Adaptive truncated regularized Newton full-waveform inversion method

The regularized Newton method is a modified cubic Newton method, which has a fast convergence speed and high computational efficiency. However, when this regularized Newton method is applied to solving the large-scale full-waveform inversion (FWI) problem, it is prohibitive to exactly solve the large-scale regularized Newton equation due to its large computations and mass storage requirements. Moreover, it is also very difficult to accurately estimate the Lipschitz constant for the highly nonlinear and large-scale FWI problem. In this study, we propose an adaptive truncated regularized Newton method based on the regularized Newton method to solve the FWI problem. The main idea of our proposed method is that the regularized Newton equation is inexactly solved by using the well-known conjugate gradient method, and the Lipschitz constant of the second-order derivatives is adaptively updated by using a similar update strategy of the trust-region radius in the framework of the trust-region scheme. The elegant advantage of the adaptive truncated regularized Newton method is that it is a matrix-free scheme. This proposed method mitigates the requirements of both large computations and mass storage. Therefore, it is very suitable for solving the large-scale inverse problems. Numerical experiments based on BP 2004, Sigsbee, and Overthrust models are presented to show the numerical performance of this proposed method. Compared with L-BFGS and the standard truncated Newton method, the adaptive truncated regularized Newton method has a faster convergence speed and higher computational efficiency.