Probing the earth and the universe with microlocal analysis

通过微局域分析探索地球和宇宙

• 批准号: DP190103302
• 负责人: A/Prof Leo Tzou
• 金额: $ 7.29万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2019
• 资助国家: 澳大利亚
• 起止时间: 2019-03-01 至 2022-05-18
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP190103302
• 关键词: Probing; earth; universe; microlocal; analysis

This project aims to use the theory of microlocal analysis to determine the amount of information one can recover about the earth and the universe by making observations on wave propagation. In addition to applications to seismic imaging and cosmology, this project will generate new knowledge in the field of differential geometry and dynamical systems. This will be accomplished by formulating the tomography problem in the language of differential geometry and introduce new analysis techniques to study them. Expected outcome of this project will be new rigidity type results in Lorentzian and Riemannian geometry. There is also the potential for downstream impacts in seismic and cosmological imaging.

该项目旨在利用微局域分析理论来确定通过观察波传播可以恢复的有关地球和宇宙的信息量。除了地震成像和宇宙学的应用之外，该项目还将产生微分几何和动力系统领域的新知识。这将通过用微分几何语言表述断层扫描问题并引入新的分析技术来研究它们来完成。该项目的预期成果将是洛伦兹和黎曼几何中的新刚性类型结果。地震和宇宙学成像也有可能对下游产生影响。