Frequency Controllable Envelope Operator and Its Application in Multiscale Full-Waveform Inversion

Full-waveform inversion (FWI) attempts to find optimal models of subsurface by using full information of the observed data. One difficulty in conventional FWI is that the misfit function has many local minima because of cycle skipping. Envelope inversion (EI), which uses the envelope operator (EO)-based misfit function, has been proven to be effective in mitigating cycle skipping and recovering long-wavelength velocity model. However, EI ignores the fact that the information within different frequency bands plays different roles in inversion. In this paper, a frequency controllable EO, which can control the frequency components being used to construct envelope, is proposed. We propose a new misfit function and a multiscale FWI method. Using synthetic experiments based on the Marmousi model, we demonstrate that the proposed method is better than EI in mitigating cycle skipping and in building an accurate initial model for conventional FWI to significantly improve its final result. In addition, this method can tolerate a wide range of noise levels. Its effectiveness has also been successfully demonstrated using a field data set.