We propose a class of spherical wavelet bases for the analysis of
geophysical models and for the tomographic inversion of global
seismic data. Its multiresolution character allows for modeling with
an effective spatial resolution that varies with position within the
Earth. Our procedure is numerically efficient and can be implemented
with parallel computing. We discuss two possible types of discrete
wavelet transforms in the angular dimension of the cubed sphere. We
discuss benefits and drawbacks of these constructions and apply them
to analyze the information present in two published seismic
wavespeed models of the mantle, for the statistics and power of
wavelet coefficients across scales. Localization and sparsity
properties allow finding a sparse solution to the inverse problem by
iterative minimization of a combination of the l2 norm of data
fit and the l norm on the wavelet coefficients. By validation
with realistic synthetic experiments we illustrate the likely gains
of using our new approach in future inversions of finite-frequency
seismic data.
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