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SUMMARY:Kelvin transform and Fourier analysis for explicit reconstruction 
 formulae in paleomagnetic context - Dmitry Ponomarev (Vienna University of
  Technology\; Steklov Mathematical Institute\, Russian Academy of Sciences
  )
DTSTART:20190912T150000Z
DTEND:20190912T153000Z
UID:TALK129472@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We consider so-called inverse magnetization problem in paleoma
 gnetic context. In such a problem the aim is to recover the average remane
 We consider so-called inverse magnetization problem in the paleomagnetic c
 ontext. In such a problem the aim is to recover the average remanent magne
 tization of a sample from measurements of one component of magnetic field 
 in a planar region above the sample. To achieve this goal\, two methods ba
 sed on complex-analysis and harmonic function theory were specially develo
 ped. The first is based on Kelvin transformation mapping planar data to th
 e family of spheres which is then followed by asymptotical analysis of sph
 erical 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 compl
 etion of the original measurement data has been performed.<br> The obtaine
 d explicit formulas estimating net moment components in terms of the norma
 l component of the measured magnetic field show good agreement with synthe
 tically generated numerical and experimental data on samples with fairly l
 ocalized magnetization distributions.<br> It is an interesting example how
  the problem can be solved using tools of discrete and continuous harmonic
  analysis.  <br> The talk is based on a joint work with Laurent Baratchart
 \, Juliette Leblond (INRIA Sophia Antipolis\, France) and Eduardo Andrade 
 Lima (MIT\, USA).
LOCATION:Seminar Room 1\, Newton Institute
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