Multiplier Waveform Inversion: Time-Domain Application with Adaptive Step-Length

Time-domain full waveform inversion (FWI) is appropriate for large-scale problems, with the general multivariate formulation to seek for model parameters and seismic wavefield by minimizing an appropriate regularization function while adhering to the wave equation and observation equation constraints. The classic FWI addresses the problem in the frame of reduced search space through eliminating the wavefield from the optimization parameters and then applying the quadratic penalty function to the resulting mono-variate problem. This conventional strategy suffers from illconditioning, slow convergence rate, and local minima trap in the lack of an appropriate starting model. To address these issues, we propose using the augmented Lagrangian function in the frame of the method of multiplier rather than the penalty function. This multiplier waveform inversion (MWI) modifies the data residual of the standard FWI with the Lagrange multiplier that is computed by the running sum of data residuals during iterations. This modifications aids in fitting the data in a stable manner in the absence of a good initial model without incurring additional computation costs that results in a faster convergence rate and more accurate models. Two synthetic numerical examples are provided to show the effectiveness of the suggested strategy.