PhD position in applied analysis: inverse magnetisation problem

Inverse magnetisation problem consists in inferring information about a static magnetic source from partial knowledge of the produced field. The PhD thesis work will be concerned with several mathematical challenges arising from such a problem in the paleomagnetic context where the ultimate goal is to get insight into evolution of magnetic fields of Earth or other celestial bodies. Some georocks contain valuable remanent magnetisation that can be extracted by analysis of ultra-weak magnetic fields measured with scanning microscopy devices, e.g. using SQUID (Superconducting Quantum Interference Device) or QDM (Quantum Diamond Microscope), on a planar patch located at some distance from a sample. Motivated by particular setups at EAPS (Earth, Atmospheric & Planetary Sciences) Department, MIT (Massachusetts Institute of Technology, USA), Harvard Paleomagnetics Lab (USA) and CEREGE (Centre de Recherche et d'Enseignement des Géosciences de l’Environnement, France), the aim of the thesis work will be advancing on the aspects related to the limitation of the available measured data, high noise content of the measurements and in-applicability of the current methodology to deal with more general sources and particularities of the experimental setting. In particular, dealing with volumetric sources, devising appropriate noise models and studying the advantages of additionally measured data will be among the topics to consider. The PhD thesis will involve theoretical design, numerical implementation and analysis of the methods, testing on synthetic and experimental data and comparison with alternative approaches. A candidate is hence required to have a solid background in applied/computational mathematics with strong interest in physical applications.

Last updated: 20 August 2024