Prestack Time Migration Method Based On Stationary-phase Principle In The Dip Angle Domain

For geological conditions with complex structure and simple velocity,the accurate imaging of subsurface media can be realized by prestack time migration,which is very suitable for the accurate imaging of continental sedimentary strata in China.The key parameters that affecting the imaging results of prestack time migration of the Kirchhoff integral class mainly include amplitude weighting function,anti-aliasing operator and migration aperture.Among them,as the control parameter of imaging boundary,migration aperture depends entirely on the information of the subsurface media,and reasonable selection of it plays an important role on the accurate imaging of the underground target.The traditional method of manual test has strong subjectivity and heavy workload,which seriously restricts the quality and efficiency of imaging.In recent years,the application of imaging dip angle scanning in the dip angle domain to determine the optimal migration aperture has become one of the most promising methods.The advantages of the method lie in: the migration response of reflected wave is an upwardly open arc in the 2D dip angle domain,and the arc bottom indicates the optimal imaging dip angle of imaging points.Then,we can easily determine the optimal imaging dip angle and its stationary phase Fresnel zone(namely the optimal migration aperture)by scanning the arc bottom.At present,the method still relies on a preset discriminative threshold in terms of the scanning algorithm,and it is necessary to perform threshold trial and setup in advance,which causes inconvenience in actual data processing.Therefore,this paper focuses on the optimal migration aperture of the dip angle domain,and strives to establish a stable and efficient optimal aperture prestack time migration method.Based on the basic theory of seismic wave imaging,this paper firstly derives the analytical formula of wavefield time extrapolation based on phase shift formula of wavefield depth extrapolation,stationary phase principle and Dix formula.Then a stationary phase of prestack time migration method(short for stationary phase migration method)is established by introducing the deconvolution imaging condition.On this basis,we established high-quality imaging dip angle gathers without stretching distortion by introducing the stretching distortion factor and the amplitude weighting coefficient in the process of migration.According to the principle of Fresnel zone,we derived the formula of first Fresnel zone which is related to travel time in the 2D dip angle domain.Then,we determined the optimal migration aperture by performing the two-step scanning of the influence factors of Fresnel zone(imaging dip angle and the dominant frequency of seismic wave)based on the criterion of optimal stacked energy.Finally,the output channel imaging mode is analyzed and selected to realize the optimal aperture imaging(namely optimal aperture migration method).In order to verify the validity and stability of the migration algorithm proposed,the model data obtained by finite difference modeling and actual data from SEGs open source are tested and processed.The local contrast and SNR quantitative analysis results of the actual data migration profiles with time-varying aperture and scanned optimal aperture show that: the migration noise is well suppressed in migration profile with scanned optimal aperture,the SNR was improved by 7.37 d B as a whole,and the imaging of geological structure is clearer.The analysis results of computational cost of the stationary phase migration method and the optimal aperture migration method show that: the computational efficiency of the optimal aperture migration method should be better than or equal to that of the stationary phase migration method.