Kelvin transform and Fourier analysis for explicit reconstruction formulae in paleomagnetic context

Duration: 33 mins 16 secs

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Description:	Ponomarev, D Thursday 12th September 2019 - 16:00 to 16:30


Created:	2019-09-12 16:40
Collection:	The complex analysis toolbox: new techniques and perspectives
Publisher:	Isaac Newton Institute
Copyright:	Ponomarev, D
Language:	eng (English)


Abstract:	We consider so-called inverse magnetization problem in paleomagnetic context. In such a problem the aim is to recover the average remaneWe consider so-called inverse magnetization problem in the paleomagnetic context. In such a problem the aim is to recover the average remanent magnetization of a sample from measurements of one component of magnetic field in a planar region above the sample. To achieve this goal, two methods based on complex-analysis and harmonic function theory were specially developed. The first is based on Kelvin transformation mapping planar data to the family of spheres which is then followed by asymptotical analysis of spherical harmonics projection integrals. The second method is due to direct two-dimensional Fourier analysis of the data in a suitable neighborhood of the origin. The latter becomes possible after a suitable asymptotic completion of the original measurement data has been performed. The obtained explicit formulas estimating net moment components in terms of the normal component of the measured magnetic field show good agreement with synthetically generated numerical and experimental data on samples with fairly localized magnetization distributions. It is an interesting example how the problem can be solved using tools of discrete and continuous harmonic analysis. The talk is based on a joint work with Laurent Baratchart, Juliette Leblond (INRIA Sophia Antipolis, France) and Eduardo Andrade Lima (MIT, USA).

Abstract:

We consider so-called inverse magnetization problem in paleomagnetic context. In such a problem the aim is to recover the average remaneWe consider so-called inverse magnetization problem in the paleomagnetic context. In such a problem the aim is to recover the average remanent magnetization of a sample from measurements of one component of magnetic field in a planar region above the sample. To achieve this goal, two methods based on complex-analysis and harmonic function theory were specially developed. The first is based on Kelvin transformation mapping planar data to the family of spheres which is then followed by asymptotical analysis of spherical harmonics projection integrals. The second method is due to direct two-dimensional Fourier analysis of the data in a suitable neighborhood of the origin. The latter becomes possible after a suitable asymptotic completion of the original measurement data has been performed. The obtained explicit formulas estimating net moment components in terms of the normal component of the measured magnetic field show good agreement with synthetically generated numerical and experimental data on samples with fairly localized magnetization distributions. It is an interesting example how the problem can be solved using tools of discrete and continuous harmonic analysis. The talk is based on a joint work with Laurent Baratchart, Juliette Leblond (INRIA Sophia Antipolis, France) and Eduardo Andrade Lima (MIT, USA).

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