A novel full waveform inversion method based on a time-shift nonlinear operator

Conventional full waveforminversion (FWI), which uses the L-2 normto measure the misfit between the observed and the synthetic data, is known to be a nonlinear and ill-posed optimization problem. Usually, this problem is solved by using iterative gradient-based methods, which are difficult to converge to the global minimum of the misfit function because of cycle-skipping. We propose a new misfit function, which uses the nonlinearly transformed data instead of the original data. Because the nonlinearly transformed data can be very rich in low frequencies, the new misfit function is less prone to cycle-skipping. In this paper, we discuss the criteria to choose a suitable nonlinear operator and propose a new nonlinear operator by introducing a frequency selection mechanism into the envelope operator. We show that the proposed nonlinear operator is equivalent to the envelope operator in the first-order, but it outperforms the envelope operator in the case of higher orders. We develop an FWI method based on the new misfit function. Using the Marmousi model, we demonstrate that, compared with conventional FWI, the proposed FWI method is less prone to cycle-skipping. By using a model produced with the proposed FWI method as the initial model, it is shown that conventional FWI can achieve much better results. In addition, we show that the proposed FWI method is better than envelope inversion at mitigating cycle-skipping.