Gravity, Topography, Magnetics: Geoscience Data Analysis in Spherical and Planar Geometry

Abstract:

Data in the Earth and planetary sciences (as well as in astronomy and cosmology, medical imaging, auditory signal processing, and computer vision) often inherently have a sphere (or an ellipsoid) as their domain. However, frequently our goal is to study phenomena in a specific region of the globe. We might either have data that only cover parts of the sphere (e.g. ocean altimetry, Shuttle radar topography), or we may seek to extract a local signal from a global data set (e.g. the continental fraction of the lithospheric magnetic field, or the portion of the time-varying geopotential that is due to ice mass changes). Spectral content is always finite: all sampled data are band-limited. When the region under study is not the whole sphere, but not small enough to justify two-dimensional projection either, the question arises how to best represent the data to perform our analysis, whatever our field of interest. We present SLEPIAN, a software suite with a multitude of numerical and computational tools, and several plotting routines, to accomplish ``spatiospectral'' spherical analysis in the geosciences and beyond.