Preconditioning Strategies for Truncated Newton Full-waveform Inversion

Abstract

ABSTRACT. Truncated Newton full waveform inversion is an attractive alternative to conventional gradient-based optimization algorithms. This method accounts for the Hessian within the inversion; however, it is implemented in a "Hessian-free" fashion, without explicit calculation or storage of the Hessian matrix. At each iteration, we obtain the search direction through a conjugate-gradient (CG) solution of the Newton linear system, which requires only evaluations of Hessian-vector products. Due to the additional cost associated with inner CG iterations, it is indispensable to apply a preconditioning strategy on the CG algorithm to improve its convergence, reducing the number of CG iterations. In this work, we study two preconditioned CG schemes. We propose a scheme based on model reparameterization that adopts a preconditioner operator that combines smoothness and the illumination compensation effect of the pseudo-Hessian. We also investigate a more conventional preconditioning scheme that uses only the pseudo-Hessian preconditioner. The numerical experiments show that preconditioning using model reparameterization, which combines pseudo-Hessian compensation with smoothing, outperforms the more conventional preconditioning scheme that exclusively uses the pseudo-Hessian operator.