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

ABSTRACTFull-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 l-BFGS inverse Hessian preconditioning...