Lossy Soil Research Articles

Evaluation of the Inductive Coupling between Coplanar Concentric Coils in the Presence of the Ground

An analytical approach is presented that allows deriving an exact series-form representation for the flux linkage between two physically large concentric circular coils located on a lossy soil. The expression comes from a three-step analytical procedure. First, the integral expression for the flux linkage is converted into a double integral consisting of a finite and a semi-infinite integral. Next, the semi-infinite integral is recognized to be a well-known tabulated Sommerfeld integral, which may be analytically evaluated straightforwardly. Finally, applying Lommel’s expansion allows rewriting the remaining finite integral as a sum of elementary integrals amenable to analytical evaluation. As a result, the flux linkage between the two coils is given as a sum of spherical Hankel functions of the wavenumber in the air and in the ground, multiplied by a coefficient depending on the geometrical dimensions of the coils. The accuracy and robustness of the proposed formulation is tested by comparing its outcomes with those generated by numerical integration of the complete integral representation for the flux linkage and with the results provided by previous analytical approaches to the same problem. It is found that the use of the derived expression for the inductance makes it possible to obtain significant time savings as compared to numerical quadrature schemes.

A perfectly matched layer for the absorption of electromagnetic waves using differential forms in three-dimensional domains

As a significant contribution, we present a novel formulation of the complex frequency-shifted perfectly matched layer (CFS-PML) for differential forms, introducing the innovative concept of a directional incidence matrix. This paper explores the application of differential forms in simulating wave propagation problems in three-dimensional domains. To confine the unbounded domain, we utilize a discretization technique based on the CFS-PML. Additionally, we provide an illustrative example that involves a system comprising a GPR (Ground Penetrating Radar) horn antenna, air, lossy soil, and a buried sphere.

LEMP and ground conductivity impact on the direct lightning performance of a medium-voltage line

• Assessment of the LEMP influence on direct lightning overvoltages of medium-voltage distribution lines of the type equipped with a shield wire and surge arresters. • Comparison between the results obtained by a 3D-FDTD method and the LIOV-EMTP code. • The LEMP contribution on the overvoltages across insulators increases with increasing values of the soil conductivity. • The appropriate modeling of the LEMP effects is important for the lightning performance assessment of the type of lines considered in this paper. In medium-voltage distribution lines equipped with a multi-grounded shield wire and with surge arresters installed along the line at relatively short intervals, lightning outages associated with indirect lightning are less frequent than those associated with direct ones. The protection for this type of distribution lines is therefore dependent on the response to direct strikes. This paper presents and analyses the response to direct lightning overvoltages of lines of such a type located over a lossy soil considering the influence of the lightning electromagnetic pulse (LEMP), which is typically disregarded in the calculation of overvoltages due to direct strikes. The calculation results, performed by means of a three-dimensional finite-difference time domain (3D-FDTD) method and of the LIOV-EMTP code, indicate that the voltage across the insulator is enhanced by LEMP effects. In addition, it is shown that the enhancement due to the LEMP increases with the increase of the soil conductivity value. The modeling of the LEMP effects is therefore important for the accurate assessment of the lightning performance of medium-voltage distribution lines of the type considered in this paper, even when direct strikes are considered.

A Marching-on-in-Time Method of Moments for Transient Modeling of a Vertical Electrode Buried in a Lossy Medium

This article proposes a full-wave time-domain method for analyzing the transient behavior of a grounding electrode buried vertically in a lossy soil. In this method, the electrode is first approximated by a thin wire, and the modified image theory is utilized to account for the soil–air interface. The governing electric field integral equation (EFIE) is then derived with the current distribution along the electrode being the unknown quantities. Finally, the EFIE is solved by the time-domain method of moments based on a marching-on-in-time (MOT) procedure. This is done by expanding the unknown currents in terms of a finite linear combination of products of appropriate spatial and temporal basis functions, and adopting the Galerkin method in space and the point matching method in time. The MOT procedure makes the proposed method more efficient computationally than its rival frequency-domain method of moments (FD-MoM). The efficiency of the proposed method is demonstrated by comparing the lightning ground potential rise of various grounding electrodes with those obtained using the FD-MoM and a commercial numerical code.

A Computational Electromagnetics and Sparsity-Based Feature Extraction Approach to Ground-Penetrating Radar Imaging

In this paper, a feature extraction technique based on the electromagnetic representation of radar signals is presented. In particular, we focus on ground penetrating radar imaging, where we model the backscatter from varying two dimensional geometric shapes with arbitrary local coordinate rotations. Due to the electrically small nature of buried targets, and the bending of the radar signal at the air-soil interface we focus on exact methods to model the surface current density induced on scattering surfaces. Overcomplete basis sets are derived from the electromagnetic descriptions to represent the scene in a sparse manner. From this proposed modeling framework we devise a novel methodology to exploit the prediction of scattering behavior to extract features for classification from radar scenes when multiple buried scattering surfaces are present. We see that our method can identify and reconstruct buried scattering geometries in the presence of false targets that are brought about from the nonlinear nature of the exact electromagnetic modelling methods. A noniterative algorithm based on the conjugate of Green’s function is developed to solve for the surface current in an unknown domain using multi-frequency, multi-aperture data. Our modeling and feature extraction algorithms are numerically validated for different target shapes buried in lossy soil profiles.

Hybrid Chaotic Salp Swarm with Crossover Algorithm for Underground Wireless Sensor Networks

Resource management in Underground Wireless Sensor Networks (UWSNs) is one of the pillars to extend the network lifetime. An intriguing design goal for such networks is to achieve balanced energy and spectral resource utilization. This paper focuses on optimizing the resource efficiency in UWSNs where underground relay nodes amplify and forward sensed data, received from the buried source nodes through a lossy soil medium, to the aboveground base station. A new algorithm called the Hybrid Chaotic Salp Swarm and Crossover (HCSSC) algorithm is proposed to obtain the optimal source and relay transmission powers to maximize the network resource efficiency. The proposed algorithm improves the standard Salp Swarm Algorithm (SSA) by considering a chaotic map to initialize the population along with performing the crossover technique in the position updates of salps. Through experimental results, the HCSSC algorithm proves its outstanding superiority to the standard SSA for resource efficiency optimization. Hence, the network's lifetime is prolonged. Indeed, the proposed algorithm achieves an improvement performance of 23.6% and 20.4% for the resource efficiency and average remaining relay battery per transmission, respectively. Furthermore, simulation results demonstrate that the HCSSC algorithm proves its efficacy in the case of both equal and different node battery capacities.

The effect of the inclined lightning channel on electromagnetic fields and the induced voltages on overhead lines

In this study, the effect of lightning channel inclination on above-ground lightning electromagnetic (LEM) fields and their induced voltages on the overhead lines at different distances from stroke location (SL) in the presence of lossy soil ground is investigated. To this end, the finite element method is used to solve the full-wave Maxwell’s equations. The results show that channel inclinations affect LEM fields significantly at all distances from the SL. At an equal distance from SL, the observation point position relative to the lightning channel is important, and LEM fields of the points located on the horizontal axis of the lightning channel are affected more than other points. If the ground is more conductive, increasing channel inclination affects the radial component of the electric field at a close distance to the SL more; if the ground is more resistive, increasing channel inclination angle affects the radial component of the electric field at a far distance to SL more significantly. The vertical electric fields and azimuthal magnetic fields are slightly affected by ground conductivity but significantly affected by the position and channel inclination angle. Seven different states are considered for the channel position relative to the overhead line, and the lightning-induced voltage along the line is calculated at three points. The obtained results show that position and soil electrical parameters significantly affect the peak and wave shape of the induced voltage. If the lightning channel passes above the overhead line, the induced voltage peak will increase at points near the SL. If the horizontal axis of the lightning channel is parallel to the overhead line, the induced voltage peak will increase for the ground with lower conductivity by increasing the channel inclination angle. In this case, at distances farther from the SL, the effect of increasing the channel angle is negligible for high-conductivity grounds, but the induced voltage peak for less conductive grounds will increase. If the lightning channel's horizontal axis is perpendicular to the overhead line and the lightning channel does not pass above the overhead line, close to the SL, the induced voltage peak will decrease by increasing channel angle. At points far from the SL, increasing the channel angle in the low-conductivity ground will increase the voltage peak, and grounds with larger conductivity will decrease the voltage peak.

Energy‐Spectral Efficiency Optimization in Wireless Underground Sensor Networks Using Salp Swarm Algorithm

Achieving high data rate transmission is critically constrained by green communication metrics in Wireless Sensor Networks (WSNs). A unified metric ensuring a successful compromise between the energy efficiency (EE) and the spectral efficiency (SE) is, then, an interesting design criterion in such systems. In this paper, we focus on EE‐SE tradeoff optimization in Wireless Underground Sensor Networks (WUSNs) where signals penetrate through a challenging lossy soil medium and nodes’ power supply is critical. Underground sensor nodes gather and send sensory information to underground relay nodes which amplify‐and‐retransmit received signals to an aboveground sink node. We propose to optimize source and relay powers used for each packet transmission using an efficient recent metaheuristic optimization algorithm called Salp Swarm Algorithm (SSA). Thus, the optimal source and relay transmission powers, which maximize the EE‐SE tradeoff under the maximum allowed transmission powers and the initial battery capacity constraints, are obtained. Further, we study the case where the underground medium properties are dynamic and change from a transmission to another. For this situation, we propose to allocate different maximum node powers according to the soil medium conditions. Simulation results prove that our proposed optimization achieves a significant EE‐SE tradeoff and prolongs the network’s lifetime compared to the fixed allocation node power scheme. Additional gain is obtained in case of dynamic medium conditions.

Parametric dependence of lightning impulse behavior of grounding electrodes buried in a dispersive and ionized lossy soil under first- and subsequent-stroke currents

Purpose The purpose of this paper is to investigate the simultaneous effects of ionization and dispersion of soil on the impulse behavior of grounding electrodes under first and subsequent stroke currents. Design/methodology/approach A recently introduced technique called improved multi-conductor transmission line (MTL) is simplified for grounding electrodes buried in both-affected soils. Findings The simulation results show that including the two effects simultaneously in highly resistive soils under high-valued subsequent stroke current is recommended. Otherwise, simultaneous effects can be disregard. Originality/value To the best of the authors’ knowledge, there is no research on sensitivity analyses for the simultaneous inclusion of the two effects on the effective length and the induced voltage on the soil surface. To this end, the simplified MTL is applied to the grounding electrodes. The simulation results show that the computational efficiency in comparison with previous methods is, first, considerably increased. Second, the simultaneous effects result in decreasing the soil surface voltage with respect to situations where either ionization or dispersion is taken into account (single-affected soils). In other words, the performance of grounding systems is improved. Third, the effective length in both-affected soil is has a middle value with respect to the single-affected soil. Such findings practically and financially are of importance.

Multiview Synthetic Aperture Ground-Penetrating Radar Detection in Rough Terrain Environment: A Real-Time 3-D Forward Model

A major problem with forward-looking ground-penetrating radar (FLGPR) detection of buried explosive threats is the scattering from the rough ground surface. The authors have previously developed a real-time 3-D algorithm for single-view emulation of synthetic aperture FLGPR scattering from rough terrain at low grazing angles. This article extends the method to the real-time 3-D simulation of a multiview moving platform transmitter/receiver array moving as fast as 15 km/h. The need to perform the new calculation at every frame for the moving antenna array platform is shown to be unnecessary, with the requirement relaxed to once for only a single frame at the center of 10–20 m forward interrogation range, leading to about 50 times faster computation. The computation of the scattered waves comprising surface clutter is reduced for all moving frames to a mere multiplication of three matrices: a pre-computed impulse response matrix of rough terrain, a pre-computed correction matrix of moving frames, and a matrix characterizing the transmitting input signal. The method is evaluated via 3-D Monte Carlo simulation for various rough surface parameters, and its applicability for subsurface scattering reconstruction to characterize the buried threat objects is shown. For a vehicle-mounted FLGPR detection system, this leads to a significant saving of computation resources. Our developed algorithm provides 3-D modeling of rough terrain scattering for lossy and frequency-dispersive soil and compares well with full-wave finite-difference frequency-domain (FDFD) method computation.

A Semi-Analytical Method to Evaluate Lightning-Induced Overvoltages on Overhead Lines Using the Matrix Pencil Method

Lightning electromagnetic fields can couple to overhead power transmission and distribution lines, causing serious effects to the power system. Lightning electromagnetic fields that couple to overhead lines have a nonuniform distribution along the line conductors. Therefore, to ensure the accuracy of the numerical calculation results, a large number of discretization points are needed along the line, which might dramatically increase the computation time since the evaluation of lightning electromagnetic fields in the presence of a lossy soil involves, in general, Sommerfeld integrals, or, even in the case of a perfectly conducting ground, numerical integration along the channel. This paper proposes a new approach to address this problem. The proposed approach is based on the Agrawal et al . coupling model, in which the horizontal lightning electric field along the line is represented by the complex exponential functions in the frequency domain using the matrix pencil method. The method is highly efficient in terms of computation time since the lightning-induced response of the line can be solved semi-analytically. The proposed approach is validated by two different validation examples.

A compressive sensing-based computational method for the inversion of wide-band ground penetrating radar data

This work presents an innovative computational approach for the inversion of wideband ground penetrating radar (GPR) data. The retrieval of the dielectric characteristics of sparse scatterers buried in a lossy soil is performed by combining a multi-task Bayesian compressive sensing (MT-BCS) solver and a frequency hopping (FH) strategy. The developed methodology is able to benefit from the regularization capabilities of the MT-BCS as well as to exploit the multi-chromatic informative content of GPR measurements. A set of numerical results is reported in order to assess the effectiveness of the proposed GPR inverse scattering technique, as well as to compare it to a simpler single-task implementation.

A Novel Approach for Qualitative Imaging of Buried PEC Scatterers

A new linear approach for support reconstruction of impenetrable objects is described and tested in case of scattered field data collected in Ground Penetrating Radar measurement configuration. Starting from the considerations that in high conductivity scatterers the currents induced inside the scatterers are only localized on its boundary and that they take up only few pixels of the entire investigation domain, a sparsity promoting inversion technique is formulated. The flexibility of the approach allows to counteract the specific difficulty to work under “aspect limited” measurement configurations, as the one at hand. Examples with numerical noisy data are given to demonstrate and validate the effectiveness of the method in localizing and in retrieving the shape of the unknown objects buried in lossy soil.

Exploiting sparsity and field conditioning in subsurface microwave imaging of nonweak buried targets

AbstractAn efficient inverse scattering strategy is proposed to achieve dielectric characterization of buried objects in lossy soils. The approach takes advantage of Virtual Experiments and Compressive Sensing to obtain quantitative reconstructions of nonweak targets which are nonsparse in the pixel representation basis, commonly adopted in microwave imaging. In addition, an original strategy is adopted to overcome the relevant information lack arising when data are gathered under aspect‐limited configurations, such as in ground penetrating radar (GPR) surveys. The proposed strategy significantly outperforms the results achievable with the “state of the art” standard approaches since it allows to achieve nearly optimal reconstructions within a linear framework and without increasing the overall computational burden. Numerical examples with simulated data are given to show the feasibility of the proposed strategy.

Evaluation of a Direct‐Coupled Time‐Domain Reflectometry for Determination of Soil Water Content and Bulk Electrical Conductivity

Core Ideas TDR‐315 sensors could be calibrated using conventional TDR methodologies. Soil water content calibrations using conventional TDR and TDR‐315 were comparable. Measured travel time using TDR‐315 was insensitive to soil electrical conductivity. Signal degradation in coaxial cables and interconnects is a long‐standing problem in the practical deployment of time‐domain reflectometry (TDR) for soil water monitoring. Acclima, Inc. has recently commercialized a TDR sensor (TDR‐315) with all electronics required for waveform acquisition embedded in the probe head. We calibrated ten TDR‐315 sensors and conventional TDR for apparent permittivity (Ka) and bulk electrical conductivity (σa) measurements. Also, soil water content calibrations were completed for a Pullman (fine, mixed, superactive, thermic torrertic Paleustolls) clay loam soil. Lastly, the sensitivity of Ka to σa was examined using a saturated solute displacement experiment with both probe technologies installed in a column packed with Pullman clay loam. A range of σa (0.65–2.8 dS m−1) was established by equilibrating the column with 0.25 dS m−1 CaCl2 and introducing a step pulse of 7.3 dS m−1 CaCl2. Permittivity calibrations of the TDR‐315 could be accomplished with conventional TDR methods and with similar sampling errors. Conventional calibrations of σa using long time amplitudes yielded a linear response for σa ≤ 3 dS m−1, above which the response was nonlinear. The fitted water content calibrations of the Pullman clay loam for the TDR‐315 were nearly indistinguishable from conventional TDR calibrations with similar root mean square errors (0.017–0.020 m3 m−3). Response of the two measurement technologies in a lossy soil during changing solution conductivities demonstrated that, in contrast to conventional TDR, travel time measured using acquired TDR‐315 waveforms was insensitive to σa up to 2.8 dS m−1.

Time-domain forward and inverse modeling of lossy soils with frequency-independent Q for near-surface applications

In this paper, we are concerned with a full-waveform-based methodology that allows the simultaneous imaging of the soil's stiffness and attenuating properties, using solely the soil's surficial response to probing waves.To date, field observations of small-strain wave attenuation in geomaterials at moderate spatial scales suggest that a commonly used metric of intrinsic and apparent attenuation, the seismic quality factor Q, is frequency-independent for a wide part of the frequency spectrum, including the frequency range of interest to seismic applications. We discuss first the forward simulation of waves in near-surface soil deposits directly in the time-domain using simplified models that adequately approximate nearly frequency-independent Q. To this end, we first review various attenuation models that aim at reproducing the frequency-independent Q behavior, and conclude, supported by site analyses, that, even though a generalized Maxwell body with eight Maxwell elements in parallel (GMB8) provides the best fit to frequency-independent Q, we favor a version of it with fewer parameters (GMB2), in order to reduce modeling complexity, while still retaining good agreement with the GMB8 model.We report on forward site analyses that lend credence to the choice of the GMB2 simplified model. We, then, use the GMB2 constitutive relation in the context of full-waveform inversion, and report on numerical experiments that lead to the imaging of the soil's properties in heterogeneous semi-infinite domains.

Parametric Study of Transient Electromagnetic Fields Due to Overhead Transmission Lines and Buried Cables in the Vicinity of Lossy Ground

In this paper, the problem of calculating transient electromagnetic fields due to frequency-dependent multiconductor overhead transmission lines above lossy ground and underground cables buried in lossy soil is studied by decomposing the transmission line into a number of small segments. A modified finite-difference time-domain technique is applied to find the current passing through each segment of the excited transmission line. The contribution of each segment on the total electric and magnetic fields is calculated using two frequency-domain analytical techniques. The theoretical background and extent of validity of each technique are presented, and the results derived by applying each method are compared with those obtained using a commercial software package. The time-domain solution is then obtained using Fourier and Inverse Fourier transforms. Finally, the effects of different electrical and geometrical parameters, such as conductivity and relative permittivity of the ground and conductor sag of the transmission line, are studied.

THE E-PILE+SMCG FOR SCATTERING FROM AN OBJECT BELOW 2D SOIL ROUGH SURFACE

A rigorous fast numerical method called E-PILE+SMCG is introduced and then used in a Monte Carlo study of scattering from a three dimensional perfectly electrical conductor (PEC) object below lossy soil rough surface. This method is the three dimensional (3D) extendability of PILE (Propagation-Inside-Layer Expansion) method which is proposed for two dimensional (2D) scattering problem. The rough surface with Gaussian proflle is used to emulate the realistic situation of statistically rough surface, while the tapered incident wave is chosen to reduce the truncation error. The 3D angular correlation function (ACF) and bistatic scattering coe-cient (BSC) are studied and applied to the detection of a target embedded in the clutter. The ACF is computed by using numerical method with circular azimuthal angle averaging technique. Because of its success in suppressing the clutter scattering, the technique appears attractive in real life

A strategy for the determination of the dielectric permittivity of a lossy soil exploiting GPR surface measurements and a cooperative target

In this paper we deal with an indirect measure of the dielectric permittivity of the soil starting from GPR surface data collected on a buried “cooperative” target, meant as an object buried on purpose and whose extent is known a-priori. This target is exploited in order to achieve, from its image obtained from a suitable GPR data processing, an indirect measure of the dielectric permittivity of the embedding soil. GPR data processing is based on a linear microwave tomographic approach funded on the Born Approximation. Using this Born approach on two-dimensional inversion tests, we investigate the effect of the soil's electrical conductivity and permittivity on this indirect measure and demonstrate that the electrical field scattered by a spot-like buried object permits an accurate estimation of the soil permittivity even when no information of the soil conductivity is available.

Improving GPR Image Resolution in Lossy Ground Using Dispersive Migration

As a compact wave packet travels through a dispersive medium, it becomes dilated and distorted. As a result, ground-penetrating radar (GPR) surveys over conductive and/or lossy soils often result in poor image resolution. A dispersive migration method is presented that combines an inverse dispersion filter with frequency-domain migration. The method requires a fully characterized GPR system including the antenna response, which is a function of the local soil properties for ground-coupled antennas. The GPR system response spectrum is used to stabilize the inverse dispersion filter. Dispersive migration restores attenuated spectral components when the signal-to-noise ratio is adequate. Applying the algorithm to simulated data shows that the improved spatial resolution is significant when data are acquired with a GPR system having 120 dB or more of dynamic range, and when the medium has a loss tangent of 0.3 or more. Results also show that dispersive migration provides no significant advantage over conventional migration when the loss tangent is less than 0.3, or when using a GPR system with a small dynamic range.