderate overburden, and having considerable depth, extent, and thickness compared to the depth of fracture burial, produce good responses resulting in high-resolution resistivity images. Lower resolution resistivity images were obtained as the thickness of the overburden increased. Also, the model investigations indicate that width of the fracture zone plays a major role in controlling image resolution. Conclusions from the synthetic modelling were confirmed by resistivity and VLF data gathered across a suspected fault in a hard rock terrain of southwestern Nigeria. The results from the field data are in general agreement with the numerical modelling experiments.

Toward a more robust and accurate CEM fast Integral equation solver for IC applications

We review recent advances in fast algorithms for fast integral equation solvers that are useful for IC applications. We review fast solvers for Laplace's equation, which is about 10 times faster than the conventional fast multipole method. Then we review the physics of low-frequency electromagnetics, and the relevant low-frequency method of moments. We describe a fast solver that allows us to solve over one million unknowns on a workstation recently. In addition, we demonstrate the applications of these fast integral equation solvers to the lithography problem. In addition, we propose a scheme whereby we first characterize blocks of linear circuits with network S, Y, or Z parameters. Then a fast real-time convolution scheme is used to calculate the interaction of a linear circuit with nonlinear terminations such as transistors and diodes. Such a scheme requires no model-order reduction of the circuits.