Low-Frequency Solution for a Perfectly Conducting Sphere in a Conductive Medium With Dipolar Excitation

Vafeas, Panayiotis; Perrusson, Gaële; Lesselier, Dominique

doi:10.2528/pier04021905

Cited by 23 publications

(27 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a previous paper [16], for the sphere case, the authors have shown that low-frequency (LF) expansions can be used and applied to fields and quantities involved. All of the scalar or vectors are written as summations in terms of powers of (jk), where k is the wave number in the surrounding medium and j is the complex number satisfying j 2 = −1.…”

mentioning

confidence: 99%

Low-frequency dipolar excitation of a perfect ellipsoidal conductor

2010

Self Cite

View full text Add to dashboard Cite

Abstract. This paper deals with the scattering by a perfectly conductive ellipsoid under magnetic dipolar excitation at low frequency. The source and the ellipsoid are embedded in an infinite homogeneous conducting ground. The main idea is to obtain an analytical solution of this scattering problem in order to have a fast numerical estimation of the scattered field that can be useful for real data inversion. Maxwell equations and boundary conditions, describing the problem, are firstly expanded using low-frequency expansion of the fields up to order three. It will be shown that fields have to be found incrementally. The static one (term of order zero) satisfies the Laplace equation. The next non-zero term (term of order two) is more complicated and satisfies the Poisson equation. The order-three term is independent of the previous ones and is described by the Laplace equation. They constitute three different scattering problems that are solved using the separated variables method in the ellipsoidal coordinate system. Solutions are written as expansions on the few analytically known scalar ellipsoidal harmonics. Details are given to explain how those solutions are achieved with an example of numerical results.

show abstract

mentioning

confidence: 99%

Low-frequency dipolar excitation of a perfect ellipsoidal conductor

2010

Self Cite

View full text Add to dashboard Cite

show abstract

“…The efficiency of the model can be successfully demonstrated via the degeneration of the ellipsoidal shape and the reduction of the present results to the already known spheroidal [10] and spherical [7] analogous, since effective formulae of limiting procedures are given. On the other hand, the obtained analytical results are presented suchlike so as a numerical method could be employed furtherly as a continuation of this project.…”

Section: Introductionmentioning

confidence: 79%

“…On the other hand, by virtue of the previous analysis about the reduction rules to the spheroidal or to the spherical geometry, the manipulation of our main results for the electromagnetic fields H 0 , H 2 , H 3 , E 1 , and E 3 in the domain Ω ≡ (R 3 ) − {r 0 } given in (58) is a straightforward task and leads to recovering the corresponding and already known results from the literature, described earlier in the Introduction section for a spheroidal [10] and a spherical [7] nonpenetrable scatterer.…”

mentioning

confidence: 99%

“…Indeed, present investigations [5,6] confirm that simple models as ours appear reliable when used to model the response of a general three-dimensional ellipsoid to a localized vector source in a homogeneous conductive medium both for low-contrast and high-contrast cases. However, the difficulty induced in performing analytical techniques when we are moving towards anisotropic geometrical models is strongly increasing due to the appearance of much more elaborate corresponding eigenfunctions of the introduced potentials, though the already rich literature with analytical works concerning the scattering by simple nonpenetrable metal shapes like spheres [7][8][9], spheroids [10,11], and as already mentioned ellipsoids [5,6] is open to accept new and useful analytical results. Indeed, very recently, similar analytical techniques based on differential analysis were adopted for targeting toroidal metallic objects within either a conductive surrounding, for example, Earth [12] or a lossless medium, for example, air [13].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Revisiting the Low-Frequency Dipolar Perturbation by an Impenetrable Ellipsoid in a Conductive Surrounding

Vafeas

2017

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

This contribution deals with the scattering by a metallic ellipsoidal target, embedded in a homogeneous conductive medium, which is stimulated when a 3D time-harmonic magnetic dipole is operating at the low-frequency realm. The incident, the scattered, and the total three-dimensional electromagnetic fields, which satisfy Maxwell's equations, yield low-frequency expansions in terms of positive integral powers of the complex-valued wave number of the exterior medium. We preserve the static Rayleigh approximation and the first three dynamic terms, while the additional terms of minor contribution are neglected. The Maxwell-type problem is transformed into intertwined potential-type boundary value problems with impenetrable boundary conditions, whereas the environment of a genuine ellipsoidal coordinate system provides the necessary setting for tackling such problems in anisotropic space. The fields are represented via nonaxisymmetric infinite series expansions in terms of harmonic eigenfunctions, affiliated with the ellipsoidal system, obtaining analytical closed-form solutions in a compact fashion. Until nowadays, such problems were attacked by using the very few ellipsoidal harmonics exhibiting an analytical form. In the present article, we address this issue by incorporating the full series expansion of the potentials and utilizing the entire subspace of ellipsoidal harmonic eigenfunctions.

show abstract

“…To calculate the target response, we avoid time-consuming spherical harmonic formulations [27] and begin with the simple parametric approximation presented by [28] for estimating the timedomain B field response of a conductive permeable sphere due to a step function excitation. This is also the electro-dynamic ALLTEM response since its excitation is integral of the step (i.e., a triangle wave), it uses dB /dt receivers, and the integral and derivative operations cancel each other.…”

Section: Signalmentioning

confidence: 99%

Combining Advances in Em Induction Instrumentation and Inversion Schemes for Uxo Characterization

Oden¹

2012

PIER B

View full text Add to dashboard Cite

Abstract-Several experimental time-domain EM induction instruments have recently been developed for unexploded ordnance (UXO) detection and characterization that use multiple transmitting and receiving coil combinations. One such system, the US Geological Survey's ALLTEM system, is unique in that it measures both the electrodynamic response (i.e., induced eddy currents) and the magneto-static response (i.e., induced magnetization). This allows target characterization based on the dyadic polarizability of both responses. This paper examines the numerical response of the ALLTEM instrument due to spheroidal, conductive, and permeable UXO targets; and to conductive and optionally viscous magnetic earth. An inversion scheme is presented for spheroidal targets that incorporates fully polarimetric measurements for both magneto-static and electro-dynamic excitations. The performance of the inversion algorithm is evaluated using both simulated and surveyed data. The results are examined as a function of the number of coil combinations, number of instrument locations, and uncertainty in sensor location and orientation. Results from the specific cases tested (prolate spheroids lying horizontally) show that 1) that collecting data from more than 12 sensor locations or from more than four coil combinations reduced the chances that inversion solutions would be from a local minimum, and 2) that uncertainties in position greater than 3 cm or in orientation greater than 10 degrees cause errors in the estimated spheroid principal lengths of greater than 100%. Soil conductivities less than 1 S/m contribute negligible interference to the target response, but viscous magnetic soils with permeabilities greater than 10 −6 MKS units do cause detrimental interference.

show abstract

Low-Frequency Solution for a Perfectly Conducting Sphere in a Conductive Medium With Dipolar Excitation

Cited by 23 publications

References 11 publications

Low-frequency dipolar excitation of a perfect ellipsoidal conductor

Low-frequency dipolar excitation of a perfect ellipsoidal conductor

Revisiting the Low-Frequency Dipolar Perturbation by an Impenetrable Ellipsoid in a Conductive Surrounding

Combining Advances in Em Induction Instrumentation and Inversion Schemes for Uxo Characterization

Contact Info

Product

Resources

About