Open AccessMaximum entropy regularization of the geomagnetic core field inverse problem
Author(s) -
Jackson Andrew,
Constable Catherine,
Gillet Nicolas
Publication year - 2007
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2007.03530.x
Subject(s) - pixel , regularization (linguistics) , inverse problem , entropy (arrow of time) , mathematics , principle of maximum entropy , earth's magnetic field , mathematical analysis , physics , magnetic field , computer science , artificial intelligence , optics , statistics , quantum mechanics
SUMMARY The maximum entropy technique is an accepted method of image reconstruction when the image is made up of pixels of unknown positive intensity (e.g. a grey‐scale image). The problem of reconstructing the magnetic field at the core–mantle boundary from surface data is a problem where the target image, the value of the radial field B r , can be of either sign. We adopt a known extension of the usual maximum entropy method that can be applied to images consisting of pixels of unconstrained sign. We find that we are able to construct images which have high dynamic ranges, but which still have very simple structure. In the spherical harmonic domain they have smoothly decreasing power spectra. It is also noteworthy that these models have far less complex null flux curve topology (lines on which the radial field vanishes) than do models which are quadratically regularized. Problems such as the one addressed are ubiquitous in geophysics, and it is suggested that the applications of the method could be much more widespread than is currently the case.