A Study On Inversion Imaging Based On Low-rank Decomposition In TTI Media

With the thorough development of oil and gas resources exploration,conventional seismic acquisition is turning to low-frequency,large offset,and wide-azimuth seismic acquisition.Therefore,seismic anisotropy has become an important factor which can not be ignored for seismic data processing.Anisotropy is widely found in various rock types.With partial regional results tallied,it was clear that a large number of anisotropic reservoirs have been found in carbonate rocks,shale oil reservoirs,and offshore exploration areas in western China,and their oil and gas reserves are extremely abundant.So the research on anisotropic reservoirs has significant strategic importance on ensuring the security of national energy strategy.Modeling based on conventional coupled equations may exist SV-wave artifacts and numerically dispersion,also suffer from strict limitations on the media parameter(?>0)and instabilities.For decoupled qP wave equation,it requires many tedious mathematical deduction,causing its numerical calculation to be very challenging,and its accuracy is limited,due to containing a pseudo-differential operator in this equation.To overcome these defects,Firstly,we derived a pure qP-wave propagator suitable for arbitrary TI media.Then the Low-rank decomposition algorithm was employed to solve the space-wavenumber domain matrix in propagator.In addition,the Cerjan's attenuation boundary condition was adopted to eliminate boundary reflections.Finally,an indirect pure qP-wave evolution scheme was implemented,which is successfully applied to perform modeling and RTM.Numerical experiments on modeling and RTM validate that,compared to the traditional approaches,the proposed scheme is more accurate and stable for anisotropic qP-wave modeling and RTM.Specifically,our method presented here include three aspects : it cannot only avoid the complicatedly mathematical deduction of decoupled equations,but also break the restrictions(?>0)on media parameters for coupled equations.Besides,SV-waves artifacts and numerical dispersion can be eliminate completely by this strategy.Synthetic results remain high quality even for large temporal and spatial intervals or high-frequency sources,which proves better adaptability of the proposed method.The computation efficiency is the key factor to restrict the practicality of anisotropic reverse time migration.In addition,pseudo shear-wave artifacts,numerical dispersion and instability are also inherent problems of TTI medium qP-wave forward modeling and reverse time migration.The Low-rank wavefield extrapolation algorithm is basically free from pseudo shear-wave artifacts,numerical dispersion and instability.However,this method is a time-consuming and inefficient due to computing speed is controlled by the model parameters.To further improve the computation efficiency,start from the idea of ??mixed-grid finite-difference method,a new compact differential template was proposed,and the adaptive difference coefficient matching the model was obtained by means of Low-rank decomposition.Then,a Low-rank finite difference modeling for TTI medium was implemented,and we successfully applied it to reverse time migration imaging.Numerical tests show that,the proposed scheme is an anisotropic reverse time migration practical technology which combines high imaging accuracy and high efficiency.Specifically,our method carried the characteristics of flexibility and efficiency of finite-difference method and inherited the merits of calculating pure qP-wave precisely of Low-rank wavefield extrapolation algorithm.That is,it can remove the pseudo shear-wave artifact and numerical instability while improving the computation efficiency of seismic wave.Seismic anisotropy of the earth medium primarily manifest as velocity anisotropy,which certainly affects the kinematic properties of seismic waves propagating inside the earth.The traditional acoustic reverse time migration(RTM)and least-squares reverse time migration(LSRTM)do not account for this distortion of phases caused by strong anisotropy,which can lead to defocusing of migration images,the warp of events and the slow searching efficiencyor non-convergence following the increase of iterations.Although reverse time migration for vertical transverse isotropic media(VTI-RTM)is capable of making up these defects,the low-frequency noise in shallow section,poor imaging due to energy loss in mid-deep part,imbalanced amplitude and others still exist in migration imaging processing.To correct for this drawback,this paper uses a linearized inversion method applicable for vertical transverse isotropic media firstly,denoted as VTI-LSRTM.The key points of this method include two parts : ?1 We use a linearized anisotropy quasi-acoustic modeling operator for forward modeling during the least-squares iterations.?2 Gradient direction of the misfit function is derived using the adjoint-state method for back propagating the residual wavefields.Then for saving the input/output and storage demands and improving the efficiency on inversion imaging,we further introduces the plane-wave encoding technique to the inversion framework of VTI media and presents the strategy of fast least-squares reverse time migration with plane-wave encoding for VTI media.Numerical tests on synthetic dataset with a simple model and a complex Marmousi model prove that,?1 the merit of the proposed method over standard acoustic RTM and LSRTM when the recorded data had strong anisotropy effects,and ?2 the crosstalk introduced by plane-waves and the low-frequency noise from itself of two-way wave propagator can be suppressed automatically,and ?3 the advantage of this approach compared with conventional VTI-LSRTM is that it both produces high quality images with better balanced amplitudes in mid-deep parts and more resolution & SNR &fidelity similar to VTI-LSRTM and decreases the computational cost significantly.The sensitivity tests for background velocity errors reveal that the liability of this method is the requirement for relatively accurate migration velocity and Thomsen parameter models.Least-squares reverse time migration based on pseudo-acoustic wave is a potential tool for seismic imaging.However,the method suffers from the limitations of anisotropic pseudo-acoustic wave approximation.Such as forward simulation for TTI medium is unstable and demigration records exists quadratic perturbation of pseudo SV-wave and numerically dispersion.In addition,least-squares reverse time migration based on pseudo-acoustic wave also faces a lot of the problems of low computational efficiency,and slow convergence andhigh dependency on velocity and other model parameters.In order to overcome the inherent shortcomings of “acoustic approximation”,under the framework of inversion,this paper realizes the linearized forward modeling of pure qP wave and the pure qP-wave least-square reverse time migration for the first time by means of Low-rank finite difference algorithm.Further,in order to speeding up the inversion efficiency,while improving the dependence of inversion method on model parameter error and enhancing the adaptability to the seismic data noise,we develop the TTI media pure-qP-wave prestack plane-wave least square reverse time migration imaging method by introduce the prestack plane-wave optimization strategy.After implementing the algorithm by programming,the advantages and potential of this approach are demonstrated through the model imaging test:on the one hand,the high efficiency is shown in processing of inversion imaging;on the other hand,the capability of anti-noise is also improved,meanwhile,dependence of inversion method on model parameters is relieved.