Full Waveform Inversion Based on Modified Quasi‐Newton Equation Quasi‐Newton Equation

Abstract Waveform inversion is a kind of method to reveal the underground structure and lithology through minimizing the residual error between predicted wavefield and true seismic record using full‐wavefield information. In this paper, we briefly present the principle of the 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) algorithms. Different from past Quasi‐Newton methods, this modified BFGS considers gradient values, model information and objective function values to approximate the inverse matrix of Hessian matrix. Moreover, it almost does not increase the calculation amount for each iteration. The numerical experiment shows that compared with the conventional Quasi‐Newton method, the modified BFGS algorithm can not only preserve the inverse accuracy, but also significantly improve calculation efficiency.