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

该项目将开发用于分析地质样品的高分辨率高灵敏度磁场图的新技术和算法。这些地图是由扫描磁显微镜（SMM）数据构建的。这项研究涉及数学家和地球科学家的合作，将有助于以几种重要方式推进科学知识，例如通过分析古代锆石来解开地球磁场的最早记录;获取可能保存在洞穴地层中的地磁场变化的高时间分辨率记录;并通过分析原始陨石中保存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。这项调查将使古地磁研究能够对目前由于缺乏灵敏度和空间分辨率的传统仪器和技术而无法获得的地质样品进行研究。从磁场图计算磁矩一般是一个不适定的反问题。本项目研究的这类问题的多管齐下办法将使用不同的分析和数字战略（例如，新的稀疏性和正则化方法），这将确保开发适用于各种标本的工具。鉴于类似的数学框架，预计相关的分析将证明对分析航空磁测和卫星磁观测数据是有用的。

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.