Reverse time migration of VSP data based on the optimal staggered-grid finite-difference method
LIU Wei1(), WANG Yan-Chun2, BI Chen-Chen2, XU Zhong-Bo2
1. Post-doctoral Research Station of Geophysics,Chengdu University of Technology,Chengdu 610059,China 2. School of Geophysics and Information Technology,China University of Geosciences,Beijing 100083,China
Compared with conventional surface seismic data,VSP seismic data have many advantages,such as abundant wavefield information,high resolution and signal-to-noise ratio information.Reverse time migration (RTM) method based on two-way wave equation is considered to be the most accurate imaging method for seismic data at present.The combination of the VSP data and RTM method is helpful to describing the structures beside wells and identifying the complex geological structures accurately.Based on the two-dimensional (2D) variable density acoustic wave equation,the authors studied the high-precision RTM method of VSP data using the optimal staggered-grid finite-difference method.For different aspects of this VSP RTM method,different measures were adopted.First,the authors used the optimal staggered-grid finite-difference method to realize high-precision wavefield extrapolation.Second,the authors used the PML absorbing boundary condition to suppress boundary reflections caused by the limited computing space of model.Third,the authors used the effective boundary storage strategy to reduce the storage requirements of source wavefields.Fourth,the authors used the normalized cross-correlation imaging condition of sources to handle RTM imaging of VSP data.Finally,the high-order Laplacian filtering method was used to suppress the low-frequency noises of RTM imaging results.The different model test results show that the VSP RTM method proposed in this paper can achieve high-precision RTM imaging for VSP data.Compared with the conventional RTM method of surface seismic data,the RTM method of VSP data can more accurately identify the underground complex geological structures, such as the high-steep structures and the structures with sharp velocity changes,which verifies the effectiveness of the proposed method.
刘炜, 王彦春, 毕臣臣, 徐仲博. 基于优化交错网格有限差分法的VSP逆时偏移[J]. 物探与化探, 2020, 44(6): 1368-1380.
LIU Wei, WANG Yan-Chun, BI Chen-Chen, XU Zhong-Bo. Reverse time migration of VSP data based on the optimal staggered-grid finite-difference method. Geophysical and Geochemical Exploration, 2020, 44(6): 1368-1380.
Xue H, Liu Y, Yang Z Q. Least-square reverse time migration of finite-difference acoustic wave equation based on an optimal time-space dispersion relation[J]. Oil Geophysical Prospecting, 2018,53(4):745-753.
Nguyen B D, McMechan G A. Five ways to avoid storing source wavefield snapshots in 2D elastic prestack reverse time migration[J]. Geophysics, 2015,80(1):S1-S18.
Yan J, Sava P. Isotropic angle-domain elastic reverse-time migration[J]. Geophysics, 2008,73(6):S229-S239.
Xie W, Yang D H, Liu F Q, et al. Reverse-time migration in acoustic VTI media using a high-order stereo operator[J]. Geophysics, 2014, 79(3):WA3-WA11.
Xiao X, Leaney W S. Local vertical seismic profiling (VSP) elastic reverse-time migration and migration resolution:Salt-flank imaging with transmitted P-to-S waves[J]. Geophysics, 2010,75(2):S35-S49.
Yan H Y, Liu Y. Numerical modeling and attenuation characteristics of seismic wavefield in Kelvin-Voigt viscoelastic media[J]. Geophysical and Geochemical Exploration, 2012,36(5):806-812.
Dablain M A. The application of high-difference to the scalar wave equation[J]. Geophysics, 1986,51(1):54-66.
Liu Y, Sen M K. A new time-space domain high-order finite-difference method for the acoustic wave equation[J]. Journal of Computational Physics, 2009,228(23):8779-8806.
Liu Y, Sen M K. Scalar wave equation modeling with time-space domain dispersion-relation-based staggered-grid finite-difference schemes[J]. Bulletin of the Seismological Society of America, 2011,101(1):141-159.
Liu Y. Globally optimal finite-difference schemes based on least squares[J]. Geophysics, 2013,78(4):T113-T132.
Liu Y. Optimal staggered-grid finite-difference schemes based on least-squares for wave equation modelling[J]. Geophysical Journal International, 2014,197(2):1033-1047.
Clapp R G. Reverse time migration:Saving the boundaries[R]. Stanford Exploration Project, 2008,136:136-144.
Song Z P, Chen K Y, Yang W, et al. Comparison of the application effect of two imaging conditions in seismic wave reverse time migration[J]. Geophysical and Geochemical Exploration, 2019,43(3):618-625.
Claerbout J F. Imaging the earth’s interior[M]. Palo Alto,California:Blackwell Scientific Publications,Inc., 1985.
Kindelan M, Kamel A, Sguazzero P. On the construction and efficiency of staggered numerical differentiators for the wave equation[J]. Geophysics, 1990,55(1):107-110.
Ren Z M, Liu Y. Acoustic and elastic modeling by optimal time-space-domain staggered-grid finite-difference schemes[J]. Geophysics, 2015,80(1):T17-T40.