Identification of Current Sources in 3D Electrostatics

Sommer, Aron; Helfrich-Schkarbanenko, Andreas; Heuveline, Vincent

doi:10.1007/978-3-642-54551-1_85

Cited by 2 publications

(8 citation statements)

References 14 publications

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“…Meanwhile, during airborne prospecting, a measured value is the amplitude of the magnetic field. This amplitude can be then converted into an electric potential using an appropriate operator, such that the presented approach based on the Tikhonov regularization can be applied 33 . The airborne/seaborne surveying provides the information on aquifers for groundwater investigations, paleochannels for shallow gas investigation and drilling hazards, on soils and overburden for engineering purposes 53,54 .…”

Section: Discussionmentioning

confidence: 99%

“…As the source identification problem was analysed by Sommer et al (ref. [33]), here we describe briefly the results of this study. Applications of the source identification problem are numerous; for example, it is the subject of research in volcanology 34,35 and in geo-explorations 36 .…”

Section: Introductionmentioning

confidence: 92%

“…Meanwhile, it is shown that a solution of this inverse problem exists, but it is not unique 33 . A Tikhonov regularization can enforce the uniqueness of a solution via a spectral shift by using the operator…”

Section: Electric Potential Determinationmentioning

confidence: 99%

“…The vectors u and f are discrete representatives of the electric potential and the current source density, respectively. Sommer et al33 showed that the numerical direct problem(10)is well-posed, and the operator B is positive definite and invertible. Hence, the solution to (10) is .…”

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confidence: 99%

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Active Cloaking and Illusion of Electric Potentials in Electrostatics

Helfrich-Schkabarenko

Ismail‐Zadeh

Sommer

2021

Preprint

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Cloaking and illusion has been demonstrated theoretically and experimentally in several research fields. Here we present for the first time an active exterior cloaking device in electrostatics operating in a two-horizontally-layered electroconductive domain, and use the superposition principle to cloak electric potentials. The device uses an additional current source pattern introduced on the interface between two layers to cancel the total electric potential to be measured. Also, we present an active exterior illusion device allowing for detection of a signal pattern corresponding to any arbitrarily chosen current source instead of the existing current source. The performance of the cloaking/illusion devices is demonstrated by three-dimensional models and numerical experiments using synthetic measurements of the electric potential. Sensitivities of numerical results to a noise in measured data and to a size of cloaking devices are analysed. The numerical results show quite reasonable cloaking/illusion performance, which means that a current source can be hidden electrostatically. The developed active cloaking/illusion methodology can be used in subsurface geo-exploration studies, electrical engineering, live sciences, and elsewhere.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 92%

Section: Electric Potential Determinationmentioning

confidence: 99%

mentioning

confidence: 99%

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Active Cloaking and Illusion of Electric Potentials in Electrostatics

Helfrich-Schkabarenko

Ismail‐Zadeh

Sommer

2021

Preprint

Self Cite

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show abstract

“…As the source identification problem was analysed by Sommer et al (ref. 32 ), here we describe briefly the results of this study. Applications of the source identification problem are numerous; for example, it is the subject of research in volcanology 33 , 34 and in geo-explorations 35 .…”

Section: Introductionmentioning

confidence: 92%