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Asymptotic method for estimating magnetic moments from field measurements on a planar grid

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 : Scanning magnetic microscopes typically measure the vertical component B_3 of the magnetic field on a horizontal rectangular grid at close proximity to the sample. This feature makes them valuable instruments for analyzing magnetized materials at fine spatial scales, e.g., in geosciences to access ancient magnetic records that might be preserved in rocks by mapping the external magnetic field generated by the magnetization within a rock sample. Recovering basic characteristics of the magnetization (such as its net moment, i.e., the integral of the magnetization over the sample's volume) is an important problem, specifically when the field is too weak or the magnetization too complex to be reliably measured by standard bulk moment magnetometers. In this paper, we establish formulas, asymptotically exact when R goes large, linking the integral of x_1 B_3, x_2 B_3, and B_3 over a square region of size R to the first, second, and third component of the net moment (and higher moments), respectively, of the magnetization generating B_3. The considered square regions are centered at the origin and have sides either parallel to the axes or making a 45-degree angle with them. Differences between the exact integrals and their approximations by these asymptotic formulas are explicitly estimated, allowing one to establish rigorous bounds on the errors. We show how the formulas can be used for numerically estimating the net moment, so as to effectively use scanning magnetic microscopes as moment magnetometers. Illustrations of the method are provided using synthetic examples.
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Preprints, Working Papers, ...
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Contributor : Sylvain Chevillard <>
Submitted on : Wednesday, September 26, 2018 - 12:52:17 AM
Last modification on : Friday, April 30, 2021 - 9:55:06 AM
Long-term archiving on: : Thursday, December 27, 2018 - 12:42:15 PM


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  • HAL Id : hal-01421157, version 2


Laurent Baratchart, Sylvain Chevillard, Juliette Leblond, Eduardo Lima, Dmitry Ponomarev. Asymptotic method for estimating magnetic moments from field measurements on a planar grid. 2018. ⟨hal-01421157v2⟩



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