Accelerating Hessian-free Gauss-Newton full-waveform inversion via l-BFGS preconditioned conjugate-gradient algorithm

Abstract

Full-waveform inversion (FWI) has emerged as a powerful strategy for estimating subsurface model parameters by iteratively minimizing the difference between synthetic data and observed data. The Hessian-free (HF) optimization method represents an attractive alternative to Newton-type and gradient-based optimization methods. At each iteration, the HF approach obtains the search direction by approximately solving the Newton linear system using a matrix-free conjugate-gradient (CG) algorithm. The main drawback with HF optimization is that the CG algorithm requires many iterations. In our research, we develop and compare different preconditioning schemes for the CG algorithm to accelerate the HF Gauss-Newton (GN) method. Traditionally, preconditioners are designed as diagonal Hessian approximations. We additionally use a new pseudo diagonal GN Hessian as a preconditioner, making use of the reciprocal property of Green’s function. Furthermore, we have developed an [Formula: see text]-BFGS inverse Hessian preconditioning strategy with the diagonal Hessian approximations as an initial guess. Several numerical examples are carried out. We determine that the quasi-Newton [Formula: see text]-BFGS preconditioning scheme with the pseudo diagonal GN Hessian as the initial guess is most effective in speeding up the HF GN FWI. We examine the sensitivity of this preconditioning strategy to random noise with numerical examples. Finally, in the case of multiparameter acoustic FWI, we find that the [Formula: see text]-BFGS preconditioned HF GN method can reconstruct velocity and density models better and more efficiently compared with the nonpreconditioned method.

Time‐lapse full waveform inversion of vertical seismic profile data: Workflow and application to the CO2CRC Otway project

“…However, this inversion requires a significant number of iterations. In our case, around 800 iterations were performed, which can probably be reduced by modifying the optimization engine (for example, by using alternative optimization algorithms) [ Pan et al ., ]. After the baseline model is recovered, each monitor survey can be inverted from the maximum available frequency, and it takes fewer iterations to converge (80 in our case).…”

Estimating P Wave Velocity and Attenuation Structures Using Full Waveform Inversion Based on a Time Domain Complex‐Valued Viscoacoustic Wave Equation: The Method

“…This method includes a nested loop in numerical implementation: an outer loop for solving a nonlinear problem to update model parameters and an inner loop for solving a linear problem to reduce Hessian effects and optimize gradients. When a large iteration number is used in the inner loop, this approach is still expensive in real applications (Pan et al, 2017). Another popular Hessian‐free method is the L‐BFGS algorithm (Byrd et al, 1994; Nocedal, 1980; Nocedal & Wright, 2006), which has a good trade‐off between computational efficiency and accuracy for large‐scale inverse problems.…”

Taming the divergent terms in the scattering series of Born by renormalization

“…(3.12) in this paper and Eq. ( 13) in [76]). Similar to the GN Hessian (equation 10 in [76]), the element of the Hessian in our approach is formed by correlating the two Frechet derivative wavefields at the receivers, which is a approximate Hessian.…”

“…( 13) in [76]). Similar to the GN Hessian (equation 10 in [76]), the element of the Hessian in our approach is formed by correlating the two Frechet derivative wavefields at the receivers, which is a approximate Hessian. Actually, it has been demonstrated that the Distorted Born iterative method is consistent with the Gauss-Newton methods of optimization (see Remis and van den Berg [74], Oristaglio and Blok [73], Jakobsen and Ursin [24].…”