Anderson-accelerated augmented Lagrangian for extended waveform inversion

The augmented Lagrangian (AL) method provides a flexible and efficient framework for solving extended-space full-waveform inversion (FWI), constrained nonlinear optimization problem whereby we seek model parameters wavefields that minimize the data residuals satisfy wave-equation constraint. AL-based wavefield reconstruction inversion, also known as iteratively refined extends search space of FWI in source dimension decreases sensitivity to initial accuracy. Furthermore, it benefits from advantages alternating direction multipliers, such generality decomposability dealing with nondifferentiable regularizers, e.g., total variation regularization, large-scale problems, respectively. In practice, any extension aiming at improving its convergence decreasing number solves would have great importance. To achieve this goal, recast general fixed-point iteration problem, which enables us apply sophisticated acceleration strategies Anderson acceleration. accelerated algorithm stores predefined previous iterates uses their linear combination together current predict next iteration. We investigate performance our on simple checkerboard benchmark Marmousi II 2004 BP salt models through numerical examples. These results confirm effectiveness terms rate quality final estimated model.