Lossy Half-space Research Articles

Assessment of an Inverse Algorithm for Cylinders Localization

We examine how an algorithm for localizing cylinders of arbitrary known radius is affected by errors in the radius knowledge. Reflection mode multi-frequency multi-bistatic configuration is considered. The problem is first examined in far zone, where analytical results can be found. Then, numerical results for the near zone case are provided and a procedure to estimate the cylinder's radius, if it is not known, is introduced. The expected behavior is tested against simulated and experimental data for both perfectly electrical conducting and dielectric cylinders embedded into a lossless homogeneous background. Numerical results of localization of objects embedded into a lossy half space are also shown.

Horizontal linear antennas above a lossy half-space: A new model for the Sommerfeld's integral kernel

Unknown current distribution (UCD) and input impedance/admittance of a horizontal dipole antenna (HDA) placed above a homogenous and isotropic lossy half-space (LHS) will be determined in this paper. Integrals of Sommerfeld's type, which occur in potential expressions, will be solved approximately applying a new simple, very accurate and efficient model. Firstly, the accuracy of the proposed model for the Sommerfeld's integral kernel (SIK) is going to be verified, comparing the obtained results with corresponding ones of other authors. In order to illustrate validity of the proposed method, the system of integral equations of Hallen's type (SIE-H) will be numerically solved using the point-matching method (PMM), assuming the polynomial approximation for the current along the antenna conductors. Results obtained for the current distribution and input impedance of the observed HDA will be graphically illustrated and, also, compared with corresponding ones of other authors.

TIME DOMAIN ANALYTICAL MODELING OF A STRAIGHT THIN WIRE BURIED IN A LOSSY MEDIUM

This paper deals with an analytical solution of the time domain Pocklington equation for a straight thin wire of ¯nite length, buried in a lossy half-space and excited via the electromagnetic pulse (EMP) excitation. Presence of the earth-air interface is taken into account via the simplified reflection coefficient arising from the Modified Image Theory (MIT). The analytical solution is carried out using the Laplace transform and the Cauchy residue theorem. The EMP excitation is treated via numerical convolution. The obtained analytical results are compared to those calculated using the numerical solution of the frequency domain Pocklington equation combined with the Inverse Fast Fourier Transform (IFFT).

Computation of the scattered fields from a dielectric object buried in a medium with a periodic surface by a decomposition method

The electromagnetic scattering from a cylindrical dielectric object of arbitrary cross-section buried in a lossy dielectric half-space having a periodic surface is investigated using a new numerical method. The method is outlined for TM z (horizontally) polarised incident wave. The surface equivalence principle and a decomposition method are employed to form a set of electric field integral equations (EFIEs) for the currents on the object and the portion of the surface most strongly interacting with the object. Then, the method of moment (MoM) is used to solve the EFIEs in the frequency domain to obtain the scattered electric field.

A novel method to calculate transient response of thin-wire structure above the layered lossy half-space

A novel hybrid method combining time domain integral equation(TDIE) with finite difference time domain(FDTD) is proposed to calculate transient response of thin wire structure above a layered lossy half-space. The time domain reflections of electromagnetic waves from layered half-space are obtained by one-dimensional FDTD method. Then, transient response of thin-wire induced by two excitation sources (incident wave and reflected wave) is achieved by employing the TDIE. The computed results illustrate the feasibility and high efficiency of the presented scheme.

Comparison of analytical and boundary element modeling of electromagnetic field coupling to overhead and buried wires

The paper deals with various approaches for the analysis of electromagnetic field coupling to horizontal straight line of finite length in the presence of a lossy half-space based on the theory of thin wire antennas. The formulation is posed in the frequency domain and it is based on the corresponding Pocklington integro-differential equation. Throughout this work the Pocklington equation is solved numerically via the Galerkin–Bubnov scheme of the indirect boundary element method (GB-IBEM) and analytically. The obtained results are compared to NEC results and to the results obtained by applying the transmission line (TL) model, i.e. to the results obtained by solving the corresponding Telegrapher’s equations.

A Novel, Fast, Approximate Target Detection Technique for Metallic Target Below a Frequency Dependant Lossy Halfspace

The extinction pulse (E-Pulse) technique has been widely applied to problems involving radar target identification. In this paper a fast approximate target detection and recognition scheme based on the E-Pulse technique is proposed and applied to a subsurface target detection and recognition scenario. Previous studies have demonstrated that the target resonances for subsurface targets are closely related to the target resonances for a target within a homogenous environment. In the proposed method, the target resonance for the target in the homogenous medium will be used to construct the E-Pulse for target detection and recognition purposes. The details of the proposed method will be described in this paper. The obvious example of a target below a dielectric halfspace is the use of ground penetrating radar (GPR) for detecting and recognizing unexploded ordnance (UXO). However, instead of a GPR related scenario, a numerical example of a biomedically related problem, of a hip prosthesis model sited within a halfspace of homogenous human tissue model with realistic dielectric properties will be used to demonstrate the feasibilities of the proposed technique for target detection and recognition. The reasons for the choice of this particular example will also be explained in the paper.

Finite Formulation for Modeling Guided Wave Structures Embedded in a Lossy Half-Space

A Finite Formulation technique, the Cell Method, is applied to a transmission line embedded in a complex medium. Cell Method is a Finite Formulation numerical technique that uses a primal-dual cell complex and global (integral) variables instead of field variables (densities). A new time-harmonic finite formulation using a non-orthogonal dual mesh is presented that is based on choosing incenters of primal triangles as an alternative to barycentric dual points. In the incentric formulation, diagonal constitutive matrices are obtained and an eigenvalue problem is solved in the first step (zero-order approximation). A minimization procedure is then utilized to efficiently improve the accuracy of the zero-order solution. In this paper the effect of the non-perfectly conducting earth on the propagation constant is investigated as the location of a bare (or insulated) conductor passes through the interface of a lossy half space. It is observed that the propagation constant depends on the burial depth when it is less than the skin depth in the earth. It is shown that analytical (thin wire-based) approximations for the above-ground and buried cases fail when the conductor is close to or partially embedded in the interface.

Analysis of electromagnetic scattering from dielectric objects above a lossy half-space by multiresolution preconditioned multilevel fast multipole algorithm

In this study, a synthesis of the multilevel fast multipole algorithm (MLFMA) and the multiresolution (MR) preconditioning technique is presented for the analysis of scattering from homogeneous dielectric targets above a lossy half-space. The Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT) integral equation and the MLFMA are used for efficient analysis of scattering problems in half-space. The MR preconditioning technique is used to speed up the convergence rate of the iterative solver. The numerical results are presented to demonstrate that the proposed method is efficient for the scattering from homogeneous dielectric objects above a lossy half-space.

Direct use of discrete complex image method for evaluating electric field expressions in a lossy half space

A modelling technique is proposed for direct use of the discrete complex image method (DCIM) to derive closed-form expressions for electric field components encountered in the electric field integral equation (EFIE) representing a lossy half space problem. The technique circumvents time consuming numerical computation of Sommerfeld integrals by approximating the kernel of the integrals with appropriate mathematical functions. This is done by appropriate use of either the least-square Prony (LS-Prony) method or the matrix pencil method (MPM) to represent electric field expressions in terms of spherical waves and their derivatives. A comparison is made between the two methods based on the computation time and accuracy and it is shown that the LS-Prony method performs two–three times faster than the MPM in approximating the integral kernels depending on the platform. The main feature of the proposed technique is its ability for direct inclusion in the kernel of computational tools based on the method of moments solution of the EFIE. This can be viewed as an advantage over the conventional DCIM approximation of spatial Green's functions for mixed potential integral equation for cases where the problem in hand can be more efficiently represented by the EFIE (e.g. the thin-wire EFIE). The accuracy of the proposed technique is validated against numerical integration of Sommerfeld integrals for an arbitrary electric dipole inside a lossy half space.

EFFICIENT EVALUATION OF GREEN'S FUNCTIONS FOR LOSSY HALF-SPACE PROBLEMS

In this paper, a new technique is developed to evaluate e-ciently the Sommerfeld integrals arising from the problem of a current element radiating over a lossy half-space. The annihilation of the asymptote and the branch-point singular behavior of the spectral Green's function is used in this technique. The contributions of the subtracted asymptotic and singularity terms are calculated analytically. The annihilation results in a remaining integral that is very smooth and can be calculated adaptively by using Gaussian quadratures and extrapolation methods to accelerate the convergence of the oscillating integrand. The accuracy and e-ciency of the new technique has been conflrmed by comparison with literature, and the commercial software NEC. The application of the proposed technique provides a robust and rapid procedure to calculate spatial Green's functions which can be used in ground-wave propagation, and lightning return stroke channel modeling.

ELECTROMAGNETIC SCATTERING BY CONDUCTING BOR COATED WITH CHIRAL MEDIA ABOVE A LOSSY HALF-SPACE

Electromagnetic scattering by conducting bodies of revolution (BOR) coated with homogeneous chiral media above a lossy half-space is formulated in terms of the Poggio-Miller-ChangHarrington-Wu surface integral equation combined with combined field integral equation. A field decomposition scheme is utilized to split a chiral media into two equivalent homogeneous media. The spatial domain half-space Green’s functions are obtained via the discrete complex image method. Due to the rotational symmetry property of BOR, the method of moment for BOR (BORMoM) is applied to the linear system solved by the multifrontal direct solver. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.

EXACT ELECTROMAGNETIC FIELD EXCITED BY A VERTICAL MAGNETIC DIPOLE ON THE SURFACE OF A LOSSY HALF-SPACE

A rigorous analytical procedure is developed that allows the exact evaluation of the complete integral representations for the time-harmonic electromagnetic (EM) fleld components generated by a vertical magnetic dipole (VMD) lying on the surface of a ∞at and homogeneous lossy half-space. Closed-form expressions for the radial distributions of the EM fleld components induced on the surface of the half-space are provided in terms of exponential functions and modifled Bessel functions. Such expressions make it possible to overcome the limitations implied by the previously published quasi-static solutions, which are valid only in the low-frequency range. Numerical results are presented to show where the quasi-static approximations deviate from the exact solutions for a given homogeneous medium as frequency is changed. The computed amplitude and phase frequency spectra of the EM fleld components demonstrate that the quasi-static approach produces inaccurate results at frequencies higher than 1MHz, and that, in particular, it leads to underestimating the EM fleld strength. Finally, it is also shown that at a frequency equal to or greater than 10MHz excellent results in terms of accuracy may be obtained by using the high-frequency asymptotic forms of the exact solutions.

Two dimensional inverse scattering from buried magnetic anomalies

This paper deals with the problem of the electromagnetic linear inverse scattering from magnetic anomalies buried in a lossy half space, for a scalar and two dimensional case. First, the formulation of the exact model of the electromagnetic scattering is given. Then, the linear inverse problem is solved by resorting to the well assessed Singular Value Decomposition tool. The reliability of the solution procedure is tested with synthetic data achieved by a FDTD code.

Well‐conditioned MLFMA for electromagnetic scattering from dielectric objects above a lossy half‐space

AbstractIn this article, the electromagnetic analysis of arbitrarily shaped three‐dimensional homogenous dielectric objects located above a lossy half space is considered with a well‐conditioned surface integral equation. The electric‐magnetic current combined‐field integral equation (JMCFIE) is extended to the half‐space situation to realize accurate and fast solution. This formulation can lead to a well‐tested equation system with the RWG basis functions and Galerkin's testing procedure. The multilevel fast multipole algorithm (MLFMA) accelerated inner‐outer Flexible Generalized Minimal Residual method (FGMRES) is used for the efficient solution. Numerical results demonstrate the accuracy and high efficiency of this method. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 381–386, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24914

An Efficient Surface Integral Equation Solution to EM Scattering by Chiral Objects Above a Lossy Half Space

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, an extension of the electric-magnetic current combined-field integral equation (JMCFIE) is presented for the efficient analysis of EM scattering by an arbitrary shaped homogenous chiral object located above a lossy half space. This formulation can lead to a well tested equation system using the method of moments (MoM) solution with the vector triangular basis functions and Galerkin's method. The multilevel fast multipole algorithm (MLFMA) is then employed to reduce the memory requirement and computational complexity of the MoM solution. The inner-outer flexible generalized minimal residual (FGMRES) method is used to further speed up the convergence. The accuracy and efficiency are confirmed with a couple of numerical examples. </para>

On the Dispersive Nature of the Power Dissipated Into a Lossy Half-Space Close to a Radiating Source

We study how the power dissipated into a lossy medium excited by a nearby antenna is affected by drifts in the electrical parameters of the lossy medium. The statistical distribution of the sensitivity of the dissipated power is determined by means of a spectral analysis of the transmission of electromagnetic energy from air into the lossy half-space. A clear link is drawn between the reactive content of the field excited by the source and the dispersiveness of the sensitivity. The case of a stratified structure is also addressed, by defining a modification factor representing the alteration of the transmissivity and of its sensitivity when a buffer layer is introduced. All of the results provided point out that, in general, the sensitivity of the total amount of power dissipated into the half-space cannot be predicted independently from a precise knowledge of the source characteristics, unless under a paraxial propagation approximation or in a far-field configuration.

Electromagnetic Field in the Vicinity of Lightning Protection Rods at a Lossy Ground

In this paper, the lightning discharge channel in the vicinity of vertical lightning protection rods is modeled in the frequency domain by a vertical mast antenna coupled with vertical parasitic elements. The ground is treated as linear, isotropic, and homogeneous lossy half-space. The vertical mast antenna and the rods are treated as a unique system as for boundary conditions that results in the electric field integral equation (EFIE) for the unknown current distributions along their axes. EFIE is numerically solved by using the method of moments and a polynomial approximation of the current distributions. The influence of the ground is taken into account through a Sommerfeld integral kernel modeled in a simple and very efficient way using one new approximation that can be classified as a two-image approximation. This approximation gives good results in the frequency domain for modeling in both near and far electromagnetic fields.

APPLICATION OF TWO-STEP SPECTRAL PRECONDITIONING TECHNIQUE FOR ELECTROMAGNETIC SCATTERING IN A HALF SPACE

To e-ciently solve large dense complex linear system arising from electric fleld integral equations (EFIE) formulation of half-space electromagnetic scattering problems, the multilevel fast multipole algorithm (MLFMA) is used to accelerate the matrix- vector product operations. The two-step spectral preconditioning is developed for the generalized minimal residual iterative method (GMRES). The two-step spectral preconditioner is constructed by combining the spectral preconditioner and sparse approximate inverse (SAI) preconditioner to speed up the convergence rate of iterative methods. Numerical experiments for scattering from conducting objects above or embeded in a lossy half-space are given to demonstrate the e-ciency of the proposed method.

A simple model for a numerical determination of electrical characteristics of a pillar foundation grounding system

Unknown leakage current distributions from vertical wire ground electrodes which form an armature of a pillar foundation grounding system are determined in this paper. Electrode system is fed by a very low-frequency current. The leakage currents are determined by a numerical solving of a scalar potential integral equation (SPIE) system. It is realized using the moment method, which actually presents the indirect boundary element method. For longitudinal current along the wire conductor's axes, a polynomial approximation of the first order is used. Then, grounding impedance and electric scalar potential (ESP) distribution on the ground surface in the surrounding of the grounding system are determined. In order to do that, the foundation grounding system is assumed as a homogeneous semi-conducting semi-spherical domain with equally located vertical wire electrodes, treating the surrounding ground as a lossy half-space. In order to form the SPIE system, new approximate expressions for the Green functions of ESP are proposed.