Modified Gauss-Newton full-waveform inversion explained — Why sparsity-promoting updates do matter

ABSTRACTFull-waveform inversion (FWI) can be formulated as a nonlinear least-squares optimization problem. This nonconvex problem can be computationally expensive because it requires repeated solutions of the wave equation. Randomized subsampling techniques allow us to work with small subsets of (monochromatic) source experiments, reducing the computational cost. However, this subsampling may weaken subsurface illumination or introduce subsampling-related incoherent artifacts. These subsampling-related artifacts — in conjunction with the desire to obtain high-fidelity inversion results — motivate us to come up with a technique to regularize this inversion problem. Following earlier work, we have taken advantage of the fact that curvelets represent subsurface models and model perturbations parsimoniously. At first impulse, promoting sparsity on the model directly seemed the most natural way to proceed, but we have determined that in certain cases it can be advantageous to promote sparsity on the Gauss-Newt...