Laplace-domain waveform inversion using the l-BFGS method

We examine the performance of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (l-BFGS) optimization method for full waveform inversions in the Laplace domain. Full waveform inversion methods generally adopt gradient-based optimization schemes for efficiency. Most Laplace-domain full waveform inversion methods published to date use the preconditioned steepest descent (PSD) method with the diagonal elements of the pseudo-Hessian as the preconditioner. These methods use a small fixed step length for stable convergence. The l-BFGS method is a quasi-Newton optimization method that efficiently approximates the inverse of the Hessian. We compare Laplace-domain inversion results from the PSD method with those from the l-BFGS method. Numerical examples using the SEG/EAGE salt model and the Pluto model demonstrate that the l-BFGS method with the Wolfe line search yields smaller cost function values than the PSD method.