Full waveform inversion (FWI) based upon least-squares is commonly solved through local optimization methods utilizing conjugate gradients or steepest descent. However, gradient optimization methods are generally considered slower and can have difficulties scaling the reconstructed model parameters in comparison to methods that require second-order information of the objective function, such as the Newton method. In this paper, we present an inexact full Newton optimization method for the full waveform inversion algorithm in the frequency domain which utilizes simultaneous sources based upon the phase encoding technique. Tests show that the full Newton minimization method achieves a high convergence rate and a reasonably accurate reconstruction of the model parameters. Taking advantage of a direct solver based on LU decomposition, the full Newton minimization method can also be implemented in a matrix-free manner. Tests with this algorithm were conducted with the BP/EAGE velocity model and highlight its high performance capabilities. To our knowledge, this is the first implementation of FWI with simultaneous sources using the full Newton method on a large scale model.

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