Retrieving lithospheric magnetisation distribution from magnetic field models

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.