Algorithmic strategies for full waveform inversion: 1D experiments

Full-waveform seismic inversion, i.e., the iterative minimization of the misfit between observed seismic data and synthetic data obtained by a numerical solution of the wave equation provides a systematic, flexible, general mechanism for reconstructing earth models from observed ground motion. However, many difficulties arise for highly resolved models and the associated large-dimensional parameter spaces and high-frequency sources. First, the least-squares data-misfit functional suffers from spurious local minima, which necessitates an accurate initial guess for the smooth background model. Second, total variation regularization methods that are used to resolve sharp interfaces create significant numerical difficulties because of their nonlinearity and near-degeneracy. Third, bound constraints on continuous model parameters present considerable difficulty for commonly used active-set or interior-point methods for inequality constraints because of the infinite-dimensional nature of the parameters. Finally, common gradient-based optimization methods have difficulties scaling to the many model parameters that result when the continuous parameter fields are discretized. We have developed an optimization strategy that incorporates several techniques address these four difficulties, including grid, frequency, and time-window continuation; primal-dual methods for treating bound inequality constraints and total variation regularization; and inexact matrix-free Newton-Krylov optimization. Using this approach, several computations were performed effectively for a 1D setting with synthetic observations.