基于Chebyshev多项式的非对称走时Kirchhoff叠前时间偏移角道集求取
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摘要
地震射线走时的求取方法是叠前时间偏移研究的核心问题之一,也是影响计算时间域角道集角度精确性的关键因素之一.本文基于Kirchhoff叠前时间偏移,应用第一类切比雪夫多项式,对弯曲射线对称走时加以改进,引进非对称项,优化后得到切比雪夫非对称走时方程,与高精度走时进行比较和误差分析,再将该走时求取方法应用于时间域角道集的求取中,得到地下较真实的入射角.通过模型计算和实际地震资料处理证明,此种非对称走时及其角道集的求取方法具有精度高、计算量少的优点.
Kirchhoff pre-stack time migration(KPSTM) is widely used in production due to its high efficiency and good suitability,especially for exploration in central and western China.Angle domain common image gathers(ADCIG) serve as the link between migration and reservoir attribute analysis.Getting ADCIG in the time domain is more efficient than in the depth domain.Seismic travel time calculation is one of the key problems of KPSTM and is also a key problem in ADCIG calculation.Using Chebyshev orthogonal polynomial and optimizing algorithm,we develop a new asymmetric Chebyshev travel time formula and compare it with high-precision taylor travel time formulas.Based on this,considering the bend-way effect,we apply the new Chebyshev travel time formula to calculate incident angles,and achieve more precise ADCIG from the original seismic gathers.The method is tested by both synthetic data and real marine data.It is verified that using our method to obtain ADCIG is more precise and consumes less computation time.
Kirchhoff pre-stack time migration(KPSTM) is widely used in production due to its high efficiency and good suitability,especially for exploration in central and western China.Angle domain common image gathers(ADCIG) serve as the link between migration and reservoir attribute analysis.Getting ADCIG in the time domain is more efficient than in the depth domain.Seismic travel time calculation is one of the key problems of KPSTM and is also a key problem in ADCIG calculation.Using Chebyshev orthogonal polynomial and optimizing algorithm,we develop a new asymmetric Chebyshev travel time formula and compare it with high-precision taylor travel time formulas.Based on this,considering the bend-way effect,we apply the new Chebyshev travel time formula to calculate incident angles,and achieve more precise ADCIG from the original seismic gathers.The method is tested by both synthetic data and real marine data.It is verified that using our method to obtain ADCIG is more precise and consumes less computation time.
引文
[1]Castle R J.A theory of normal moveout.Geophysics,1994,59(6):983-999.
[2]Sun C W,Wang H W,Nartinez R D.Optimized 6th orderNMO correction for long-offset seismic data.72nd AnnualInternational Meeting,SEG,Expanded Abstracts,2002.
[3]Alkhalifah T,Tsvankin I.Velocity analysis for transverselyisotropic media.Geophysics,1995,60(5):1550-1566.
[4]尤建军,常旭,刘伊克.VTI介质长偏移距非双曲动校正公式优化.地球物理学报,2006,49(6):1770-1778.You J J,Chang X,Liu Y K.Optimization of nonhyperbolicmoveout correction equation of long-offset seismic data inVTI media.Chinese J.Geophys.(in Chinese),2006,49(6):1770-1778.
[5]程玖兵,王楠,马在田.表驱三维角度域Kirchhoff叠前时间偏移成像方法.地球物理学报,2009,52(3):792-800.Cheng J B,Wang N,Ma Z T.Table-driven 3-D angle-domain imaging approach for Kirchhoff prestack timemigration.Chinese J.Geophys.(in Chinese),2009,52(3):792-800.
[6]刘洋.反射波分式展开时距方程及其精度分析.石油物探,2003,42(4):441-447.Liu Y.Fraction expansion time-distance equation of reflectionwave and its accuracy analysis.Geophysical Progress forPetroleum(in Chinese),2003,42(4):441-447.
[7]刘洪,刘国锋,李博等.基于横向导数的走时计算方法及其在叠前时间偏移中的应用.石油物探,2009,48(1):3-10.Liu H,Liu G F,Li B,et al.The travel time calculationmethod via lateral derivative of velocity and its application inpre-stack time migration.Geophysical Progress for Petroleum(in Chinese),2009,48(1):3-10.
[8]Zhang J H,Wang W M,Wang S Q.Optimized ChebyshevFourier migration:A wide-angle dual-domain method formedia with strong velocity contrasts.Geophysics,2010,75(2):S23-S24.
[9]丁帆,张金海,姚振兴.长偏移距地震资料的优化契比雪夫动校正方法.地球物理学进展,2011,26(3):836-842.Ding F,Zhang J H,Yao Z X.Optimized Chebyshev methodfor normal moveout of long-offset seismic data.Progress inGeophysics(in Chinese),2011,26(3):836-842.
[10]刘璐,梁光河,符超等.基于Chebyshev多项式的弯曲射线Kirchhoff叠前时间偏移.地球物理学报,2011,54(10):2665-2672.Liu L,Liang G H,Fu C,et al.Bend-ray Kirchhoff pre-stacktime migration based on Chebyshev polynomial.Chinese J.Geophys.(in Chinese),2011,54(10):2665-2672.
[11]de Bruin,C G M,Wapenaar C P A,Berkhout A J.Angle-dependent reflectivity by means of prestack migration.Geophysics,1990,55(9):1223-1234.
[12]Biondo B,William W S.Angle-domain common-imagegathers for migration velocity analysis by wavefield-continuation imaging.Geophysics,2004,69(5):1283-1298.
[13]刘奇琳,刘伊克,常旭.双平方根波动方程偏移速度分析.地球物理学报,2009,52(7):1891-1898.Liu Q L,Liu Y K,Chang X.Wave-equation migrationvelocity analysis by double square root method.Chinese J.Geophys.(in Chinese),2009,52(7):1891-1898.
[14]Brandsberg-Dahl S,de Hoop M V,Ursin B.Focusing in dipand AVA compensation on scattering-angle/azimuth commonimage gathers.Geophysics,2003,68(1):232-254.
[15]Lee S,King D,Lin S.Efficient true-amplitude weights inKirchhoff time migration.74th Annual International Meeting,SEG,Expanded Abstracts,2004:1089-1092.
[16]Rickett J,Sava P.Offset and angle-domain common image-point gathers for shot-profile migration.Geophysics,2002,67(3):883-889.
[17]陈凌,吴如山,王伟君.基于Gabor-Daubechies小波束叠前深度偏移的角度域共成像道集.地球物理学报,2004,47(5):876-885.Chen L,Wu R S,Wang W J.Common angle image gathersobtained from Gabor-daubechies beamlet prestack depthmigration.Chinese J.Geophys.(in Chinese),2004,47(5):876-885.
[18]Sava P,Fomel S.Angle-domain common-image gathers bywavefield continuation methods.Geophysics,2003,68(3):1065-1074.
[19]Perez G,Marfurt K J.Improving lateral and verticalresolution of seismic images by correcting for wavelet stretchin common-angle migration.Geophysics,2007,72(6):94-104.
[20]王棣,王华忠,马在田等.叠前时间偏移方法综述.勘探地球物理进展,2004,27(5):313-316.Wang D,Wang H Z,Ma Z T,et al.Review of prestack timemigration methods.Progress in Exploration Geophysics(inChinese),2004,27(5):313-316.
[21]邹振,刘洪,刘红伟.Kirchhoff叠前时间偏移角度道集.地球物理学报,2010,53(5):1207-1214.Zou Z,Liu H,Liu H W.Common-angle gathers based onKirchhoff pre-stack time migration.Chinese J.Geophys.(inChinese).2010,53(5):1207-1214.
[22]Slotnick M.Lessons in Seismic Computing:A Memorial tothe Author.Lawrence:Society of Exploration Geophysicists,1959.
[23]Taner M T,Koehler F.Velocity spectra-digital computerderivation applications of velocity functions.Geophysics,1969,34(6):859-881.
[24]Dellinger J A,Gray S H,Murphy G E,et al.Efficient 2.5-Dtrue-amplitude migration.Geophysics,2000,65(3):943-950.
[25]张廉萍,刘洪.适于Kirchhoff叠前深度偏移的地震走时李代数积分算法.地球物理学报,2010,53(8):1893-1901.Zhang L P,Liu H.Lie algebra integral algorithm of travel-time calculation for pre-stack Kirchhoff depth migration.Chinese J.Geophys.(in Chinese),2010,53(8):1893-1901.
[2]Sun C W,Wang H W,Nartinez R D.Optimized 6th orderNMO correction for long-offset seismic data.72nd AnnualInternational Meeting,SEG,Expanded Abstracts,2002.
[3]Alkhalifah T,Tsvankin I.Velocity analysis for transverselyisotropic media.Geophysics,1995,60(5):1550-1566.
[4]尤建军,常旭,刘伊克.VTI介质长偏移距非双曲动校正公式优化.地球物理学报,2006,49(6):1770-1778.You J J,Chang X,Liu Y K.Optimization of nonhyperbolicmoveout correction equation of long-offset seismic data inVTI media.Chinese J.Geophys.(in Chinese),2006,49(6):1770-1778.
[5]程玖兵,王楠,马在田.表驱三维角度域Kirchhoff叠前时间偏移成像方法.地球物理学报,2009,52(3):792-800.Cheng J B,Wang N,Ma Z T.Table-driven 3-D angle-domain imaging approach for Kirchhoff prestack timemigration.Chinese J.Geophys.(in Chinese),2009,52(3):792-800.
[6]刘洋.反射波分式展开时距方程及其精度分析.石油物探,2003,42(4):441-447.Liu Y.Fraction expansion time-distance equation of reflectionwave and its accuracy analysis.Geophysical Progress forPetroleum(in Chinese),2003,42(4):441-447.
[7]刘洪,刘国锋,李博等.基于横向导数的走时计算方法及其在叠前时间偏移中的应用.石油物探,2009,48(1):3-10.Liu H,Liu G F,Li B,et al.The travel time calculationmethod via lateral derivative of velocity and its application inpre-stack time migration.Geophysical Progress for Petroleum(in Chinese),2009,48(1):3-10.
[8]Zhang J H,Wang W M,Wang S Q.Optimized ChebyshevFourier migration:A wide-angle dual-domain method formedia with strong velocity contrasts.Geophysics,2010,75(2):S23-S24.
[9]丁帆,张金海,姚振兴.长偏移距地震资料的优化契比雪夫动校正方法.地球物理学进展,2011,26(3):836-842.Ding F,Zhang J H,Yao Z X.Optimized Chebyshev methodfor normal moveout of long-offset seismic data.Progress inGeophysics(in Chinese),2011,26(3):836-842.
[10]刘璐,梁光河,符超等.基于Chebyshev多项式的弯曲射线Kirchhoff叠前时间偏移.地球物理学报,2011,54(10):2665-2672.Liu L,Liang G H,Fu C,et al.Bend-ray Kirchhoff pre-stacktime migration based on Chebyshev polynomial.Chinese J.Geophys.(in Chinese),2011,54(10):2665-2672.
[11]de Bruin,C G M,Wapenaar C P A,Berkhout A J.Angle-dependent reflectivity by means of prestack migration.Geophysics,1990,55(9):1223-1234.
[12]Biondo B,William W S.Angle-domain common-imagegathers for migration velocity analysis by wavefield-continuation imaging.Geophysics,2004,69(5):1283-1298.
[13]刘奇琳,刘伊克,常旭.双平方根波动方程偏移速度分析.地球物理学报,2009,52(7):1891-1898.Liu Q L,Liu Y K,Chang X.Wave-equation migrationvelocity analysis by double square root method.Chinese J.Geophys.(in Chinese),2009,52(7):1891-1898.
[14]Brandsberg-Dahl S,de Hoop M V,Ursin B.Focusing in dipand AVA compensation on scattering-angle/azimuth commonimage gathers.Geophysics,2003,68(1):232-254.
[15]Lee S,King D,Lin S.Efficient true-amplitude weights inKirchhoff time migration.74th Annual International Meeting,SEG,Expanded Abstracts,2004:1089-1092.
[16]Rickett J,Sava P.Offset and angle-domain common image-point gathers for shot-profile migration.Geophysics,2002,67(3):883-889.
[17]陈凌,吴如山,王伟君.基于Gabor-Daubechies小波束叠前深度偏移的角度域共成像道集.地球物理学报,2004,47(5):876-885.Chen L,Wu R S,Wang W J.Common angle image gathersobtained from Gabor-daubechies beamlet prestack depthmigration.Chinese J.Geophys.(in Chinese),2004,47(5):876-885.
[18]Sava P,Fomel S.Angle-domain common-image gathers bywavefield continuation methods.Geophysics,2003,68(3):1065-1074.
[19]Perez G,Marfurt K J.Improving lateral and verticalresolution of seismic images by correcting for wavelet stretchin common-angle migration.Geophysics,2007,72(6):94-104.
[20]王棣,王华忠,马在田等.叠前时间偏移方法综述.勘探地球物理进展,2004,27(5):313-316.Wang D,Wang H Z,Ma Z T,et al.Review of prestack timemigration methods.Progress in Exploration Geophysics(inChinese),2004,27(5):313-316.
[21]邹振,刘洪,刘红伟.Kirchhoff叠前时间偏移角度道集.地球物理学报,2010,53(5):1207-1214.Zou Z,Liu H,Liu H W.Common-angle gathers based onKirchhoff pre-stack time migration.Chinese J.Geophys.(inChinese).2010,53(5):1207-1214.
[22]Slotnick M.Lessons in Seismic Computing:A Memorial tothe Author.Lawrence:Society of Exploration Geophysicists,1959.
[23]Taner M T,Koehler F.Velocity spectra-digital computerderivation applications of velocity functions.Geophysics,1969,34(6):859-881.
[24]Dellinger J A,Gray S H,Murphy G E,et al.Efficient 2.5-Dtrue-amplitude migration.Geophysics,2000,65(3):943-950.
[25]张廉萍,刘洪.适于Kirchhoff叠前深度偏移的地震走时李代数积分算法.地球物理学报,2010,53(8):1893-1901.Zhang L P,Liu H.Lie algebra integral algorithm of travel-time calculation for pre-stack Kirchhoff depth migration.Chinese J.Geophys.(in Chinese),2010,53(8):1893-1901.
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