Robust total-variation based geophysical inversion using split Bregman and proximity operators

Two-dimensional linear and non-linear seismic travel-time tomography are studied to evaluate the efficiency of the proposed formulation for handling a robust measure of the misfit term in recovering blocky solutions. We consider the first arrival travel-times which are contaminated by outliers and also a mixed combination of Gaussian and outliers. Finally, Seinsfeld cross-hole tomography data set is used to investigate the performance of the robust approach on real data sets.