TTI介质有限差分逆时偏移的稳定性探讨
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摘要
在沉积学中,可假设在相同时期的沉积层具有相近的物理性质和演化过程.因此,沿层传播的地震波和垂直于地层传播的地震波具有各向异性的特点.在纵波资料的处理中,考虑各向异性对逆时偏移的影响,通常假设介质的横波速度为零,这样可以得到纵波在TTI介质中的传播方程,但是该方程在实际计算中仍存在数值稳定性问题.本文加入横波分量可有效解决数值稳定性问题,并选取适当的横波速度减小对纵波成像的影响,实现地震波在TTI介质中的逆时偏移.实际测算表明,P-SV波的方程中包含横波分量,若假设SV的速度为零,则会导致方程的差分格式不稳定;若加入SV波,选择合适的SV波速度可以使SV波的全区各向异性和反射系数达到极小,并可有效的抑制SV波对纵波勘探的影响.本文的方法是一种稳定的TTI介质中的逆时偏移方法.
The strata in same deposition period have the same physics feature and evolutionary process in sedimentology.So,the anisotropic feature exists between the wave propagating along the strata and the wave propagating vertically along strata.In P wave reverse time migration(PRTM),considering the effect of anisotropic propagation,an hypothesis that share wave velocity should be zero has been generally involved.In this case,the wave equation in TTI media could be obtained,but it suffer from numerical stability problem in practice.In this paper,to get the stable algorithms,the hypothesis of zero shear wave velocity has been discarded.the right SV velocity has been chosen to reduce the affect of SV wave in PRTM.the actual test indicate that If set the velocity of SV wave equal to zero,the differential scheme will be unstable;if not,choosing the right velocity of SV wave can minim the anisotropic feature and reflector coefficients of SV wave.In this way,the effective of SV wave to P wave exploration will be restricted.This is a stable method for P wave Reverse Time Migration in TTI media.
The strata in same deposition period have the same physics feature and evolutionary process in sedimentology.So,the anisotropic feature exists between the wave propagating along the strata and the wave propagating vertically along strata.In P wave reverse time migration(PRTM),considering the effect of anisotropic propagation,an hypothesis that share wave velocity should be zero has been generally involved.In this case,the wave equation in TTI media could be obtained,but it suffer from numerical stability problem in practice.In this paper,to get the stable algorithms,the hypothesis of zero shear wave velocity has been discarded.the right SV velocity has been chosen to reduce the affect of SV wave in PRTM.the actual test indicate that If set the velocity of SV wave equal to zero,the differential scheme will be unstable;if not,choosing the right velocity of SV wave can minim the anisotropic feature and reflector coefficients of SV wave.In this way,the effective of SV wave to P wave exploration will be restricted.This is a stable method for P wave Reverse Time Migration in TTI media.
引文
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[15]Duveneck,Peter M B.Stable P-wave modeling for reverse time migration in tilted TI media.Geophysics,2011,76(2):S65-S75.
[16]Leon Thomsen.Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966.
[17]郝重涛,姚陈,王迅.任意空间取向TI介质中速度随方位变化特征.地球物理学进展.2006,21(2):524-530.Hao C T,Yao C,Wang X.The characteristics of velocities with azimuth variation for arbitrary spatial orientation TI media.Progress in Geophysics(in Chinese),2006,21(2):524-530.
[18]Virieux J.P-SV wave propagation in heterogeneous media:Velocity stress finite difference method.Geophysics,1986,51(4):889-901.
[19]杜向东,刘军荣,戚艳平等.三维VTI介质qP波方程频率空间域有限差分高阶加权算子.地球物理学进展,2009,24(1):211-222.Du X D,Liu J R,Qi Y P,et al.Finite difference high-order weighted-averaging operator for frequency-space domain qP wave in3-D VTI media.Progress in Geophysics(in Chinese),2009,24(1):211-222.
[20]吴国忱,梁锴.VTI介质qP波方程高精度有限差分算子.地球物理学进展,2007,22(3):896-904.Wu G C,Liang K.High precision finite difference operators for qP wave equation in VTI media.Progress in Geophysics(in Chinese),2007,22(3):896-904.
[21]Kwangjin Yoon,Sang Suh,et al.Stability and speedup issues in TTI RTM implementation.80th Annual International Meeting,SEG,Expanded Abstracts,2010:3221-3225.
[22]Grechka V,Zhang L B,James W R.Shear waves in acoustic anisotropic media.Geophysics,2004,69(2):576-582.
[23]梁锴,印兴耀,吴国忱.TTI介质qP波入射精确和近似反射透射系数.地球物理学报,2011,54(1):208-217.Liang K,Yin X Y,Wu G C.Exact and approximate reflection and transmission coefficient for incident qP wave in TTI media.Chinese J.Geophys.(in Chinese),2011,54(1):208-217.
[2]刘红伟,刘洪,李博等.起伏地表叠前逆时偏移理论及GPU加速技术.地球物理学报,2011,54(7):1883-1892.Liu H W,Liu H,Li B,et al.Pre-stack reverse timemigration for rugged topography and GPU acceleration technology.Chinese J.Geophys.(in Chinese),2011,54(7):1883-1892.
[3]侯安宁,何樵登.各向异性介质中弹性波动高阶差分法及其稳定性的研究.地球物理学报,1995,38(2):243-251.Hou A N,He Q D.Study of a elastic wave high-order difference method and its stability in anisotropic media.Chinese J.Geophys.(in Chinese),1995,38(2):243-251.
[4]杜启振,秦童.横向各向同性介质弹性波多分量叠前逆时偏移.地球物理学报,2009,52(3):801-807.Du Q Z,Qin T.Multi-component pre-stack reverse-time migration of elastic waves in transverse isotropic medium.Chinese J.Geophys.(in Chinese),2009,52(3):801-807.
[5]吴国忱,梁锴,印兴耀.TTI介质弹性波相速度与偏振特征分析.地球物理学报,2010,53(8):1914-1923.Wu G C,Liang K,Yin X Y.The analysis of phase velocity and polarization feature for elastic wave in TTI media.Chinese J.Geophys.(in Chinese),2010,53(8):1914-1923.
[6]黄翼坚,朱光明,刘池洋.一个近似的VTI介质声波方程.地球物理学报,2011,54(8):2117-2123.Huang Y J,Zhu G M,Liu C Y.An approximate acoustic wave equation for VTI media.Chinese J.Geophys.(in Chinese),2011,54(8):2117-2123.
[7]Alkhalifah.An acoustic wave equation for anisotropic media.Geophysics,2000,65(4):1239-1250.
[8]Tsvankin.Seismic signatures and analysis of reflection data in anisotropic media:Geophysics,2001,69(2):576-582.
[9]Zhou H B,Zhang G Q,Bloor R.An anisotropic acoustic wave equation for modeling and mi-gration in2DTTI media.76th Annual International Meeting,SEG,Expanded Abstracts,2006:194-198.
[10]Hestholm S.Acoustic VTI modeling using high-order finite differences.Geophysics,2009,74(5):T67-T73.
[11]Duveneck,Milcik P.Acoustic VTI wave equations and their application for anisotropic reverse-time migration.78th Annual International Meeting,SEG,Expanded Abstracts,2008:2186-2190.
[12]Zhang H Z,Zhang Y.Reverse time migration in3D heterogeneous TTI meida.78th Annual International Meeting,SEG,Expanded Abstracts,2008:2196-2200.
[13]Fletcher R P,Du X,Paul J F.Reverse time migration in tilted transversely isotropic(TTI)media.Geophysics,2009,74(6):WCA179-WCA187.
[14]Zhang Y,Zhang H Z.A stable TTI reverse time migration and its implementation.79th Annual International Meeting,SEG,Expanded Abstracts,2009:2794-2798.
[15]Duveneck,Peter M B.Stable P-wave modeling for reverse time migration in tilted TI media.Geophysics,2011,76(2):S65-S75.
[16]Leon Thomsen.Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966.
[17]郝重涛,姚陈,王迅.任意空间取向TI介质中速度随方位变化特征.地球物理学进展.2006,21(2):524-530.Hao C T,Yao C,Wang X.The characteristics of velocities with azimuth variation for arbitrary spatial orientation TI media.Progress in Geophysics(in Chinese),2006,21(2):524-530.
[18]Virieux J.P-SV wave propagation in heterogeneous media:Velocity stress finite difference method.Geophysics,1986,51(4):889-901.
[19]杜向东,刘军荣,戚艳平等.三维VTI介质qP波方程频率空间域有限差分高阶加权算子.地球物理学进展,2009,24(1):211-222.Du X D,Liu J R,Qi Y P,et al.Finite difference high-order weighted-averaging operator for frequency-space domain qP wave in3-D VTI media.Progress in Geophysics(in Chinese),2009,24(1):211-222.
[20]吴国忱,梁锴.VTI介质qP波方程高精度有限差分算子.地球物理学进展,2007,22(3):896-904.Wu G C,Liang K.High precision finite difference operators for qP wave equation in VTI media.Progress in Geophysics(in Chinese),2007,22(3):896-904.
[21]Kwangjin Yoon,Sang Suh,et al.Stability and speedup issues in TTI RTM implementation.80th Annual International Meeting,SEG,Expanded Abstracts,2010:3221-3225.
[22]Grechka V,Zhang L B,James W R.Shear waves in acoustic anisotropic media.Geophysics,2004,69(2):576-582.
[23]梁锴,印兴耀,吴国忱.TTI介质qP波入射精确和近似反射透射系数.地球物理学报,2011,54(1):208-217.Liang K,Yin X Y,Wu G C.Exact and approximate reflection and transmission coefficient for incident qP wave in TTI media.Chinese J.Geophys.(in Chinese),2011,54(1):208-217.
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