The Research Of Least-squares One-way Wave Migration In VTI Media

With the developing of oil and gas exploration,the precision of seismic migration is higher and higher.The traditional migration methods are mostly based on the assumption that the underground media is complete elastic and isotropic.It will lead to the traveling time deviation of seismic wave in the anisotropic area where the underlying layer or fracture develops,and the propagation of seismic waves can not be accurately simulated underground.On the imaging section,the reflection wave will not be moved to the right position,the diffraction wave will not be convergent,and the imaging events' resolution and the signal to noise ratio are low.Based on different theories the migration methods can be divided into two types: the ray based migration and wave equation migration,such as Kirchhoff migration,Gauss beam migration and Control beam migration,which have high computational efficiency.But the accuracy of wave propagation in strong complex medium is limited.The wave equation migration algorithms are divided into two-way wave equations,represented by RTM and one-way wave equation,represented by SSF,FFD and GSP.The two-way wave equation has high computation accuracy,which can simulate the propagation of the full wave field in the underground.However,the high memory and computation time are the key factors that restrict the popularization of the two-way wave methods.One-way wave methods have two advantages,such as high precision and high efficiency,which has great potential for practical application.In this paper,from the elastic wave equation of VTI medium,we first derive the dispersion relation equation of qP(quasi-P)wave by the acoustic approximation assumption.On the basis of the isotropic FFD(Fourier finite-difference)migration imaging method,the one-way wave VTI-FFD operator is derived.This operator is made up of three parts: the frequency wavenumber domain phase shift term,the frequency space domain time shift term and finite difference compensation term.By fast Fourier transform the phase-shift term and the time-shift term are calculated in alternating wavenumber domain and spatial domain,the finite difference compensation term is used to correct the high angle spread wave field to adapt to the lateral variation of velocity and anisotropic parameters.The compensation operator can be written as a fractional summation form.The more number of the terms involved,the higher simulation accuracy of the high angle propagation wave field will be obtained.Meanwhile,the computation cost will also be increased correspondingly.Then,through error analysis,impulse response test and SEG/EAGE salt model pre-stack depth migration imaging test,we verify the adaptability of VTI-FFD operator to strong lateral varying media and the imaging of steep dipping reflector.Secondly,the preconditioned pre-stack VTI-FFD migration method is proposed with high order wave field propagator.By improving the approximate order of the FFD operator,the propagator has higher imaging accuracy.Then the illumination precondition operator is used to further balance the imaging amplitude constructed at different depths.On this basis,the VTI medium one-way wave migration operator and the anti-migration operator are derived to realize the least square pre-stack depth migration algorithm of the VTI medium.Finally,the test of simple anisotropic trapezoidal model,strong lateral varying standard Hess model and field data are carried out,the results show that the least squares migration method proposed in this paper can correct the anisotropic medium travel time deviation,significantly improve the imaging accuracy of underground high steep dipping structures,balance deep imaging amplitude and provides high SNR ratio imaging results.According to the least-squares migration's drawbacks of large amount of calculation and strong coherent imaging noise,the optimized methods were proposed: first through the introduction of plane wave encoding strategy,which is used to compress seismic data,the computational efficiency is greatly improved;secondly,in the iterative process we extract the CIG gathers,and apply PWC operator to the CIG gathers to suppress the coherent noise and improve signal to noise ratio.Based on the optimization algorithm,the numerical tests results of the anisotropic Marmousi2 model show that the optimized migration method has three improvements: 1)the new method is suitable for complex VTI medium with strong lateral velocity variation;2)the imaging method is more efficient and of higher signal-to-noise ratio;3)using the plane wave encoding strategy can overcome the one-way wave method's defect of low near surface imaging precision.