Waveform inversion with modified quasi-Newton algorithm

Abstract

Waveform inversion is a kind of method to reveal the underground structure and lithology information through minimizing the residual error between predicted wavefield and true seismic record using full-wavefield information. In this paper, we briefly state the principle of conventional Quasi-Newton algorithm, and then exploit a new modified Quasi-Newton equation to modify the conventional Davidon-Fletcher-Powell (DFP) and Broyden-Fletcher- Goldfarb-Shanno (BFGS) algorithm (Zhang et al, 2001). Furthermore, we take BFGS for instance to implement a comparison between modified method and conventional one. Different from past Quasi-Newton methods, this modified one considers gradient value, model information and objective function value together to approximate the inverse matrix of Hessian matrix, which leads a fast convergence for inversion; moreover, it almost does not increase the calculation amount for each iteration. Finally, numerical experiment shows that compared with conventional Quasi-Newton method, modified BFGS algorithm can not only speed up convergence and decrease consuming time, but also preserve the inverse accuracy well