Source-Independent Full Waveform Inversion In Laplace-Fourier Domain

In order to solve the problems encountered in the processing of actual data,scholars have extended the full waveform inversion to Laplace-Fourier domain in recent years.Compared with the traditional inversion methods in time domain and frequency domain,full waveform inversion in Laplace-Fourier domain is not sensitive to the initial model.So even if there is a big difference between the initial model and the actual model,full waveform inversion in Laplace-Fourier domain is easier than tradition full waveform inversion method to find the global minimum and finally obtain the convergence inversion result.At the same time,the Laplace transform of the wavefield is essentially the attenuation of the wavefield in a certain degree.Through the attenuation,the original spectrum is transformed.In this way,some frequency components that did not exist before appear in the spectrum,so that the amplitude of some frequency components with small energy is significantly enhanced.Then there is a significant increase in the amplitude near the low frequency.In this way,the model components corresponding to long wavelength information can be obtained,and a better initial velocity model can be provided for full waveform inversion in frequency domain.However,conventional full waveform inversion in Laplace-Fourier domain has always been a challenging topic,partly due to the lack of accurate source wavelet information.Because the available method is usually source estimation,the inversion result depends on the quality of source information.Therefore,this paper introduced three source-independent full waveform inversion methods in Laplace-Fourier domain.They are Average Trace Normalization(ATN)method,Standard Trace Normalization(STN)method and Similarity On Data(SOD)method.Through these three methods,the potential inversion error caused by source estimation can be eliminated.These three methods need to transform seismic records into Laplace-Fourier domain at first.Then the ATN method and STN method will process each gather in Laplace-Fourier domain to normalize the wavefield.By this way,the influence of source wavelet information can be eliminated in the process of normalization.The SOD method does not need to normalize the wavefield,and can eliminate the influence of seismic wavelet in the process of constructing the objective function.With the elimination of the influence of source wavelet,the normalized wavefield allows us to construct an inversion algorithm without source information.On this basis,this paper has tested the three methods under the simulation of four different seismic wavelets.The results show that the inversion results of the three methods are almost the same,which proves that the three methods are independent of the wavelet characteristics.At the same time,noise has been introduced,and the noise immunity of the three methods has been tested.The results show that SOD method has the best noise immunity.Although the full waveform inversion method has been widely concerned,it has not been widely used,especially in high-density seismic acquisition.The huge amount of computation required by full waveform inversion has become a major bottleneck in practical application.In order to alleviate this phenomenon,this paper introduced an efficient iterative inversion method based on the conventional full waveform inversion in Laplace-Fourier domain.By separating the wavefield into background wavefield and disturbance wavefield,this method can make the impedance matrix decomposition result of the first iteration be used in multiple iterations of the same complex frequency,thus effectively improving the inversion efficiency.Through the model test,it is found that the calculation time of Laplace-Fourier domain full waveform inversion after the introduction of efficient iterative method is significantly less than that of the traditional Laplace-Fourier domain full waveform inversion method,which proves that the calculation efficiency of this method has been effectively improved both in theory and in practice,and further illustrates the advantages of this method compared with the traditional Laplace-Fourier domain full waveform inversion method.