Time-domain Adaptive Full Waveform Inversion Based On The Matched Filtering

As the exploration targets trend to the complex area,a high-precision and high-resolution velocity rebuilding method is needed to support the processing and interpretation of seismic data.FWI(Full waveform inversion)is based on the fitting of the observed data and the predicted data.It takes full advantage of the full wavefield information of the pre-stack seismic data to rebuild velocity model.It is a high-precision velocity rebuilding method,which has the ability to reflect the details of the geo-structures under the exploration area.FWI has strong nonlinearity,which restricts the application of this method.This paper performed a deep research on the time-domain FWI,for the cycle skipping problem caused by the strong nonlinearity,this paper proposed a method based on matched filtering to solve this problem from the data preprocessing point of view.Rebuilding the predicted data can reduce the number of local minima in the objective function,and improve the stability of the inversion.This paper proposed a time-domain full waveform inversion method based on the least squares filtering(LS-FWI).This new method can effectively reduce the dependency of inversion on the start model and low frequency information,and improve the stability of the FWI.We have studied the basic theory about the matched filtering in time domain.According to the least square principle,we can calculate the matched filter operator,and remould the phase of predicted data by matched filtering to narrow the phase difference between the predicted data and observed data.Meanwhile,a new objective function is constructed with the new predicted data.Due to the effection of filtering,the new objective function has fewer local minimum,it can be steadily decreased,thus the inversion procedure can steadily converge to the global minimum.Because the matched filtering can replace the wavelet shaping to eliminate feature difference between different seismic data,this method not only can narrow the phase difference between predicted data and observed data,but also can eliminate the influence of wavelet difference,hence the LS-FWI still has a better performance when the wavelet difference existed.This paper performed a research on the least squares filtering method in wavelet domain.Based on the multi-scales FWI with wavelet transform,a multi-scales adaptive full waveform inversion method based on the wavelet transform is proposed to improve the stability of inversion.The new method realizes the matched filtering in the wavelet domain to rebuild the predicted data.With the multi-scales characteristic of wavelet transform,the data can be divided into different frequency bands,starts the inversion from the low frequency band and enlarges the frequency range to implement the multi-scales inversion.The result of numerical simulation experiment demonstrates that these new methods can be immune to cycle skipping,and more robust than conventional FWI.