Fast Gauss-Newton full-waveform inversion with sparsity regularization

Full-waveform inversion (FWI) can be considered as a controlled data fitting process, in which we approximately fit observed data by iteratively updating the initial velocity model, we expect the final model can reveal subsurface structure till the wavefield misfit can converge to designed tolerance. The conventional FWI approach is expensive since it requires the inversion of a linear system, which involves extremely large multi-experiment data volumes. To overcome this issue we percent a curvetlet based sparsity-promoting Gauss-Newton inversion method. In this presentation we invert for the model updates by replacing the normal Gauss-Newton linearized subproblem for subsampled FWI with a sparsity promoting FWI formulation. We speed up the algorithm and avoid over fitting the data by solving the problem approximately. Aside from this, we control wavefield dispersion by gradually increasing grid size as we move to higher frequencies. Our approach is successful because it reduces the size of seismic data volumes without loss of information. With this reduction, we can compute a Newton-like update with the reduced data volume at the cost of roughly one gradient update for the fully sampled wavefield.