基于程函方程的VTI介质初至波走时层析反演
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摘要
VTI介质初至波走时层析是反演各向异性参数的有效方法,其难点是初至波走时的计算和各向异性参数的联合反演。本文用垂直速度、动校正速度和非椭圆系数三个参数表征介质各向异性参数,使用基于Runge-Kutta算法的射线追踪,并根据相应的群慢度近似表达式推导了上述三个参数的敏感核函数表达式;利用最小二乘正交分解算法,分别用两种参数选择方法进行联合反演;数值模拟结果表明本文参数选择方法比传统Thomsen参数选择方法具有更高反演精度,从走时层析角度也证明了基于Runge-Kutta算法的射线追踪方法适用于VTI介质。
The first break traveltime tomography is an effective method for the inversion of anisotropic parameter,its difficulties are the calculation of first break traveltime and joint inversion of anisotropic parameters in VTI medium.In this paper,we use,NMO velocity,and non-elliptic coefficient to characterize the anisotropy.The ray tracing based on Runge-Kutta algorithm is used to calculate Fréchetkernel.According to group slowness approximate ters are derived.In order to overcome the magnitude between the three parameters,a double-roundstrategy is employed.The least squares orthogonal out the joint inversion of the two methods.Numerical simulations show that the proposed methodhas a better inversion accuracy than the Thomsen Kutta algorithm is not only applicable to isotropic medium but also to VTI medium.
The first break traveltime tomography is an effective method for the inversion of anisotropic parameter,its difficulties are the calculation of first break traveltime and joint inversion of anisotropic parameters in VTI medium.In this paper,we use,NMO velocity,and non-elliptic coefficient to characterize the anisotropy.The ray tracing based on Runge-Kutta algorithm is used to calculate Fréchetkernel.According to group slowness approximate ters are derived.In order to overcome the magnitude between the three parameters,a double-roundstrategy is employed.The least squares orthogonal out the joint inversion of the two methods.Numerical simulations show that the proposed methodhas a better inversion accuracy than the Thomsen Kutta algorithm is not only applicable to isotropic medium but also to VTI medium.
引文
[1] 秦宁,李振春,张凯等.高斯波束角道集的旅行时层析速度分析.石油地球物理勘探,2013,48(3):366-371.Qin Ning,Li Zhenchun,Zhang Kai et al.Traveltime velocity tomography based on ADCIGs of Gaussian beam.OGP,2013,48(3):366-371.
[2] Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966.
[3] Tsvankin I.Inversion of reflection traveltime for transverse isotropic media.Geophysics,1995,60(1):268-284.
[4] Alkhalifah T.Traveltime computation with the lineari-zed eikonal equation for anisotropic Media.Geophysical Prospecting,2002,50(4):373-382.
[5] Alkhalifah T.Acoustic approximations for processing in transversely isotropic media.Geophysics,1998,63(2):623-631.
[6] Alkhalifah T.The offset-midpoint traveltime pyramid for transversely isotropic media.Geophysics,2000,65(4):1316-1325.
[7] Alkhalifah T.An acoustic wave equation for aniso-tropic media.Geophysics,2000,65(4):1239-1250.
[8] Alkhalifah T,Fomel S.Implementing the fast mar-ching eikonal solver:spherical versus Cartesian coordinates.Geophysical Prospecting,2001,49(2):165-178.
[9] Sethian J A.Fast marching methods.Siam Review,1999,41(2):199-235.
[10] Sethian J A.Level Set Methods and Fast Marching Methods.Cambridge University Press,Cambridge,1999.
[11] Fomel S.On an elliptic approximations for qP velocities in transversally isotropic media.Geophysical Prospecting,2004,52(1):247-259.
[12] Chapman C H,Pratt R G.Traveltime tomography in anisotropic media-Ⅰ:Theory.Geophysical Journal International,1992,109(1):1-19.
[13] 张文生,何樵登.各向异性介质中利用跨孔qP波和qSV波走时的统计法成像.地球物理学报,1999,42(增刊1):195-203.Zhang Wensheng,He Qiaodeng.Statistical tomography in anisotropic media by using crosshole traveltimes of qP wave and qSV wave.Chinese Journal of Geophysics,1999,42(S1):195-203.
[14] 卢明辉,唐建侯,杨慧珠等.正交各向异性介质波走时分析及Thomsen参数反演.地球物理学报,2005,48(5):1167-1171.Lu Minghui,Tang Jianhou,Yang Huizhu et al.P-wave traveltime analysis and Thomsen parameters inversion in orthorhombic media.Chinese Journal of Geo-physics,2005,48(5):1167-1171.
[15] Zhou B,Greenhalgh S A,Green A.Nonlinear traveltime inversion scheme for crosshole seismic tomography in tilted transversely isotropic media.Geophysics,2008,73(4):17-33.
[16] 黄光南,邓居智,李红星等.P-SV波和P-SH波非线性旅行时层析成像.石油地球物理勘探,2015,50(6):1127-1133.Huang Guangnan,Deng Juzhi,Li Hongxing et al.Non-linear traveltime tomography of P-SV and P-SH waves.OGP,2015,50(6):1127-1133.
[17] 秦宁,李振春,杨晓东等.自动拾取的成像空间域走时层析速度反演.石油地球物理勘探,2012,47(3):392-398.Qin Ning,Li Zhenchun,Yang Xiaodong et al.Image domain travel-time tomography velocity inversion based on automatic picking.OGP,2012,47(3):392-398.
[18] 刘玉柱,董良国.初至波层析影响因素分析.石油地球物理勘探,2007,42(5):544-553.Liu Yuzhu,Dong Liangguo.Analysis of influence factor of first-breaks tomography.OGP,2007,42(5):544-553.
[19] 刘玉柱,丁孔芸,董良国.初至波走时层析成像对初始模型的依赖性.石油地球物理勘探,2010,45(4):502-511.Liu Yuzhu,Ding Kongyun and Dong Liangguo.The dependence of first arrival travel time tomography on initial model.OGP,2010,45(4):502-511.
[20] 刘玉柱,王光银,董良国等.VTI介质多参数联合走时层析成像方法.地球物理学报,2014,57(10): 3402-3410.Liu Yuzhu,Wang Guangyin,Dong Liangguo et al.Joint inversion of VTI parameters using nonlinear traveltime tomography.Chinese Journal of Geophysics,2014,57(10):3402-3410.
[21] Jiang F,Zhou H W.Traveltime inversion and error analysis for layered anisotropy.Journal of Applied Geo-physics,2011,73(2):101-110.
[22] Jiang F,Zhou H W.A strategy to estimate anisotropic parameters by error analysis of traveltime inversion.SEG Technical Program Expanded Abstracts,2010,29:323-327.
[23] Tsvankin I.P-wave signatures and notation for transversely isotropic media.Geophysics,1996,61(2):467-483.
[24] 丁鹏程,杨国权,李振春等.基于三维多模板快速推进算法的复杂近地表射线追踪.石油物探,2016,55(4):483-492.Ding Pengcheng,Yang Guoquan,Li Zhenchun et al. Ray tracing based on 3D multi-stencils fast marching algorithm for complex near-surface model.GPP,2016,55(4):483-492.
[25] 杨国权,丁鹏程,李振春等.应用线性程函方程和整形正则化的三维初至波旅行时层析.石油地球物理勘探,2017,52(2):264-272.Yang Guoquan,Ding Pengcheng,Li Zhenchun et al.3D first-arrival traveltime tomography with linearized eikonal equation and shaping regularization.OGP,2017,52(2):264-272.
[26] 王琦,朱盼,叶佩等.起伏地表地震波旅行时混合网格线性插值射线追踪计算方法.石油地球物理勘探,2018,53 (1):35-46.Wang Qi,Zhu Pan,Ye Pei et al.Seismic wave travel time mixed grid linear interpolation ray tracing algorithm for relief surface.OGP,2018,53(1):35-46.
[2] Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966.
[3] Tsvankin I.Inversion of reflection traveltime for transverse isotropic media.Geophysics,1995,60(1):268-284.
[4] Alkhalifah T.Traveltime computation with the lineari-zed eikonal equation for anisotropic Media.Geophysical Prospecting,2002,50(4):373-382.
[5] Alkhalifah T.Acoustic approximations for processing in transversely isotropic media.Geophysics,1998,63(2):623-631.
[6] Alkhalifah T.The offset-midpoint traveltime pyramid for transversely isotropic media.Geophysics,2000,65(4):1316-1325.
[7] Alkhalifah T.An acoustic wave equation for aniso-tropic media.Geophysics,2000,65(4):1239-1250.
[8] Alkhalifah T,Fomel S.Implementing the fast mar-ching eikonal solver:spherical versus Cartesian coordinates.Geophysical Prospecting,2001,49(2):165-178.
[9] Sethian J A.Fast marching methods.Siam Review,1999,41(2):199-235.
[10] Sethian J A.Level Set Methods and Fast Marching Methods.Cambridge University Press,Cambridge,1999.
[11] Fomel S.On an elliptic approximations for qP velocities in transversally isotropic media.Geophysical Prospecting,2004,52(1):247-259.
[12] Chapman C H,Pratt R G.Traveltime tomography in anisotropic media-Ⅰ:Theory.Geophysical Journal International,1992,109(1):1-19.
[13] 张文生,何樵登.各向异性介质中利用跨孔qP波和qSV波走时的统计法成像.地球物理学报,1999,42(增刊1):195-203.Zhang Wensheng,He Qiaodeng.Statistical tomography in anisotropic media by using crosshole traveltimes of qP wave and qSV wave.Chinese Journal of Geophysics,1999,42(S1):195-203.
[14] 卢明辉,唐建侯,杨慧珠等.正交各向异性介质波走时分析及Thomsen参数反演.地球物理学报,2005,48(5):1167-1171.Lu Minghui,Tang Jianhou,Yang Huizhu et al.P-wave traveltime analysis and Thomsen parameters inversion in orthorhombic media.Chinese Journal of Geo-physics,2005,48(5):1167-1171.
[15] Zhou B,Greenhalgh S A,Green A.Nonlinear traveltime inversion scheme for crosshole seismic tomography in tilted transversely isotropic media.Geophysics,2008,73(4):17-33.
[16] 黄光南,邓居智,李红星等.P-SV波和P-SH波非线性旅行时层析成像.石油地球物理勘探,2015,50(6):1127-1133.Huang Guangnan,Deng Juzhi,Li Hongxing et al.Non-linear traveltime tomography of P-SV and P-SH waves.OGP,2015,50(6):1127-1133.
[17] 秦宁,李振春,杨晓东等.自动拾取的成像空间域走时层析速度反演.石油地球物理勘探,2012,47(3):392-398.Qin Ning,Li Zhenchun,Yang Xiaodong et al.Image domain travel-time tomography velocity inversion based on automatic picking.OGP,2012,47(3):392-398.
[18] 刘玉柱,董良国.初至波层析影响因素分析.石油地球物理勘探,2007,42(5):544-553.Liu Yuzhu,Dong Liangguo.Analysis of influence factor of first-breaks tomography.OGP,2007,42(5):544-553.
[19] 刘玉柱,丁孔芸,董良国.初至波走时层析成像对初始模型的依赖性.石油地球物理勘探,2010,45(4):502-511.Liu Yuzhu,Ding Kongyun and Dong Liangguo.The dependence of first arrival travel time tomography on initial model.OGP,2010,45(4):502-511.
[20] 刘玉柱,王光银,董良国等.VTI介质多参数联合走时层析成像方法.地球物理学报,2014,57(10): 3402-3410.Liu Yuzhu,Wang Guangyin,Dong Liangguo et al.Joint inversion of VTI parameters using nonlinear traveltime tomography.Chinese Journal of Geophysics,2014,57(10):3402-3410.
[21] Jiang F,Zhou H W.Traveltime inversion and error analysis for layered anisotropy.Journal of Applied Geo-physics,2011,73(2):101-110.
[22] Jiang F,Zhou H W.A strategy to estimate anisotropic parameters by error analysis of traveltime inversion.SEG Technical Program Expanded Abstracts,2010,29:323-327.
[23] Tsvankin I.P-wave signatures and notation for transversely isotropic media.Geophysics,1996,61(2):467-483.
[24] 丁鹏程,杨国权,李振春等.基于三维多模板快速推进算法的复杂近地表射线追踪.石油物探,2016,55(4):483-492.Ding Pengcheng,Yang Guoquan,Li Zhenchun et al. Ray tracing based on 3D multi-stencils fast marching algorithm for complex near-surface model.GPP,2016,55(4):483-492.
[25] 杨国权,丁鹏程,李振春等.应用线性程函方程和整形正则化的三维初至波旅行时层析.石油地球物理勘探,2017,52(2):264-272.Yang Guoquan,Ding Pengcheng,Li Zhenchun et al.3D first-arrival traveltime tomography with linearized eikonal equation and shaping regularization.OGP,2017,52(2):264-272.
[26] 王琦,朱盼,叶佩等.起伏地表地震波旅行时混合网格线性插值射线追踪计算方法.石油地球物理勘探,2018,53 (1):35-46.Wang Qi,Zhu Pan,Ye Pei et al.Seismic wave travel time mixed grid linear interpolation ray tracing algorithm for relief surface.OGP,2018,53(1):35-46.