The Research Of True Amplitude Gaussian Beam Migration In The Image Domain

With the further development of oil and gas exploration,the targets of seismic exploration have gradually changed from large-scale structural oil and gas reservoirs to small-scale and complex lithologic reservoirs.Moreover,the conventional seismic processing technology has been difficult to meet the demand for oil and gas exploration nowadays.The seismic migration method is the core during the whole process of the seismic data processing.The high-resolution imaging profile obtained by the migration can not only provide the evidence for the layer division and the fault identification,but also guide the geological modeling and the numerical reservoir simulation in the development stage.In addition,the results of migration after the true amplitude processing can further provide reliable petrophysical parameters,help to predict the reservoir,and reduce the risk of oil and gas exploration.True amplitude migration has always been the focus for experts and scholars in the field of geophysical exploration,and it is also a difficulty of research.According to the general theory of true amplitude,in order to get the true amplitude imaging result,the imaging conditions and the process of wavefields propagation must be amplitude-preserved.However,the amplitude fidelity of these two aspects will be affected by many factors in general.In this paper,we mainly discuss two aspects as follows: On the one hand,the wavefields propagation process in viscoacoustic media will be affected by the absorption,while the conventional migration methods do not consider the amplitude attenuation and phase distortion of the seismic wave caused by the quality factor Q.As a result,the amplitude distortion and the reduction of imaging resolution may occur in the migration results.On the other hand,due to the limited acquisition aperture and sparse receivers,conventional crosscorrelation imaging condition may cause the amplitude imbalance and low imaging resolution.The seismic migration methods can be divided into two major algorithms which include ray and wave equation.Kirchhoff migration is the representative of ray-based migration methods,which have the advantages of high computational efficiency.In contrast,one-way wave migration and reverse time migration have the advantages of high imaging accuracy.However,Gaussian beam migration is a compromise method that not only has the high accuracy of the wave equation migration,but also retains the flexibility and efficiency of Kirchhoff migration.Therefore,Gaussian beam migration method is chosen as the research object in this paper.Based on the general theory of true amplitude migration,the viscoacoustic media theory and the least square theory are introduced into the Gaussian beam migration,and then we develop the true amplitude Gaussian beam migration in the image domain.As a result,the amplitude fidelity and the resolution of the migration result can all improve a lot in this way.The specific contents of this paper mainly include the following points:(1)Based on the ray theory,we introduce the basic theory of Gaussian beam method,Gaussian beam expression,and the Green function of Gaussian beam integral in viscoacoustic medium.Meanwhile,the influence of different quality factor Q on Gaussian beam and Green function is also discussed;(2)Based on the theory of true amplitude Gaussian beam migration,we successfully derive the Gaussian beam migration formula based on crosscorrelation imaging condition.Based on it and considering the principle of compensation in true amplitude migration of one-way wave equation,we compensate the upgoing and downgoing wavefields by complex traveltime correction method,which are constructed by Green function in term of Gaussian beam.So that we realize the Gaussian beam migration in viscoacoustic media;(3)Based on the theory of Gaussian beam migration in viscoacoustic media and the least square theory,we can derive the viscoacoustic Gaussian beam Born forward operator and the viscoacoustic Gaussian beam conjugate migration operator.What's more,we accelerate the process of forward and migration by the inverse slant stack and the slant stack algorithm respectively and finally implement the viscoacoustic least square Gaussian beam migration by the conjugate gradient method;(4)Based on the inverse Hessian compensation theory,the true amplitude Gaussian beam migration method in the image domain is developed.On the one hand,starting from the least square target functional,we explain the mathematical and physical meanings of linear Hessian operator,and illustrate the principle of amplitude compensation in the image domain using inverse Hessian operator.On the other hand,based on the linear Hessian operator expression and the Green function expressed by Gaussian beam integral,we derive the approximate diagonal Hessian operator characterized by Gaussian beam.At the same time,we use the plane wave phase encoding strategy to accelerate the single-trace solving process.Finally,we can regard the inverse of Hessian operator as the amplitude weighting coefficient and apply it to the result of Gaussian beam migration.That way,we can realize the true amplitude Gaussian beam migration in the image domain.