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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Kelvin transform and Fourier analysis for explicit
reconstruction formulae in paleomagnetic context
- Dmitry Ponomarev (Vienna University of Technolog
y\; Steklov Mathematical Institute\, Russian Acade
my of Sciences )
DTSTART;TZID=Europe/London:20190912T160000
DTEND;TZID=Europe/London:20190912T163000
UID:TALK129472AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/129472
DESCRIPTION:We consider so-called inverse magnetization proble
m in paleomagnetic context. In such a problem the
aim is to recover the average remaneWe consider so
-called inverse magnetization problem in the paleo
magnetic context. In such a problem the aim is to
recover the average remanent magnetization of a sa
mple from measurements of one component of magneti
c field in a planar region above the sample. To ac
hieve this goal\, two methods based on complex-ana
lysis and harmonic function theory were specially
developed. The first is based on Kelvin transforma
tion mapping planar data to the family of spheres
which is then followed by asymptotical analysis of
spherical harmonics projection integrals. The sec
ond method is due to direct two-dimensional Fourie
r analysis of the data in a suitable neighborhood
of the origin. The latter becomes possible after a
suitable asymptotic completion of the original me
asurement data has been performed.

The obtaine
d explicit formulas estimating net moment componen
ts in terms of the normal component of the measure
d magnetic field show good agreement with syntheti
cally generated numerical and experimental data on
samples with fairly localized magnetization distr
ibutions.

It is an interesting example how the
problem can be solved using tools of discrete and
continuous harmonic analysis.

The talk is b
ased on a joint work with Laurent Baratchart\, Jul
iette Leblond (INRIA Sophia Antipolis\, France) an
d Eduardo Andrade Lima (MIT\, USA).
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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