We consider the inverse problem of recovering the position and moment of a magnetic dipole from sparse measurements of the field it generates, known on sections of three orthogonal cylinders enclosing it. This problem is motivated by recent measurements performed on Moon rocks, in view of determining their magnetic properties. The key ingredient of the presented method is the use of rational approximation techniques, together with properties of the poles of the approximants, in order to estimate the position of the dipole.
ClercM.LeblondJ.MarmoratJ.-P. and PapadopouloT., Source localization using rational approximation on plane sections, Inverse Problems28 (2012).
2.
GolubG.H. and van LoanCh.F., Matrix Computations, 3rd edn, John Hopkins University Press, 1996.
3.
JacksonJ.D., Classical Electrodynamics, 3rd edn, John Wiley & Sons, 2001.
4.
MosherJ.C. and LeahyR.M., Recursive MUSIC: A framework for EEG and MEG source localization, IEEE Trans. Biomed. Eng.45(11) (1998).
5.
UeharaM.GattaccecaJ.QuesnelY.LepaulardC.LimaE.A.ManfrediM. and RochetteP., A spinner magnetometer for large Apollo lunar samples, Review of Scientific Instruments, American Institute of Physics88(10) (2017).
6.
WeissB.P. and TikooS.M., The lunar dynamo, Science346(6214) (2014).
