Full Waveform Inversion Of The Truncated Newton Method

Full waveform inversion is a highly resolution seismic imaging technique,which can be described as solving a nonlinear optimization problem.The second-order derivative information(Hessian matrix)of the objective function plays an important role in solving the full waveform inversion problem.This paper studies an efficient truncated Newton full waveform inversion algorithm based on the second-order derivative information,for the acoustic wave equation in frequency domain,including:For the multiple local minimum problem,a truncated Newton full waveform inversion method based on the inexact non-monotone line search is provided to mitigate this problem.For the large-scale computation and mass storage requirement,a matrix-free truncated Newton inversion method using Lanczos diagonalizable technique to efficiently solve the Newton's equation approximately,is presented.A comprehensive comparison between the inexact monotone and non-monotone line search is illustrated to demonstrate the computational performance of proposed truncated Newton inversion method.A truncated Newton full waveform inversion method based on the MINRES-QLP algorithm is proposed to deal with the non-positive definite problem of Hessian matrix of the objective function,which approximately solves the Newton's equation with matrix-free.For the large-scale computation of the Hessian matrix,an efficient matrixvector multiplication algorithm is derived based on adjoint-state theory,which greatly improves the computational efficiency of this MINRES-QLP truncated Newton full waveform inversion algorithm.Based on 2D Sigsbee model and 2004 BP model,the validity of MINRES-QLP truncated Newton full waveform inversion algorithm is verified.Compared with the pre-processing nonlinear conjugate gradient method(PCG),limited memory quasi-Newton method(L-BFGS)and truncated Newton method based on conjugate gradient method(CG-Newton),the proposed method has a good performance in terms of computational efficiency and inverted resolution.