The Study On Time-frequency Domain Full Waveform Inversion Based On The Weak Model Dependent Objective Function

With the development of petroleum exploration technology and the the demand for energy in national economic construction,the focus of petroleum exploration has gradually shifted from the structural exploration stage to the lithology exploration stage,and efforts have been made to explore the mineral resources in the second space,which needs high-resolution of the seismic exploration technology.Since the core of seismic exploration is the velocity of seismic waves,an accurate velocity model is the key to understanding the underground structures and lithology distribution.At the same time,the resolution of the velocity model will directly affect the accuracy of the migration imaging and interpretation results.At present,seismic velocity building methods can be mainly divided into stack velocity analysis,traveltime tomography,migration velocity analysis and full waveform inversion(FWI),but the first three methods cannot satisfy high-resolution requirements of seismic exploration in the complex geological structures.The seismic waves of the kinematics and dynamics can be fully used by the FWI method to obtain the underground model parameters,which has the advantages of high-resolution imaging of complex structures and good inversion results.Although the FWI method has obvious advantages in many aspects,it still faces a lot of problems to be solved,such as cycle skipping,initial velocity model dependence,absence of low frequency components and weak scattering gradient operator.In this paper,the FWI problems are solved from the perspectives of seismic waveform matching,initial velocity model dependence,low-frequency reconstruction and energy scattering based direct envelope derivative.The four types of methods proposed in this paper and the research results can be summarized as follows:(1)From the perspective of waveform matching,the time-frequency domain phase correction technique is used to mitigate the cycle skipping.First,the phase information of the time-frequency domain synthetic data is used as a template to correct the phase information of the observed data,which is to make the phasedifference between the observed and synthetic data within half cycle,in this way,the cycle skipping in the FWI process can be successfully mitigated.And then,a phase correction factor was introduced into the misfit function,in this case,we can flexibly control the amount of phase correction of the observed data.It is also pointed out that the phase correction method can not only correct the phase deviation caused by the difference of the velocity model,but also correct the phase difference caused by the source wavelet inaccuracy,in this way,it can improve the accuracy and stability of the FWI method.At last,the numerical tests show that the time-frequency domain phase correction FWI method has a certain advantage in overcoming the cycle skipping.(2)The phase information of the time-frequency domain seismic data is used to weaken the non-linearity of the FWI misfit function,thus,it can reduce the dependence of the FWI method on the initial velocity model.In the process of phase inversion,the exponential phase information in the time-frequency domain was used to avoid the problem of phase wrapping and algorithm instability.In addition,the amplitude component of the seismic data is used as the weight factor in the time-frequency domain misfit function,which can effectively attenuate the unmatched seismic events and small perturbations,and it also can further avoid the the problem of unbalance gradient caused by the pure phase misfit function.In the numerical test,even if the seismic data absence of low frequency component below 6 Hz,the time-frequency domain weighted phase cross-correlation FWI method can still obtain high-resolution results.In addition,the noise-containing test results show that it not only has a certain advantage of reducing the initial velocity model dependence,but also has strong anti-noise ability.(3)A waveform mode decomposition method is proposed to reconstruct the low frequency components of the seismic data,thus,it can increase the range of waveform mismatching.And then,applying the reconstructed ultra-low frequency seismic data to the FWI method,it can effectively obtain the large-scale structure of the velocity model.In this paper,we analyzed the reliability of the reconstructed waveform and the low-frequency components.After analyzed the characteristics of the Hilbert envelope signal,it is pointed out that the shape of the Hilbert envelope is quite different from the the original waveform.In addition,from the perspective of digital signal processing and strong scattering theory,we give a detailed explanation about the limitations of the chain-rule envelope inversion gradient operator and thebasic reasons of the absence of the low-frequency components in the adjoint sources.Therefore,in order to preserve the reconstructed low-frequency components in the adjoint source,the waveform mode decomposition process was regarded as a pre-processing method of seismic data,so as to avoid the double linearization and loss of low-wavenumber components in the gradient.In order to further enhance the algorithm stability and anti-noise ability of the WMDFWI method,a multi-step inversion strategy was proposed to gradually reduce the proportion of reconstructed low-frequency waveform in the misfit function.Numerical experiments have proved that the multi-step WMDFWI method can obtain high-resolution inversion results,even if initial velocity model is far from the true velocity model and the seismic data absence of low-frequency components.(4)In this paper,based on the direct envelope derivative,it breaks the limitation of Born approximation and effectively reduces the dependence of initial velocity model.In the time-frequency domain,we first give a specific definition of envelope-amplitude and envelope-phase.Additionally,a weight factor was introduced to adjust the ratio of envelope-amplitude and envelope-phase in the misfit function,in this way,the seismic reflection signal of the deep velocity model can be enhanced.To achieve the purpose of improving image results of the strong-contrast model of salt bottom and sub-salt.In addition,in the inversion process of strong-contrast model,the direct envelope derivative based on the energy scattering theory is used to replace the chain-rule Fréchet derivative,which breaks through the Born approximation weak scattering hypothesis of the conventional FWI method.To update the detail information in the strong-contrast velocity model,we proposed a joint multi-scale direct envelope inversion of phase and amplitude in the time-frequency domain(PAFWI)method.