Abstract
Summary We investigate to which extent the radially averaged magnetisation of the lithosphere can be recovered from the information content of a spherical harmonic model of the generated magnetic field when combined with few simple hypotheses. The results obtained show firstly that a hypothesis of magnetisation induced by a field of internal origin, even over a localised area, is not sufficient to recover uniquely the radially averaged magnetisation and, secondly, that this magnetisation can be recovered when a constant magnetisation direction is assumed. An algorithm to recover the magnetisation direction and distribution is then described and tested over a synthetic example. It requires to introduce a cost function that vanishes when estimated in a system of coordinates with its Z axis aligned with the magnetisation direction. Failing to find a vanishingly small value for the cost function is an indication that a constant magnetisation direction is not a valid hypothesis for the studied magnetic field model. The range of magnetisation directions that are compatible with the magnetic field model and a given noise level, can also be estimated. The whole process is illustrated by analysing a local, isolated maximum of the Martian magnetic field.
Highlights
Rock magnetization, its remanent part, carries important information about a planet history
Two other cases are presented: (i) First, we consider in Section 4 the case of a localized distribution of magnetization induced by a field of internal origin and we show here that a localized susceptibility distribution cannot be uniquely estimated from surface magnetic field measurements assuming an internal dipolar inducing field
We insist on the fact that these distributions of magnetization are unique; no other magnetization distribution of maximum spherical harmonic degree L − 2 can fit the data and comply with the hypothesis of constant magnetization direction
Summary
Its remanent part, carries important information about a planet history. We point out that the simplest hypothesis where the hidden magnetization vanishes is, most of the time, a poor choice This is because the visible magnetization alone is not compatible with physically acceptable hypotheses such as assuming that the magnetization is induced by an internal field (Vervelidou et al 2017b). We point out that a constant magnetization direction is generally not an acceptable hypothesis unless working over a very small area This case is a limit case of localized distribution of internally induced magnetization for a very small area. By shortly recalling results from Gubbins et al (2011) that are presented here using a slightly different normalization
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