Source-independent envelope-based FWI to build an initial model
AO Rui-De;DONG Liang-Guo;CHI Ben-Xin;State Key Laboratory of Marine Geology,Tongji University;
Full waveform inversion(FWI)is facing many difficulties in practice.One of the issues is how to construct a relatively precise initial model.Another one is the treatment of source wavelet.Both seriously affect the final inversion result.To tackle this problem,we propose a source-independent envelope-based FWI approach to build an initial model for the traditional FWI.On one hand,the cross-convolved wavefields,including the convolution of observed wavefields with a reference trace from the modeled wavefields and the convolution of modeled wavefields with a reference trace from the observed wavefields,can eliminate source wavelet effect in the misfit function of waveform inversion.On the other hand,the envelope of wavefields contains abundant low-frequency components,which are crucial for initial model inversion.Therefore,we use the envelope of cross-convolved wavefields to establish misfit functions,the feasibility of which is proved by theoretical analysis.The expressions of the corresponding gradient and adjoint source are derived.Furthermore,we use a Marmousi synthetic data example to test our method.The proposed method is tested by using different reference traces,misfit functions andsource wavelets.(1)The normalized misfit of long offset reference trace converges more slowly than that of short-offset reference trace for noise-free data and the average trace as reference trace is better than the minimum-offset reference trace for noisy data.(2)The logarithmic envelope is the best and the squared envelope is the worst misfit function to invert the deep part of the model.The initial model built by our method choosing the logarithmic misfit function and minimum-offset reference trace is much better than that of the traditional envelope-based FWI when the source wavelet is incorrect.(3)Using other kinds of source wavelets,such as 20 Hz Ricker wavelet without low frequency below 5 Hz and 12 Hz Gauss wavelet,both of which are quite different from the true 8Hz Ricker wavelet,the inversion result of our method can provide agood initial model for the traditional FWI.In addition,the initial model can be used in seismic depth migration,and the imaging result is close to the RTM result with true velocity model and much better than that with gradient initial model.In conclusion,first,we propose a source-independent envelope-based FWI approach to build an initial model for the traditional FWI without any prior information when the source wavelet is unknown and even the data lack low frequency.The initial model built by our method can also be used as the velocity model for pre-stack depth migration.Second,the short-offset reference trace is better than long-offset reference trace for noise-free data and average trace as reference trace is better than the minimum-offset reference trace for noisy data.Third,the logarithmic envelope misfit function is the optimal misfit function.Finally,by changing the source wavelet,it is further proved that our method is source-independent.
【CateGory Index】： P631.44
【CateGory Index】： P631.44