Time-frequency domain multi-scale full waveform inversion based on adaptive non-stationary phase correction

In this paper, we propose a non-stationary phase correction objective function to mitigate the waveform mismatch problem for the time-frequency domain Full-Waveform Inversion (FWI). At the same time, according to the difference between recorded data and synthetic data, we introduce an adaptive correction factor to adjust the size of the phase correction. Based on the objective function of time frequency domain FWI, we use the chain rule to deduce the corresponding adjoint source and theoretically prove the feasibility and superiority of the Adaptive Non-stationary Phase correction Time-frequency multi-scale Full Waveform Inversion ( ANPTFWI ). In the process of numerical testing, we combine the advantages of low-pass filtering and multi-scale inversion strategy to alleviate the non-linearity of FWI. The numerical tests without low frequency information show that when the seismic data lack low frequency information below 7 Hz, the ANPTFWI method combined with the conventional FWI method still can obtain high accuracy inversion results. The numerical tests with an inaccurate wavelet show that even if there is a large phase difference between the two wavelets, we still can use the non-stationary phase correction method to mitigate the cycle skipping problem. The numerical test proves that the ANPTFWI has a strong ability for building good initial velocity models and mitigating the cycle skipping problem.