Study On Wave Equation Pre-stack Depth Migration In Angle Domain

Wave equation prestack depth migration,which makes full use of the structural and lithological information carried by seismic waves,is a high-precision imaging method,while the common image gather generated by migration is the direct embodiment of this implicit information.In the case of strong lateral velocity variation,conventional common image gathers,such as offset domain or shot domain common imaging gathers,have the defect of ray multipath,which leads to the illusion in kinematics and dynamics,thus reducing the imaging accuracy under complex structure.The angle domain common imaging gathers(ADCIG)avoid the phenomenon of ray multipath,and correctly reflects the information of structure and lithology underground,so it's the only common image gathers that has no illusion at present.The core technology of angle domain migration method is to extract high precision ADCIG,and the method that based on double square root equation migration is the best among many methods.In this paper,we implemented a method of extracting ADCIG based on double square root equation migration in image space,which has improvement in computing efficiency and precision.Effected by the noise and formation tuning,the phase axis of ADCIG cannot be completely leveled even under the correct velocity,In this paper,we discussed the problem of waveform distortion at the high angle of ADCIG,and by cutting the stretching on ADCIG to eliminate the low frequency noise on the stacked section.Further more,in order to improve the imaging quality of the angle domain stack section,we analyzed the applicability of the denoising method based on singular value decomposition to ADCIG.For ADCIG with horizontal coherent phase axis,the singular value decomposition denoising method can effectively remove the interference of random noise,and can also suppress high angle low frequency waveform stretching.Finally,the signal-to-noise ratio and resolution of the stacked section are effectively improved.Most of the rocks in the earth has the characteristics of anisotropy,in seismic imaging,ignore the anisotropy will results in the positioning of target space reflection not accurate,the diffraction wave cannot be completely convergence,and even lead to structural distortion or illusion.With the increase requirements of precision in exploration,the effect of anisotropy on seismic imaging is more remarkable.In this paper,the dispersion equation of qP wave in the VTI medium is introduced into the wave field extension of the double square root equation.Based on the idea of velocity splitting,the wave field extension operator of the VTI medium double square root equation migration is derived,which effectively improves the accuracy of the wave field extension in the VTI medium and realizes the pre stack migration method of the angle domain of the VTI medium.The method avoids the defect of the ADCIG in isotropic migration,and has more abundant angle information.The diffraction wave of the VTI medium section is more convergent,the characterization of the structure is clearer,and the signal to noise ratio and the resolution are all improved.After obtaining high-precision ADCIG,the application of angle domain migration in data processing is discussed in this paper.First,it has been proved that there are some errors and false in conventional image gathers in a complex survey,so it is difficult to obtain accurate velocity field by using this CIG for velocity analysis,while ADCIG is the only one with no false at present and it is sensitive to velocity error,so it is very suitable for velocity analysis.In this paper,after analyzed residual depth of ADCIG in the presence of velocity error,we deduced the velocity updating equation in angle domain based on the theory of residual curvature method.For the velocity spectrum we adopt high resolution correlation function to calculate,then combine these two aspects we designed the flow of ADCIG velocity analysis.This velocity analysis method can quantitative estimate velocity error through ADCIG,so it can obtain more accurate velocity update and finally improves the velocity accuracy.Another important uses of ADCIG is for AVA analysis.This paper derived the double square root amplitude preserving migration operator and realized amplitude preserving migration in angle domain,the obtained ADCIG can provide real underground structure and lithology information.Through the study of forward and inversion for AVA features and ADCIG,this paper analyzed the relationship between AVA curve and amplitude characteristic form angle gather,discussed the adaptive of AVA analysis,which was based on ADCIG in complex structure area,the results showed that the AVA feature of ADCIG extracted from angle domain amplitude preserving migration is more closer to theoretical curve,all those proved that ADCIG is conducive to AVA analysis and attribute inversion.Finally,the theoretical analysis and the test of different models have laid a foundation for the theory development of prestack depth migration,and also provide a reference for the application of angle domain migration in data processing.