| The need to enhance imaging accuracy and resolution in complex geologic environments such as subsalt or in highly stressed,faulted,and fractured media is more and more serious as the growing challenges in oil and gas exploration.Better understanding and usage of the intricate details of seismic anisotropy has great value for enhancing model building,imaging,and inversion schemes.Transverse isotropy(TI)is the most common anisotropic model,including vertical axis of symmetry(VTI)and tilted axis(TTI).The full elastic anisotropic wave equation could accurately account for the wave propagation in TI media.However,for migration based on wave equation(especially for the two-way wave equation migration),it not only requires an anisotropic velocity model that consistently describes P-and S-wave kinematics,but also is computationally very demanding,leads to difficult for widespread use.Therefore,the study of using only P-wave in TTI anisotropic media for seismic data imaging processing is considerable realistic significance.Acoustic wave equation in TTI media is classified into two methods today.The first method is on the base of Alkhalifah's pseudo-acoustic approximation,namely setting S-velocity along direction of symmetric axis to zero.Starting from the fourth-order dispersion relation in VTI media,we could arrived at a system of coupled second-order acoustic wave equations.Another method is directly from the elastic-dynamic equation,which could be simplified by the pseudo-acoustic assumption as well,resulting a coupled system formally alike the first method.The second order PDEs could be solved by finite difference numerical method in time-space domain,it's similar with the common method for isotropic media,for example,we can use second order or fourth order finite differencing for time derivatives,and use high order finite difference or pseudo spectral method for space derivatives.The second-order coupled equations from both above methods have almost same kinematic characteristics,which makes them has good performance in modeling P-wave propagation.While the dynamic characteristics of the two methods are totally different in nature,that's the reason why in many specific usual geologic conditions,there are more instability for formal method than for latter method.Besides,as non-zero values of S-wave exist in directions except symmetric axis,unwanted S-waves will present in P-wave simulation results,and artifacts will be bought into P-wave RTM images.That's the question of S-waves in simulation of P-waves,and it's one of the necessary points for removing the S-waves.Decoupled pure P-wave simulation application is a promising method for P-wave modeling in TI media.The uncoupled method bases on the integral time continuation in mixed space-wavenumber domain.It could eliminate the interference of S-waves completely,and has the advantage of modeling stably in large time step without numerical dispersion.Such that it doesn't has any problems of stability and remaining S-wave,that common in coupled methods.The uncoupled method has weakness in accuracy for P-wave kinematic,however,it could satisfy requirement of exploration development for accuracy,so it's still a valuable method for P-wave modeling in TI media.The basic principle of uncoupled method is based on the Tsvankin's exact dispersion relation,P-wave and S-wave could uncoupled formally in wave number domain,obtaining completely decoupled P-wave equation by different numerical method in mixed space-wavenumber domain.Pseudo-acoustic methods studied in this paper are for the purposes of the application of reverse time migration(RTM).The RTM implementation includes three steps,namely the forward wavefield extrapolation,backward wavefield extrapolation,and the using of imaging conditions.In order to obtain higher accuracy and resolution pseudo-acoustic RTM results in TI media,we not only need to consider the qP-wave equation derivation and implementation issues,but also considering other issues such as low-frequency noise in isotropic RTM,which is an important factor affecting imaging in TI media.Therefore imaging denoising is an important aspect of the RTM.To facilitate the analysis and comparison in accuracy of the imaging results,this paper also gave full study and description for the full elastic wave equations based RTM in TI media.Compared with scalar pseudo-acoustic wavefield equations,vector wavefield elastic wave equations have problem of the coupling and conversion for P-and S-waves.The major issue in elastic wave RTM is related to the elastic wavefield imaging condition.The traditional elastic wave imaging conditions can not obtain accurate images of P-and S-waves.The imaging condition based on the decomposition of P-S waves has possible to overcome the problem,obtaining physical meaning clear migration results in favor of the application in subsequent seismic data processing and interpretation.The decomposition of P-S waves in TTI media can not use the direct method as in isotropic medium,which is based on the convergence and curl operators.Construction separation operators related to the local media parameters can accurately separate P-S waves in TI inhomogeneous media,and it will has a greater effect when applied to the elastic RTM in TI media.By comparison of migration results from qP-wave RTM and elastic RTM under the same geological model parameters,we can have the preliminary evaluation in precision of acoustic methods.Combined with above contents,I propose the processing idea and implementation method for qP-wave RTM in TTI media.It shows better applicability and effectiveness for resolving anisotropic imaging problem,after the tests of model and real data application,providing high resolution migration sections for complex seismic exploration.However,the paper cannot cover all aspects in RTM application,and now it also has many parts that need to improve,so it is important to do more depth,more extensive research for many problems.Finally,the explanation for this question and the next plan are presented. |
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