Collaborative Research: Computational methods for ultra-high sensitivity magnetometry of geological samples

该项目将开发新的技术和算法，用于分析高分辨率、高灵敏度的地质样品磁场图。这样的地图是根据扫描磁性显微镜(SMM)数据构建的。这项研究涉及数学家和地球科学家的合作，将有助于在几个重要方面促进科学知识的发展，例如通过分析古代锆石来解锁地球磁场的最早记录；获取可能保存在洞穴形成中的高时间分辨率的地磁场变化记录；以及通过分析保存在原始陨石中的磁化记录来提高我们对太阳系演化和行星形成过程的理解。这项调查将使人们能够对目前由于缺乏灵敏度和传统仪器和技术的空间分辨率而无法获取的地质样品进行古地磁研究。从场图计算磁矩通常是一个不适定的逆问题。本项目正在研究的这类问题的多管齐下的方法将使用不同的分析和数值策略(例如，新的稀疏化和正则化方法)，以确保开发适用于各种样本的工具。鉴于类似的数学框架，预计相关分析将有助于分析来自航磁调查和卫星磁力观测的数据。

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.