Efficient analysis and representation of geophysical processes using localized spherical basis functions

Abstract

While many geological and geophysical processes such as the melting of icecaps, the magnetic expression of bodies emplaced in the Earth's crust, or the surface displacement remaining after large earthquakes are spatially localized, many of these naturally admit spectral representations, or they may need to be extracted from data collected globally, e.g. by satellites that circumnavigate the Earth. Wavelets are often used to study such nonstationary processes. On the sphere, however, many of the known constructions are somewhat limited. And in particular, the notion of `dilation' is hard to reconcile with the concept of a geological region with fixed boundaries being responsible for generating the signals to be analyzed. Here, we build on our previous work on localized spherical analysis using an approach that is firmly rooted in spherical harmonics. We construct, by quadratic optimization, a set of bandlimited functions that have the majority of their energy concentrated in an arbitrary subdomain of the unit sphere. The `spherical Slepian basis' that results provides a convenient way for the analysis and representation of geophysical signals, as we show by example. We highlight the connections to sparsity by showing that many geophysical processes are sparse in the Slepian basis.

To appear in the Proceedings of the SPIE, as part of the Wavelets XIII conference in San Diego, August 2009

References in corpus (5)

• Spatiospectral concentration on a sphere
• Spherical Slepian functions and the polar gap in geodesy
• Spectral estimation on a sphere in geophysics and cosmology
• Fast directional continuous spherical wavelet transform algorithms
• A spatiospectral localization approach to estimating potential fields on the surface of a sphere from noisy, incomplete data taken at satellite altitudes

Cited by in corpus (8)

• Slepian functions and their use in signal estimation and spectral analysis
• Spatiospectral concentration in the Cartesian plane
• Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion
• Efficient Computation of Slepian Functions for Arbitrary Regions on the Sphere
• Determining the depth of Jupiter's Great Red Spot with Juno: a Slepian approach
• Slepian Scale-Discretised Wavelets on the Sphere
• Potential-field estimation from satellite data using scalar and vector Slepian functions
• Spatiospectral concentration of vector fields on a sphere