Reflection waveform inversion(RWI) provides an effective initial model for full waveform inversion(FWI) by alternately updating the low-to-intermediate and high wavenumber components in the model.However,time-domain RWI requires storing the cross-correlation between the source background wavefield and the receiver scattered wavefield over the entire time series to compute gradients,demanding substantial computational storage.Although frequency-domain RWI exhibits multi-scale properties,it also imposes high demands on computational memory.Based on the discrete Fourier transform,this study proposed a RWI method that extracts frequency-domain wavefields from corresponding time-domain wavefields for multi-scale inversion in the time-frequency domain.The proposed method requires storing only a few single-frequency wavefield snapshots,showing significantly lower storage demands compared to conventional time-domain RWI and reduced computational costs relative to frequency-domain RWI.Therefore,the proposed method effectively combines the computational efficiency of time-domain RWI with the multi-scale properties of frequency-domain RWI.Considering the frequently missing low-frequency data in actual seismic data,this study further integrated envelope-based RWI to reconstruct low-frequency information for medium-deep subsurface structures.This enables stage-wise optimization of the inversion process,reducing the dependency on low-frequency long-offset data.Finally,numerical examples validate the effectiveness of the time-frequency domain RWI method based on envelope data in recovering low-frequency information.
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