Moments estimation of magnetic source terms from partial data

Laurent Baratchart 1 Sylvain Chevillard 1 Juliette Leblond 1 Eduardo Lima 2 Dmitry Ponomarev 3
3 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : In this article, we give asymptotic formulas that link the (first and higher order) moments of the magnetic density distribution (also called magnetization) of a compactly supported magnetized sample with the 0-th and 1st order moments of the vertical component of the magnetic field it produces on a square piece of horizontal plane lying above it. Such a framework typically arises in geosciences when one measures the field generated by a small piece of (magnetized) rock with a magnetic microscope. In such a case, the magnetic moments of the sample are usually unknown and one is interested in recovering them from the data measured with the microscope, i.e. the vertical component of the magnetic field on a planar region above the sample. The formulas given in this article provide a practical way of recovering an estimate of the 0-th order moment of the magnetization (usually also called net moment) from simple computations with the measurements. This estimate is asymptotically exact when the square where the measurements are performed gets large. This allows one for implementing an actual "numerical magnetometer".
Type de document :
Pré-publication, Document de travail
2016
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Dernière modification le : mardi 17 avril 2018 - 09:08:25
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MomentsFromPartialData.pdf
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  • HAL Id : hal-01421157, version 1

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Laurent Baratchart, Sylvain Chevillard, Juliette Leblond, Eduardo Lima, Dmitry Ponomarev. Moments estimation of magnetic source terms from partial data. 2016. 〈hal-01421157〉

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