The Memoryless Quasi-Newton Method for Full Waveform Inversion

Full waveform inversion (FWI) is an efficient parameter reconstructing method; however, the amount of parameters to be inverted is very large leading to the computation cost is high which finally limits the application of FWI to large scale problems. In the study, a new optimization method named memoryless quasi-Newton (MLQN) method is presented in FWI. The computation of Hessian matrix in MLQN method is avoided, so its computation cost is low; since only the gradient and updated model instead of the Hessian matrix from previous iteration are stored in each iteration, the memory storage is reduced. To test the efficiency of MLQN method in FWI, we apply it to a modified Marmousi model and an overthrust model; the reconstructed models are contrasted with the ones obtained by L-BFGS method from the aspects of memory storage of each iteration, computing time and precision; the analysis suggests that with maintaining the nearly same precision, the memory storage of MLQN method is less than that of L-BFGS method by (2p-2) vectors, and there is no p-selecting in MLQN method. Our numerical tests show the feasibility of MLQN method.