Truncated trust region method for nonlinear inverse problems and application in full-waveform inversion

Abstract We present a general truncated trust region method to solve large-scale nonlinear inverse problems. The truncated trust region method can serve as an implicit regularization method, and it can take advantage of the second-order derivative information of the misfit functional. The convergence of the truncated trust region method is provided under some smoothness assumptions. To improve the computational efficiency and reduce the memory requirement, we develop a second-order adjoint-state method to efficiently estimate matrix–vector products, and solve the trust region subproblem using the truncated conjugate gradient method with the matrix-free strategy. The full-waveform inversion problem is used to test the numerical performance of the proposed method. Numerical results show that the truncated trust region method can perform better than conventional methods (e.g. nonlinear conjugate gradient method and L-BFGS) for highly nonlinear inverse problems, in terms of inverting resolution.