Spherical Wavelet Analysis of Geophysical Data

尽管是非常不同的研究领域，但宇宙学中的暗物质测绘和地球物理学中的地球内部地震属性(例如波速)的成像目前面临着类似的技术挑战。例如，随着这两个学科的大数据集的爆炸性增长，不同的研究小组制作了同一对象的许多地图和图像。它们之间往往有很大的差异，但缺乏对其统计特性的充分定量、客观的分析。此外，大多数图像和地图不报告不确定性，这限制了它们对了解其下面的基本物理过程的有用性。该项目通过在宇宙学和地球物理学之间双向转让知识来应对这些挑战，办法是：(1)将为绘制宇宙学暗物质图而开发的一些新方法应用于地球物理，特别是小波和稀疏/压缩传感方法以及贝叶斯分层模型；(2)将目前用于地球物理学的新型贝叶斯跨维方法应用于宇宙学制图。

Despite being very distinct research areas, dark matter mapping in cosmology and the imaging of the seismic properties of the Earth's interior (e.g., wave speeds) in geophysics currently face similar technical challenges. For example, with the explosion of big data sets in both disciplines, many maps and images of the same object have been produced by different research groups. There are often substantial differences between them, but fully quantitative, objective analyses of their statistical properties are lacking. In addition, most images and maps do not report uncertainties, which limits their usefulness to understand the fundamental physical processes underneath them. This project addresses these challenges through a two-way transfer of knowledge between cosmology and geophysics by: (i) applying some new methods developed for dark matter mapping in cosmology to the geophysical context, notably wavelet and sparse/compressed sensing approaches, and Bayesian Hierarchical modelling; and, (ii) adapting novel Bayesian trans-dimensional approaches currently used in geophysics to cosmological mapping.