Spherical Wavelet Analysis of Geophysical Data

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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.