L1-L2范数联合约束稀疏脉冲反演的应用
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摘要
稀疏脉冲反演实际上就是利用反褶积原理,从带有噪声的地震道中计算出具有稀疏分布特征的反射系数的振幅和时间.稀疏脉冲反演是非线性优化问题,通常都是把非线性优化问题转化为线性优化问题,然后用线性优化算法求解.以范数约束为基础,提出L1-L2范数联合约束求解的方法.该算法采用了目前国际流行的内点算法,与传统的优化算法相比,这种算法具有精度高,速度快的优点.通过研究人工模型和南海某油田实际数据,表明该算法的计算结果和测井记录吻合好,提高了地震分辨率,目的层段分辨率优于8m.利用反射系数剖面预测的储层厚度和开发井吻合很好,大大地降低了资源量计算的风险和油田开发的不确定性.
Sparse-spike deconvolution is an inverse issue which estimates the time and the amplitudes of the sparseness reflectivity(spikes)from the noisy seismic traces.Sparseness spike inverse is highly non-linear optimization problem that can be solved using the L1-L2 norm constrained method introduced in this paper.This method is characterized with its application of the log-barrier interior point to solve the sparseness inverse problem which is higher in terms of resolution and faster than conventional optimization methods.Results from the synthetic and real 3D data show that the physically meaningful high-resolution sparse-spike profile can be derived from the band-limited noisy data.Real data show that the method improves seismic resolution and estimates the thickness of thin bed which can reduce the uncertainty of resource estimation and oil field production.
Sparse-spike deconvolution is an inverse issue which estimates the time and the amplitudes of the sparseness reflectivity(spikes)from the noisy seismic traces.Sparseness spike inverse is highly non-linear optimization problem that can be solved using the L1-L2 norm constrained method introduced in this paper.This method is characterized with its application of the log-barrier interior point to solve the sparseness inverse problem which is higher in terms of resolution and faster than conventional optimization methods.Results from the synthetic and real 3D data show that the physically meaningful high-resolution sparse-spike profile can be derived from the band-limited noisy data.Real data show that the method improves seismic resolution and estimates the thickness of thin bed which can reduce the uncertainty of resource estimation and oil field production.
引文
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Gill,P.E.,Murray,W.,Ponceleon,D.B.,et al.,1991.Sol-ving reduced KKTsystems in barrier methods for linearand quadratic programming.Techniccal Report SOL91-7,Stanford University,U.S.A..
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Kormylo,J.,Mendel,J.,1978.On maximum-likelihood de-tection and estimation of reflection coefficients.48thAnnual International Meeting,SEG Expanded Ab-stracts,Tulsa,U.S.A.,45-46.
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Sacchi,M.D.,Velis,D.R.,Comínguez,A.H.,1994.Mini-mumentropy deconvolution withfrequency domain con-straints.Geophysics,59(6):938-945.
Veeken,P.C.H.,Da Silva,M.,2004.Seismic inversionmethods and some of their constraints.First Break,22:47-72.
Velis,D.R.,2006.Parametric sparse-spike deconvolutionand the recovery of the acoustic impedance.76th AnnualInternational Meeting,SEG Expanded Abstracts,Tulsa,U.S.A.,2141-2144.
Wang,J.,Wang,X.,Perz,M.,2006.Structure preservingregularization for sparse deconvolution.76th Annual In-ternational Meeting,SEG Expanded Abstracts,25:2072-2076.
Widess,M.B.,1973.Howthinis a thin bed-Geophysics,38(6):1176-1180.
Wright,M.H.,1992.Interior methods for constrained opti-mization.Acta Numeica,1:341-407.
Wright,S.J.,1996.Primal-dual interior-point method.SI-AM,Philadelphia.
Xu,G.M.,2003.Inverse theory and applications.SeismicPress(in Chinese).
黄红选,韩续业,2006.数学规划.北京:清华大学出版社.
徐果明,2003.反演理论及其应用.北京:地震出版社.
Gill,P.E.,Murray,W.,Ponceleon,D.B.,et al.,1991.Sol-ving reduced KKTsystems in barrier methods for linearand quadratic programming.Techniccal Report SOL91-7,Stanford University,U.S.A..
Huang,H.X.,Han,X.Y.,2006.Mathematic programming.Qinghua University Press(in Chinese).
Kormylo,J.,Mendel,J.,1978.On maximum-likelihood de-tection and estimation of reflection coefficients.48thAnnual International Meeting,SEG Expanded Ab-stracts,Tulsa,U.S.A.,45-46.
Roos,C.,Terlaky,T.,Vial,J.P.,1997.Theory and algo-rithms for linear optimization:An interior point ap-proach.Wiley,Chichester,UK.
Sacchi,M.D.,Velis,D.R.,Comínguez,A.H.,1994.Mini-mumentropy deconvolution withfrequency domain con-straints.Geophysics,59(6):938-945.
Veeken,P.C.H.,Da Silva,M.,2004.Seismic inversionmethods and some of their constraints.First Break,22:47-72.
Velis,D.R.,2006.Parametric sparse-spike deconvolutionand the recovery of the acoustic impedance.76th AnnualInternational Meeting,SEG Expanded Abstracts,Tulsa,U.S.A.,2141-2144.
Wang,J.,Wang,X.,Perz,M.,2006.Structure preservingregularization for sparse deconvolution.76th Annual In-ternational Meeting,SEG Expanded Abstracts,25:2072-2076.
Widess,M.B.,1973.Howthinis a thin bed-Geophysics,38(6):1176-1180.
Wright,M.H.,1992.Interior methods for constrained opti-mization.Acta Numeica,1:341-407.
Wright,S.J.,1996.Primal-dual interior-point method.SI-AM,Philadelphia.
Xu,G.M.,2003.Inverse theory and applications.SeismicPress(in Chinese).
黄红选,韩续业,2006.数学规划.北京:清华大学出版社.
徐果明,2003.反演理论及其应用.北京:地震出版社.
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