Full waveform inversion using truncated Newton optimization

Optimization is an important tool for most geophysical inverse problem. In this work, we propose the time-domain full waveform inversion (FWI) using truncated Newton optimization, meanwhile we indirectly gain the knowledge of Hessian matrix information through Hessian-vector products calculated by 2nd-order central finite-difference approximation, and the above products can be obtained with no difficulty by gradients of two adjacent models. The proposed method is a Hessian-free and applicable Newton method while the explicit construction of conventional Hessian or of its inverse is beyond nowaday computational capability. The study of synthetic Marmousi2 model demonstrates that: in terms of computational efficiency and convergence speed, the truncated Newton method preforms better than L-BFGS and other methods in FWI, and the Newton direction or Hessian matrix plays a crucial role in rebuilding the subsurface velocity models, especially in the deep areas.