Full-waveform Inversion with Randomized Space Shift

Full-waveform inversion (FWI) has the great potential to retrieve high-fidelity subsurface models, with the constraint that the traveltime difference between the predicted data and the observed data should be less than half of the period at the lowest available frequency. If the above constraint is not satisfied, FWI will suffer from severe convergence problems and may get stuck in erroneous local minimum. To mitigate the dependence of FWI on the quality of the starting model, we apply the robust gradient sampling algorithm (GSA) on nonsmooth, nonconvex optimization problems to FWI. The original implementation of GSA requires explicit calculation of the gradient at each sampling point. When combined with FWI, this procedure involves tremendous computational costs for calculating the forward- and backward-propagated wavefields at each sampled velocity model within the vicinity of the current model estimate. Through numerical analyses, we find that the gradients corresponding to slightly perturbed velocity models can be approximated by space shifting the gradient obtained from the current velocity model. By randomly choosing one space shift at each time step during the gradient calculation, the computational cost is thus the same as conventional FWI. Numerical examples based on the 2004 BP model demonstrate that the proposed method can provide much better results than conventional FWI when starting from a crude initial velocity model.