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

Frederik J. Simons, Ignace Loris, Guust Nolet, Ingrid C. Daubechies, S. Voronin, J. S. Judd, P. A. Vetter, J. Charléty, C. Vonesch
2011 Geophysical Journal International  
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 describe benefits and
more » ... ks of these constructions and apply them to analyze the information in two published seismic wavespeed models of the mantle, using the statistics of wavelet coefficients across scales. The localization and sparsity properties of wavelet bases allow finding a sparse solution to inverse problems by iterative minimization of a combination of the ℓ 2 norm of the data residuals and the ℓ 1 norm of the wavelet coefficients. By validation with realistic synthetic experiments we illustrate the likely gains of our new approach in future inversions of finitefrequency seismic data and show its readiness for global seismic tomography.
doi:10.1111/j.1365-246x.2011.05190.x fatcat:3y76j3bjkvad3kze3gtapq4iwu