VTI介质非双曲时差方程叠前时间偏移方法对比
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摘要
介质垂向非均匀性和内在各向异性都会导致反射时距曲线偏离双曲形状。基于传统双曲时差方程的时间域成像方法不能准确归位远偏移距或大入射角地震波能量。将已有非双曲时差方程总结归纳为级数展开逼近、时移双曲近似、反椭圆近似和正交多项式逼近4类,面向Kirchhoff叠前时间偏移推导了级数展开四阶逼近、时移双曲近似和反椭圆近似的双平方根时差方程。数值试验结果表明,反椭圆近似在垂向变化横向各向同性(VTI)介质中有很高的精度,它在各向异性介质时间域成像方面有大的应用潜力。
Vertical heterogeneity and intrinsic anisotropy will result in deviation of the time-distance curve from hyperbolic shape.Time imaging based on normal hyperbolic moveout equation fails to focus the reflection and diffraction of far offsets or large angles.In this paper,the existed non-hyperbolic NMO equations were classified into four types,namely,forth-order approximation based on series expanding.shifted hyperbolic approximation,anelliptic approximation and orthogonally polynomial approxima-tion.Then the forward three NMO equations were extended to their double-square-root counterparts to implement Kirchhoff presatck lime migration.Migrated sections and common-image gathers on a theoretical model demonstrate their difference in accuracy.The numerical results show that anelliptic approximation has great potential for time imaging in anisotropic medium.
Vertical heterogeneity and intrinsic anisotropy will result in deviation of the time-distance curve from hyperbolic shape.Time imaging based on normal hyperbolic moveout equation fails to focus the reflection and diffraction of far offsets or large angles.In this paper,the existed non-hyperbolic NMO equations were classified into four types,namely,forth-order approximation based on series expanding.shifted hyperbolic approximation,anelliptic approximation and orthogonally polynomial approxima-tion.Then the forward three NMO equations were extended to their double-square-root counterparts to implement Kirchhoff presatck lime migration.Migrated sections and common-image gathers on a theoretical model demonstrate their difference in accuracy.The numerical results show that anelliptic approximation has great potential for time imaging in anisotropic medium.
引文
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[6]Sun C,Martinez R.3D Kirchhoff PS-wave prestackti me migra-tion for V(z)and VTI media[M].73rd SEG Meeting Expand-ed Abstracts,2003:957-960.
[7]Malovichko A A.Anewrepresentation of the travel ti me curve of reflected waves in horizontally layered media[J].Applied Geophysics,1978,91(4):47-53.
[8]de Bazelaire E.Normal moveout revisited:inhomogeneous media and curvedinterfaces[J].Geophysics,1988,53(2):143-157.
[9]Castle RJ.Atheory of normal moveout[J].Geophysics,1994,59(6):983-999.
[10]Siliqi R,BousquiN.An elliptic ti me processing based on a shifted hyperbola approach[M].70th SEG Meeting Expanded Abstracts,2000:2245-2248.
[11]Muir F,Dellinger J.A practical anisotropic system[C].Stan-ford Exploration Project,1985,Report44:55-58.
[12]Fomel S.On anelliptic approxi mations for qP velocities in VTI media[J].Geophysical Prospecting,2004,52(3):247-259.
[13]Zhang F,Uren N.Approxi mate explicit ray velocity functions and travel ti mes for P-wavesin TI Media[M].71st SEG Meet-ing Extended Abstract,2001:106-109.
[14]May B T,Straley D K.Higher-order move out spectra[J].Ge-ophysics,1979,44(1):193-207.
[15]Causse E.Seismic travelti me approxi mations with high accura-cy at all offsets[M].72nd SEG Meeting Expanded Abstracts,2002.
[16]Ursin B,Hokstad K.Geometrical spreading in a layered trans-verselyisotropic medium with vertical symmetry axis[J].Geo-physics,2003,68(2):2082-2091.
[17]Ursin B,Stovas A.Travel ti me approxi mations for a layered transverselyisotropic medium[J].Geophysics,2006,71(2):23-33.
[18]Thomsen L.Weak elastic anisotropy[J].Geophysics,1986,51(2):1954-1966.
[19]尤建军,常旭,刘伊克.VTI介质长偏移距非双曲动较正公式优化[J].地球物理学报,2006,49(6):1770-1778.
[2]Taner M T,Koehler F.Velocity spectra digital computer deri-vation and applications of velocity functions[J].Geophysics,1969,34(3):859-881.
[3]Hake H,Helbig K,Mesdag C S.Three-term Taylor series for t2-x2curves over layered transversely isotropic ground[J].Geophysical Prospecting,1984,32(3):828-850.
[4]Tsvankin I,Thomsen L.Nonhyperbolic reflection moveout in anisotropic media[J].Geophysics,1994,59(8):1290-1304.
[5]Alkhalifah T,Tsvankin I.Velocity analysis for transversely i-sotropic media[J].Geophysics,1995,60(5):1550-1566.
[6]Sun C,Martinez R.3D Kirchhoff PS-wave prestackti me migra-tion for V(z)and VTI media[M].73rd SEG Meeting Expand-ed Abstracts,2003:957-960.
[7]Malovichko A A.Anewrepresentation of the travel ti me curve of reflected waves in horizontally layered media[J].Applied Geophysics,1978,91(4):47-53.
[8]de Bazelaire E.Normal moveout revisited:inhomogeneous media and curvedinterfaces[J].Geophysics,1988,53(2):143-157.
[9]Castle RJ.Atheory of normal moveout[J].Geophysics,1994,59(6):983-999.
[10]Siliqi R,BousquiN.An elliptic ti me processing based on a shifted hyperbola approach[M].70th SEG Meeting Expanded Abstracts,2000:2245-2248.
[11]Muir F,Dellinger J.A practical anisotropic system[C].Stan-ford Exploration Project,1985,Report44:55-58.
[12]Fomel S.On anelliptic approxi mations for qP velocities in VTI media[J].Geophysical Prospecting,2004,52(3):247-259.
[13]Zhang F,Uren N.Approxi mate explicit ray velocity functions and travel ti mes for P-wavesin TI Media[M].71st SEG Meet-ing Extended Abstract,2001:106-109.
[14]May B T,Straley D K.Higher-order move out spectra[J].Ge-ophysics,1979,44(1):193-207.
[15]Causse E.Seismic travelti me approxi mations with high accura-cy at all offsets[M].72nd SEG Meeting Expanded Abstracts,2002.
[16]Ursin B,Hokstad K.Geometrical spreading in a layered trans-verselyisotropic medium with vertical symmetry axis[J].Geo-physics,2003,68(2):2082-2091.
[17]Ursin B,Stovas A.Travel ti me approxi mations for a layered transverselyisotropic medium[J].Geophysics,2006,71(2):23-33.
[18]Thomsen L.Weak elastic anisotropy[J].Geophysics,1986,51(2):1954-1966.
[19]尤建军,常旭,刘伊克.VTI介质长偏移距非双曲动较正公式优化[J].地球物理学报,2006,49(6):1770-1778.
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