Computational Methods for Ultra-High Sensitivity Magnetometry of Geological Samples

This project will develop new techniques and algorithms for analyzing high-resolution high-sensitivity magnetic field maps of geological samples. Such maps are built from scanning magnetic microscopy (SMM) data. This research, which involves a collaboration of mathematicians and geoscientists, will help advance scientific knowledge in several significant ways, such as unlocking the earliest records of the Earth's magnetic field by analyzing ancient zircons; accessing high temporal resolution records of variations in the geomagnetic field that may be preserved in cave formations; and improving our understanding of the evolution of the solar system and planet formation processes by analyzing magnetization records preserved in primitive meteorites.

This investigation will allow paleomagnetic studies to be conducted on geological samples that are currently inaccessible due to lack of sensitivity and spatial resolution of conventional instrumentation and techniques. The computation of magnetic moments from field maps is generally an ill-posed inverse problem. The multi-pronged approach to such problems under study in this project will use different analytical and numerical strategies (e.g., new sparsity and regularization methods) that will ensure the development of tools applicable to a variety of specimens. Given the similar mathematical framework, it is expected that the associated analysis will prove useful for the analysis of data from aeromagnetic surveys and satellite magnetic observations.