Study On Waveform Inversion Method Of Seismic Data

Full waveform inversion is a highly nonlinear inverse problem,and it is difficult to obtain the global optimal solution.The global optimization method is limited by the huge amount of computation,which is difficult to be widely used in the current computer environment.Most of the commonly used full-waveform inversion methods are based on the first-order Born approximation for local linearization.However,due to the strong nonlinearity between the waveform wave-field and the model parameters(such as velocity),the local linearization method based on the first-order Born approximation after abandoning the higher order Born term leads to full waveform inversion highly dependent on the initial model and low frequency data.However,in the oil exploration,accurate initial model,low-frequency information of seismic data are difficult to obtain,which resulted in local minima solution,cycle-skipping and other problems in full waveform inversion.This paper mainly uses the idea of "wave field replacement" to solve this problem,that is,use the linear transformation or nonlinear transformation,transform the waveform wave-field into other forms which has weak nonlinear relationship with the model parameters,thus reducing negative effect of using first-order Born approximation.Specific implementation methods are:1:N-order time-integral wavefield inversion method.We first define a numerical operator "N-order time integral" then make N-order time integral on the regular wavefield,obtain the N-order time-integral wavefield,and derive the propagation equation of the N-order time integral scattering wave field.Using the ajoint state method,we obtain a full waveform inversion method based on N-order time integral wavefield.In this method,the higher order time integral is used to raise the proportion of the low frequency component in the total energy,to restore the long wavelength background structure of the model,and then to reduce the order of time integration to reconstruct the high frequency information of the model.Secondly,we introduce the time damping factor into the objective function of full waveform inversion,and realize the full waveform inversion from shallow to deep.Using the recursive theory,the inversion problem is divided and the risk of the inversion fall into the local optimal solution is reduced.Finally,we combine the two methods to propose a multi-scale localization method:N-order time integration and time damping full-wave inversion to further improve the applicability of inversion.In the numerical experiment,we apply this method to SEG/EAGE overthrust model and SEG/EAGE salt model.The numerical results show that the method is correct and efficient,and anti-noise.2:Linear transformation method has the advantages of high efficiency,which can accelerate the inversion convergence,improve the inversion precision,reduce the possibility of inversion into local minima,and have good research value.However,the shortcoming of the linear transformation method is also obvious,that is,it can not restore the missing low-frequency information in seismic data.When the velocity model has a strong contrast structure,such as the SEG/EAGE salt model,the huge salt body requires ultra-low frequency to reconstruct.Using linear filtering method to achieve multi-scale inversion strategy is unable to meet the requirement.Different from the linear filtering method,the inversion method uses the nonlinear transformation provides the possibility of reconstructing the missing low frequency information in the seismic data.Envelope inversion can reconstruct low-frequency components from the envelope of seismic data to invert the large-scale structure of the model.However,the conventional envelope inversion still use the waveform Frechet derivative which resulting in the inefficient use of the low frequency information in the envelope data,and the application scope is very limited.In this paper,we use the new envelope Frechet derivative,the seismic data of the envelope field to replace the conventional waveform,significantly improve the application effect of the envelope inversion.In order to invert the velocity model with strong contrast structure,such as the salt model,we introduce the multi-scale inversion strategy into the envelope inversion,and obtain a new multi-scale envelope inversion based on the new envelope Frechet derivative,which is different from the traditional envelope inversion.In order to improve the inversion precision and efficiency of multi-scale envelope inversion,conventional full-wave inversion is introduced into multi-scale envelope inversion in the joint objective function form,and multi-offset inversion strategy is used.In the SEG/EAGE salt model,the numerical experiments using seismic data lack of low-frequency information show the correctness and effectiveness of multi-scale envelope inversion.3:Sufficient low-frequency information is necessary for full-waveform inversion(FWI)to obtain global optimal solution.Multi-scale envelope inversion(MSEI)based on the new Frechet derivative is used to invert the long wavelength components of the model by directly using the low frequency components contained in the envelope of seismic data.Although MSEI can restore the main structure of the model,the inversion quality of the model deep part still needs to be improved.Reflected waveform inversion(RWI)reduces the dependency of inversion on low-frequency and long-offset data by using travel time information in the reflected waves.However,when the underground medium contains a strong velocity contrast structure or the initial model is far from the true model,it is difficult to obtain a reliable reflection layer to produce reflected waves.We propose a combination inversion algorithm-reflection multi-scale envelope inversion(RMSEI)to overcome the limitations of multi-scale envelope inversion andreflection waveform inversion.Firstly,the wavefield decomposition is introduced into multi-scale envelope inversion to improve the inversion quality of the long wavelength component of the model.Then,after the initial model is established sufficiently accurate,the migration/demigration is introduced to realize the multi-scale reflection waveform inversion.The numerical results of the salt layer model and the SEG/EAGE salt model validate the effectiveness of the proposed method and it's potential.4:In the above-mentioned multi-scale envelope inversion method,we only use the amplitude demodulation method to obtain the low frequency information in the seismic data data.However,only to use the amplitude demodulation method will lead to the loss of the wavefield polarity information,thus increasing the possibility of multi-solution of inversion.In order to solve this problem,we propose a signed demodulation method that can contain amplitude and polarity information of seismic data at the same time.Then we introduce the signed demodulation method into multi-scale envelope inversion and propose a new inversion method:multi-scale signed envelope inversion.The numerical experiments on the salt layer model,SEG/EAGE salt model and Marmousi model demonstrate the necessity and validity of the introduction of polarity information.