Improving Full-Waveform Inversion Based On Wavefield Reconstruction Via Bregman Iterations

Full waveform inversion (FWI) is a multi-objective constrained optimization which provides subsurface model with a seismic wavelength resolution. However, this high resolution potential also makes the inverse problem highly nonlinear. The frequency-domain FWI based on wavefield reconstruction (WRI) recasts the constrained optimization in a penalty method, which iteratively reconstructs the wavefield and the subsurface parameters in an alternating mode. At each iteration of a cycle work-flow, the wavefield reconstruction is first steered towards the observations such that the subsurface parameters are estimated from an improved wavefield in a second step. Here, we recast the two sub-problems embedded in WRI as linear problems and use Bregman iterations to strictly enforce the constraints in the penalty method through the iterative refinement of the right-hand sides (seismic sources and data) of the two linear sub-problems. The improvements resulting from this iterative refinement are illustrated with a toy example and the MarmousiII model when a crude initial model is used. We show how the iterative refinement improves the reconstruction of the short-scale structures, speeds up convergence and makes the method more resilient to noise although no regularization was used. The method can be improved with additional constraints such as total variation minimization.