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We propose a class of spherical wavelet bases for the analysis of geophysicalmodels and forthe tomographic inversion of global seismic data. Itsmultiresolution character allows for modeling with an effective spatialresolution that varies with position within the Earth. Our procedure isnumerically efficient and can be implemented with parallel computing. Wediscuss two possible types of discrete wavelet transforms in the angulardimension of the cubed sphere. We discuss benefits and drawbacks of theseconstructions and apply them to analyze the information present in twopublished seismic wavespeed models of the mantle, for the statistics and powerof wavelet coefficients across scales. The localization and sparsity propertiesof wavelet bases allow finding a sparse solution to inverse problems byiterative minimization of a combination of the $\ell_2$ norm of data fit andthe $\ell_1$ norm on the wavelet coefficients. By validation with realisticsynthetic experiments we illustrate the likely gains of our new approach infuture inversions of finite-frequency seismic data and show its readiness forglobal seismic tomography.

Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity