基于L_1范数多项式拟合的多次波消除方法
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摘要
如何在不损伤一次波的情况下压制多次波是地震信号处理的难点之一。在CDP道集中,一次波和多次波的运动学特征可以由叠加速度和零炮检距时间确定。利用AVO特性可以表示一次波(多次波)的振幅随炮检距的变化。假设在速度谱上,多次波和一次波一般是分开的,从而可以进行多次波和一次波的识别。本文提出一种沿着多次波的双曲线轨迹,利用基于L1范数的多项式拟合技术估计多次波的方法,可以有效地消除一次波和随机噪声对预测多次波的影响。人工合成和实际地震数据处理结果表明,与基于L2范数多项式拟合技术的方法相比,本文算法在有效压制多次波的同时,能更好地保护一次波。
The removal of multiples without simultaneously distorting primaries is one of the big challenges in seismic signal processing.On CDP gathers,the trajectories of primaries and multiples are determined from the velocity and zero-offset traveltime,and their amplitude variations with offset are modeled from known AVO properties.Supposing that primaries and multiples fall in different area on the velocity spectrum,we can identify them in the velocity domain.This paper proposes a multiples prediction method,which estimate the multiples along their hyperbolic paths using the L1-norm based polynomial approximation.The primaries estimation is obtained by simply subtracting the predicted multiples from the original seismic data.Comparisons are made between the proposed method and the conventional L2-norm based polynomial approximation method.The results of both synthetic and seismic data show that the proposed method is very promising in practical applications because it can suppress the multiples efficiently while preserving the primary amplitudes well.
The removal of multiples without simultaneously distorting primaries is one of the big challenges in seismic signal processing.On CDP gathers,the trajectories of primaries and multiples are determined from the velocity and zero-offset traveltime,and their amplitude variations with offset are modeled from known AVO properties.Supposing that primaries and multiples fall in different area on the velocity spectrum,we can identify them in the velocity domain.This paper proposes a multiples prediction method,which estimate the multiples along their hyperbolic paths using the L1-norm based polynomial approximation.The primaries estimation is obtained by simply subtracting the predicted multiples from the original seismic data.Comparisons are made between the proposed method and the conventional L2-norm based polynomial approximation method.The results of both synthetic and seismic data show that the proposed method is very promising in practical applications because it can suppress the multiples efficiently while preserving the primary amplitudes well.
引文
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[2]Liu J,Lu W.Ai mproved predictive deconvolutionbased on maxi mization of non-Gaussianity.AppliedGeophysics,2008,5(3):189～196
[3]Fomel S.Adaptive multiple subtraction using regular-ized nonstationary regression.Geophysics,2009,74(1):25～33
[4]Lu W,Liu L.Adaptive multiple subtraction based onconstrained independent component analysis.Geo-physics,2009,74(1):V1～V7
[5]Pang T,Lu W.Adaptive multiple subtraction using aconstrainedL-1-norm method with lateral continuity.Applied Geophysics,2009,6(3):241～247
[6]Alvarez G and Larner K.I mplications of multiplesuppression for AVOanalysis and CMP-stacked data.SEG Technical Program Expanded Abstracts,1996,15:1518～1521
[7]Lumley D E,Nichols D and Rekdal T.Amplitude-preserved multiple suppression.SEG Technical Pro-gram Expanded Abstracts,1995,14:1460～1463
[8]Foster DJ and Mosher C C.Suppression of multiplereflections using the radon transformation.Geophy-sics,1992,57(3):386～395
[9]Hampson D.Inverse velocity stacking for multipleeli mination.SEG Technical Program ExpandedAbstracts,1986,5:422～424
[10]Nurul Kabir M Mand Marfurt KJ.Toward true am-plitude multiple removal.The Leading Edge,1999,18(1):66～73
[11]Linville AFand Meek R A.Aprocedure for opti mal-ly removing localized coherent noise.Geophysics,1995,60(1):191～203
[12]Lu Wet al.Multiple removal based on detection andesti mation of localized coherent signal.Geophysics,2003,68(2):745～750
[13]Ursin B and Dahl T.Least-squares esti mation of re-flectivity polynomials.SEG Technical Program Ex-panded Abstracts,1990,9:1069～1071
[14]Bube K P and Langan R T.Hybrid L1/L2 mini miza-tion with applications to tomography.Geophysics,1997,62(4):1183～1195
[2]Liu J,Lu W.Ai mproved predictive deconvolutionbased on maxi mization of non-Gaussianity.AppliedGeophysics,2008,5(3):189～196
[3]Fomel S.Adaptive multiple subtraction using regular-ized nonstationary regression.Geophysics,2009,74(1):25～33
[4]Lu W,Liu L.Adaptive multiple subtraction based onconstrained independent component analysis.Geo-physics,2009,74(1):V1～V7
[5]Pang T,Lu W.Adaptive multiple subtraction using aconstrainedL-1-norm method with lateral continuity.Applied Geophysics,2009,6(3):241～247
[6]Alvarez G and Larner K.I mplications of multiplesuppression for AVOanalysis and CMP-stacked data.SEG Technical Program Expanded Abstracts,1996,15:1518～1521
[7]Lumley D E,Nichols D and Rekdal T.Amplitude-preserved multiple suppression.SEG Technical Pro-gram Expanded Abstracts,1995,14:1460～1463
[8]Foster DJ and Mosher C C.Suppression of multiplereflections using the radon transformation.Geophy-sics,1992,57(3):386～395
[9]Hampson D.Inverse velocity stacking for multipleeli mination.SEG Technical Program ExpandedAbstracts,1986,5:422～424
[10]Nurul Kabir M Mand Marfurt KJ.Toward true am-plitude multiple removal.The Leading Edge,1999,18(1):66～73
[11]Linville AFand Meek R A.Aprocedure for opti mal-ly removing localized coherent noise.Geophysics,1995,60(1):191～203
[12]Lu Wet al.Multiple removal based on detection andesti mation of localized coherent signal.Geophysics,2003,68(2):745～750
[13]Ursin B and Dahl T.Least-squares esti mation of re-flectivity polynomials.SEG Technical Program Ex-panded Abstracts,1990,9:1069～1071
[14]Bube K P and Langan R T.Hybrid L1/L2 mini miza-tion with applications to tomography.Geophysics,1997,62(4):1183～1195
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