  Many flexible parameterizations exist to represent data on the sphere. In
addition to the venerable spherical harmonics, we have the Slepian basis,
harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we
focus on the latter two: spherical wavelets developed for geophysical
applications on the cubed sphere, and the Slepian "tree", a new construction
that combines a quadratic concentration measure with wavelet-like
multiresolution. We discuss the basic features of these mathematical tools, and
illustrate their applicability in parameterizing large-scale global geophysical
(inverse) problems.
