应用近似L_0范数的稀疏脉冲反演
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摘要
根据地下地层反射系数是稀疏的假设,本文提出一种新的波阻抗反演方法。首先将地震波阻抗反演中的目标函数表示为L0范数约束下的基追踪问题,并用平滑函数近似表征L0范数;然后将L0范数约束下的基追踪问题转化为无约束最优化问题,并利用基于导数的最优化方法求解无约束优化问题,求取反射系数;最后计算得到波阻抗。模型和实际资料计算结果均表明该方法是可行的。
Under the assumption that the reflectivity is a series of sparse spike,a sparse spike inversion for seismic reflection coefficients is proposed.First the inversion is accomplished by minimizing an objective function which includes a quadratic error term(L2 norm)combined with a sparseness-inducing regularization term(L0 norm).Then the L0 norm is approximated by a smoothing function,so that the L0 penalty becomes differentiable,and the minimization algorithm for continuous functions based on derivative is used to solve the problems.The proposed method is tested on both model data and real field data,and the results show this method is feasible.
Under the assumption that the reflectivity is a series of sparse spike,a sparse spike inversion for seismic reflection coefficients is proposed.First the inversion is accomplished by minimizing an objective function which includes a quadratic error term(L2 norm)combined with a sparseness-inducing regularization term(L0 norm).Then the L0 norm is approximated by a smoothing function,so that the L0 penalty becomes differentiable,and the minimization algorithm for continuous functions based on derivative is used to solve the problems.The proposed method is tested on both model data and real field data,and the results show this method is feasible.
引文
[1]Oldenburg D,Scheuer T,Levy S.Recovery of the acoustic impedance from reflection seismograms.Geophysics,1983,48(10):1318-1337.
[2]Debeye H W J and Riel P.Lp-norm deconvolution.Geophysical Prospecting,1990,38(4):381-403.
[3]Mallat S and Zhang Z.Matching pursuit in a time-frequency dictionary.IEEE Transactions on Signal Processing,1993,41(12):3397-3415.
[4]刘小龙,刘天佑,王华等.基于匹配追踪算法的频谱成像技术及其应用.石油地球物理勘探,2010,45(6):850-855.Liu Xiaolong,Liu Tianyou,Wang Hua et al.Spectrum imaging technique and its application.OGP,2010,45(6):850-855.
[5]张繁昌,李传辉.基于正交时频原子的地震信号快速匹配追踪.地球物理学报,2012,55(1):277-283.Zhang Fanchang,Li Chuanhui.Seismic signal fast matching pursuit based on the orthogonal time-frequency atom.Chinese Journal of Geophysics,2012,55(1):277-283.
[6]张繁昌,李传辉,印兴耀.三角洲砂岩尖灭线的地震匹配追踪瞬时谱识别方法.石油地球物理勘探,2012,47(1):82-88.Zhang Fanchang,Li Chuanhui,Yin Xingyao.Delta fringe line recognition based on seismic matching pursuit instantaneous spectral characteristics.OGP,2012,47(1):82-88.
[7]张繁昌,李传辉.地震信号复数域高效匹配追踪分解.石油地球物理勘探,2013,48(2):171-175.Zhang Fanchang,Li Chuanhui.Seismic signal complex domain efficient matching pursuit decomposition.OGP,2013,48(2):171-175.
[8]武国宁,曹思远,孙娜.基于复数道地震记录的匹配追踪算法及其在储层预测中的应用.地球物理学报,2012,55(6):2027-2034.Wu Guoning,Cao Siyuan,Sun Na.Matching pursuit method based on complex seismic traces and its application of hydrocarbon exploration.Chinese Journal of Geophysics,2012,55(6):2027-2034.
[9]杨昊,郑晓东,李劲松等.基于匹配追踪的薄层自动解释方法.石油地球物理勘探,2013,48(3):429-435.Yang Hao,Zheng Xiaodong,Li Jinsong et al.Thin-bed automatic interpretation based on matching pursuit.OGP,2013,48(3):429-435.
[10]李海山,杨午阳,田军等.匹配追踪煤层强反射分离方法.石油地球物理勘探,2014,49(5):866-870.Li Haishan,Yang Wuyang,Tian Jun et al.Coal seam strong reflection separation with matching pursuit.OGP,2014,49(5):866-870.
[11]周东勇,文晓涛,贺振华等.双极子分解匹配追踪算法在薄层反演中的应用.石油地球物理勘探,2014,49(6):1179-1183.Zhou Dongyong,Wen Xiaotao,He Zhenhua et al.Matching pursuit based on dipole decomposition in seismic thin-bed inversion.OGP,2014,49(6):1179-1183.
[12]Wen X,Zhang B,Pennington W et al.Relative P-impedance estimation using a dipole-based matching pursuit decomposition strategy.Interpretation,2015,3(4):T197-T206.
[13]刘晓晶,印兴耀,吴国忱等.基于正交匹配追踪算法的叠前地震反演方法.石油地球物理勘探,2015,50(5):925-935.Liu Xiaojing,Yin Xingyao,Wu Guochen et al.Prestack seismic inversion based on orthogonal matching pursuit algorithm.OGP,2015,50(5):925-935.
[14]Zhang R,Castagna J.Seismic sparse-layer reflectivity inversion using basis pursuit decomposition.Geophysics,2011,76(6):R147-R158.
[15]Zhang R,Sen M K,Phan S et al.Stochastic and deterministic seismic inversion methods for thin-bed resolution.Journal of Geophysics and Engineering,2012,9(5):611-618.
[16]Zhang R,Sen M K,Srinivasan S.Multi-trace basis pursuit inversion with spatial regularization.Journal of Geophysics and Engineering,2013,10(3):035012.
[17]Zhang R,Sen M K,Srinivasan S.A prestack basis pursuit seismic inversion.Geophysics,2013,78(1):R1-R11.
[18]Zhang R,Daley T M,Vasco D.Improving thin-bed resolution:Application of a sparse-layer inversion on3Dseismic observations from the In Salah carbon dioxide storage project.Interpretation,2015,3(3):SS65-SS71.
[19]Deborah P,Israel C,Anthony V.Multichannel sparse spike inversion.Journal of Geophysics and Engineering,2017,14(5):1290-1299.
[20]印兴耀,刘晓晶,吴国忱等.模型约束基追踪反演方法.石油物探,2016,55(1):115-122.Yin Xingyao,Liu Xiaojing,Wu Guochen et al.Basis pursuit inversion method under model constraint.GPP,2016,55(1):115-122.
[21]张丰麒,金之钧,盛秀杰等.基于低频软约束的叠前AVA稀疏层反演.石油地球物理勘探,2017,52(4):770-782.Zhang Fengqi,Jin Zhijun,Sheng Xiujie et al.AVAsparse layer inversion with the soft-low frequency constraint.OGP,2017,52(4):770-782.
[22]彭军,周家雄,王宇等.基追踪在薄层识别中的研究与应用.地球物理学进展,2017,32(3):1243-1250.Peng Jun,Zhou Jiaxiong,Wang Yu et al.Basis pursuit study and application in the identification thin layer.Progress in Geophysics,2017,32(3):1243-1250.
[23]曹静杰.基于广义高斯分布和非凸Lp范数正则化的地震稀疏盲反褶积.石油地球物理勘探,2016,51(3):428-433.Cao Jingjie.Seismic sparse blind deconvolution based on generalized Gaussian distribution and non-convex Lpnorm regularization.OGP,2016,51(3):428-433.
[24]梁东辉,陈生昌.基于L0范数稀疏约束的地震数据反褶积.石油物探,2014,53(4):397-403.Liang Donghui,Chen Shengchang.Deconvolution of seismic data based on L0 norm sparse constraint.GPP,2014,53(4):397-403.
[25]陈宝林.最优化理论与算法.北京:清华大学出版社,2005.Chen Baoling.Theory and Algorithms of Optimization.Tsinghua University Press,Beijing,2005.
[2]Debeye H W J and Riel P.Lp-norm deconvolution.Geophysical Prospecting,1990,38(4):381-403.
[3]Mallat S and Zhang Z.Matching pursuit in a time-frequency dictionary.IEEE Transactions on Signal Processing,1993,41(12):3397-3415.
[4]刘小龙,刘天佑,王华等.基于匹配追踪算法的频谱成像技术及其应用.石油地球物理勘探,2010,45(6):850-855.Liu Xiaolong,Liu Tianyou,Wang Hua et al.Spectrum imaging technique and its application.OGP,2010,45(6):850-855.
[5]张繁昌,李传辉.基于正交时频原子的地震信号快速匹配追踪.地球物理学报,2012,55(1):277-283.Zhang Fanchang,Li Chuanhui.Seismic signal fast matching pursuit based on the orthogonal time-frequency atom.Chinese Journal of Geophysics,2012,55(1):277-283.
[6]张繁昌,李传辉,印兴耀.三角洲砂岩尖灭线的地震匹配追踪瞬时谱识别方法.石油地球物理勘探,2012,47(1):82-88.Zhang Fanchang,Li Chuanhui,Yin Xingyao.Delta fringe line recognition based on seismic matching pursuit instantaneous spectral characteristics.OGP,2012,47(1):82-88.
[7]张繁昌,李传辉.地震信号复数域高效匹配追踪分解.石油地球物理勘探,2013,48(2):171-175.Zhang Fanchang,Li Chuanhui.Seismic signal complex domain efficient matching pursuit decomposition.OGP,2013,48(2):171-175.
[8]武国宁,曹思远,孙娜.基于复数道地震记录的匹配追踪算法及其在储层预测中的应用.地球物理学报,2012,55(6):2027-2034.Wu Guoning,Cao Siyuan,Sun Na.Matching pursuit method based on complex seismic traces and its application of hydrocarbon exploration.Chinese Journal of Geophysics,2012,55(6):2027-2034.
[9]杨昊,郑晓东,李劲松等.基于匹配追踪的薄层自动解释方法.石油地球物理勘探,2013,48(3):429-435.Yang Hao,Zheng Xiaodong,Li Jinsong et al.Thin-bed automatic interpretation based on matching pursuit.OGP,2013,48(3):429-435.
[10]李海山,杨午阳,田军等.匹配追踪煤层强反射分离方法.石油地球物理勘探,2014,49(5):866-870.Li Haishan,Yang Wuyang,Tian Jun et al.Coal seam strong reflection separation with matching pursuit.OGP,2014,49(5):866-870.
[11]周东勇,文晓涛,贺振华等.双极子分解匹配追踪算法在薄层反演中的应用.石油地球物理勘探,2014,49(6):1179-1183.Zhou Dongyong,Wen Xiaotao,He Zhenhua et al.Matching pursuit based on dipole decomposition in seismic thin-bed inversion.OGP,2014,49(6):1179-1183.
[12]Wen X,Zhang B,Pennington W et al.Relative P-impedance estimation using a dipole-based matching pursuit decomposition strategy.Interpretation,2015,3(4):T197-T206.
[13]刘晓晶,印兴耀,吴国忱等.基于正交匹配追踪算法的叠前地震反演方法.石油地球物理勘探,2015,50(5):925-935.Liu Xiaojing,Yin Xingyao,Wu Guochen et al.Prestack seismic inversion based on orthogonal matching pursuit algorithm.OGP,2015,50(5):925-935.
[14]Zhang R,Castagna J.Seismic sparse-layer reflectivity inversion using basis pursuit decomposition.Geophysics,2011,76(6):R147-R158.
[15]Zhang R,Sen M K,Phan S et al.Stochastic and deterministic seismic inversion methods for thin-bed resolution.Journal of Geophysics and Engineering,2012,9(5):611-618.
[16]Zhang R,Sen M K,Srinivasan S.Multi-trace basis pursuit inversion with spatial regularization.Journal of Geophysics and Engineering,2013,10(3):035012.
[17]Zhang R,Sen M K,Srinivasan S.A prestack basis pursuit seismic inversion.Geophysics,2013,78(1):R1-R11.
[18]Zhang R,Daley T M,Vasco D.Improving thin-bed resolution:Application of a sparse-layer inversion on3Dseismic observations from the In Salah carbon dioxide storage project.Interpretation,2015,3(3):SS65-SS71.
[19]Deborah P,Israel C,Anthony V.Multichannel sparse spike inversion.Journal of Geophysics and Engineering,2017,14(5):1290-1299.
[20]印兴耀,刘晓晶,吴国忱等.模型约束基追踪反演方法.石油物探,2016,55(1):115-122.Yin Xingyao,Liu Xiaojing,Wu Guochen et al.Basis pursuit inversion method under model constraint.GPP,2016,55(1):115-122.
[21]张丰麒,金之钧,盛秀杰等.基于低频软约束的叠前AVA稀疏层反演.石油地球物理勘探,2017,52(4):770-782.Zhang Fengqi,Jin Zhijun,Sheng Xiujie et al.AVAsparse layer inversion with the soft-low frequency constraint.OGP,2017,52(4):770-782.
[22]彭军,周家雄,王宇等.基追踪在薄层识别中的研究与应用.地球物理学进展,2017,32(3):1243-1250.Peng Jun,Zhou Jiaxiong,Wang Yu et al.Basis pursuit study and application in the identification thin layer.Progress in Geophysics,2017,32(3):1243-1250.
[23]曹静杰.基于广义高斯分布和非凸Lp范数正则化的地震稀疏盲反褶积.石油地球物理勘探,2016,51(3):428-433.Cao Jingjie.Seismic sparse blind deconvolution based on generalized Gaussian distribution and non-convex Lpnorm regularization.OGP,2016,51(3):428-433.
[24]梁东辉,陈生昌.基于L0范数稀疏约束的地震数据反褶积.石油物探,2014,53(4):397-403.Liang Donghui,Chen Shengchang.Deconvolution of seismic data based on L0 norm sparse constraint.GPP,2014,53(4):397-403.
[25]陈宝林.最优化理论与算法.北京:清华大学出版社,2005.Chen Baoling.Theory and Algorithms of Optimization.Tsinghua University Press,Beijing,2005.