基于Curvelet变换的稀疏反褶积
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摘要
常规反褶积方法通常需要假设地层反射系数是稀疏的,然后再利用L1范数反褶积求得稀疏的反射系数来提高分辨率,但常规反褶积方法在提高分辨率的同时降低了信噪比,并且反褶积后同相轴的连续性会变差。针对上述问题,提出了基于Curvelet变换的反褶积方法。Curvelet变换对多维信号具有最好的稀疏表示,能获得最优的非线性逼近,因而可利用Curvelet变换来表示地震反射信号,将其引入到L1范数反褶积后,可利用稀疏的Curvelet系数来描述反射系数,从而无需地层反射信号是稀疏的假设。根据有效信号和随机噪声在Curvelet域中的分布特点,可通过阈值法来压制噪声提高信噪比,并且利用Curvelet变换对地震信号进行多维表示,可实现多维反褶积保持同相轴的连续性。最后,给出了一种阈值循环迭代算法来计算L1范数反褶积问题。研究结果表明,基于Curvelet变换的稀疏反褶积方法在提高地震分辨率的同时能有效地压制随机噪声,并保持同相轴的连续性。
Traditional deconvolution methods usually need to assume a sparse distribution for seismic reflectivity,and then apply the L1 norm deconvolution to get sparse reflectivity so as to improve resolution,but this doesn't conform to reality.In addition,when traditional methods improve the resolution,they reduce the signal to noise ratio at the same time,making the continuity of a seismic profile poor.In view of these problems,the sparse deconvolution based on the Curvelet transform was proposed in the present paper.The Curvelet transform is characterized by an optimum sparseness expression for multidimensional signals to have the best nonlinear approximation,thus it can be used to express seismic reflectivity.When the Curvelet transform was introduced to the L1 norm deconvolution,a sparse Curvelet coefficient representing reflectivity could be obtained without assuming the sparseness of reflectivity.In addition,according to the distribution characteristics of effective signals and noise the signal to noise ratio could be improved by using a threshold method to suppress noise,and consequently the multidimensional seismic deconvolution was obtained to maintain the continuity of seismic profiles.Finally,a threshold iterative algorithm was proposed to solve the L1 norm deconvolution problem.The results show that this proposed method can effectively improve resolution and continuity of seismic profiles while suppressing random noise.
Traditional deconvolution methods usually need to assume a sparse distribution for seismic reflectivity,and then apply the L1 norm deconvolution to get sparse reflectivity so as to improve resolution,but this doesn't conform to reality.In addition,when traditional methods improve the resolution,they reduce the signal to noise ratio at the same time,making the continuity of a seismic profile poor.In view of these problems,the sparse deconvolution based on the Curvelet transform was proposed in the present paper.The Curvelet transform is characterized by an optimum sparseness expression for multidimensional signals to have the best nonlinear approximation,thus it can be used to express seismic reflectivity.When the Curvelet transform was introduced to the L1 norm deconvolution,a sparse Curvelet coefficient representing reflectivity could be obtained without assuming the sparseness of reflectivity.In addition,according to the distribution characteristics of effective signals and noise the signal to noise ratio could be improved by using a threshold method to suppress noise,and consequently the multidimensional seismic deconvolution was obtained to maintain the continuity of seismic profiles.Finally,a threshold iterative algorithm was proposed to solve the L1 norm deconvolution problem.The results show that this proposed method can effectively improve resolution and continuity of seismic profiles while suppressing random noise.
引文
[1]李勇,李保柱,胡永乐,等.反褶积法在气井早期地层测试解释中的应用[J].石油学报,2010,31(2):298-301.Li Yong,Li Baozhu,Hu Yongle,et al.Application of deconvolu-tion algorithm to early formation interpretation of gas wells[J].Acta Petrolei Sinica,2010,31(2):298-301.
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[12]乐友喜,王才经,屠世杰.约束L1模反褶积[J].石油地球物理勘探,1997,32(2):171-180.Le Youxi,Wang Caijing,Tu Shijie.Restrained L1modulo deconvolution[J].Oil Geophysical Prospecting,1997,32(2):171-180.
[13]冯志强,孙国昕,蒙启安,等.海拉尔盆地贝中次凹--留型叠合小断陷盆地油气勘探的成功案例[J].石油学报,2011,32(4):551-563.Feng Zhiqiang,Sun Guoxi,Meng Qi'an,et al.Beizhong sub-depression in the Hailaer Basin:a successful case for oil exploration in small residual superimposed rift basins[J].Acta Petrolei Sinica,2011,32(4):551-563.
[14]Felix J H.Seismic deconvolution by atomic decomposition:aparametric approach with sparseness constraints[J].Integrated Computer-Aided Engineering,2005,12(1):69-91.
[15]Cand′es E J,Donoho D L.Curvelets:a surprisingly effectivenonadattive representation for objects with edges[G]∥Cohen A,Rabut C,Schumaker L L.Curves and surface fitting.Nashville:Vanderbilt University Press,2000:105-120.
[16]张恒磊,刘天佑,李红巧.Curvelet域面波衰减方法研究[J].中南大学学报:自然科学版,2011,42(8):2372-2378.Zhang Henglei,Liu Tianyou,Li Hongqiao.Attenuation of surface wave in Curvelet domain[J].Journal of Central South University:Science and Technology,2011,42(8):2372-2378.
[17]Cand′es E J,Laurent D L,David D,et al.Fast discrete Curvelet transforms[J].Multiscale Modeling and Simulation,2006,5(3):861-899.
[18]Herrmann F J,Hennenfent G,Non parametric seismic data recovery with Curvelet frames[J].Geophysical Journal International,2008,173(1):233-248.
[19]Wang Deli,Tong Zhongfei,Tang Chen.An iterative Curvelet thresholding algorithm for seismic random noise attenuation[J].Applied Geophysics,2010,7(4):315-324.
[20]刘喜武,刘洪.地震盲反褶积综述[J].地球物理学进展,2003,18(2):203-209.Liu Xiwu,Liu Hong.Survey on seismic blind deconvolution[J].Progress in Geophysics,2003,18(2):203-209.
[21]Danilo R.Stochastic sparse-spike deconvolution[J].Geophysics,2008,73(1):R1-R9.
[22]Elad M,Starck J L,Querre P.Simultaneous cartoon and texture image imprinting using morphological component analysis[J].Applied and Computational Harmonic Analysis,2005,19(3):340-358.
[23]Daubechies I,Defrise M,Demol C.An iterative thresholding algorithm for linear inverse problems with a sparsity constraint[J].Communications on Pure and Applied Mathematics,2004,57(11):1413-1457.
[2]张昌民,张尚峰,朱锐,等.珠江口盆地砂岩侵入体的识别特征及石油地质意义[J].石油学报,2012,33(2):188-194.Zhang Changmin,Zhang Shangfeng,Zhu Rui,et al.Recongnitioncriteria for sand injectites in the Zhujiangkou Basin and their sig-nificance in petroleum geology[J].Acta Petrolei Sinica,2012,33(2):188-194.
[3]Taylor H L,Banks S C,Mccoy J F.Deconvolution with L1-norm[J].Geophysics,1979,44(1):39-52.
[4]Shlomo L,Peter K F.Reconstruction of a sparse spike train fromaportion of its spectrum and application to high-resolution de-convolution[J].Geophysics,1981,46(9):1235-1243.
[5]Mauricio D.Reweighting strategies in seismic deconvolution[J].Geophysics,1997,129:651-656.
[6]Lei L,Terence P S.Parametric deconvolution of positive spiketrains[J].Annals of Statistics,2000,28(5):1279-1301.
[7]Danilo R V.Parametric sparse-spike deconvolution and the recovery of the acoustic impedance:the76th annual international meeting of society of exploration geophysicists,New Orleans,2006[C].Tulsa:Society of Exploration Geophysicists,2006:2141-2144.
[8]王宇,韩立国,周家雄,等.L1-L2范数联合约束稀疏脉冲反演的应用[J].地球科学--中国地质大学学报,2009,34(5):835-840.Wang Yu,Han Liguo,Zhou Jiaxiong,et al.Application of combined norm constrained sparseness spike inverse[J].Earth Science:Journal of China University of Geosciences,2009,34(5):835-840.
[9]刘喜武,刘洪.实现稀疏反褶积的预条件双共轭梯度法[J].物探化探计算技术,2003,25(3):215-219.Liu Xiwu,Liu Hong.The preconditional dual conjugate gradient algorithm for sparse deconvolution[J].Computing Techniques for Geophysical and Geochemical Exploration,2003,25(3):215-219.
[10]朱振宇,刘洪.稀疏反褶积方法及其应用[J].石油大学学报:自然科学版,2005,29(6):20-22.Zhu Zhenyu,Liu Hong.Sparse deconvolution method and its application[J].Journal of the University of Petroleum,China:Natural Science Edition,2005,29(6):20-22
[11]Hennenfent G,Felix J H.Sparseness-constrained seismic deconvolution with Curvelets[G]∥Sacchi M,Perz M.Canadian society of exploration geophysicists national convention,Canada,Vancouver:Canadian Society of Exploration Geophysicists,2005:89-92.
[12]乐友喜,王才经,屠世杰.约束L1模反褶积[J].石油地球物理勘探,1997,32(2):171-180.Le Youxi,Wang Caijing,Tu Shijie.Restrained L1modulo deconvolution[J].Oil Geophysical Prospecting,1997,32(2):171-180.
[13]冯志强,孙国昕,蒙启安,等.海拉尔盆地贝中次凹--留型叠合小断陷盆地油气勘探的成功案例[J].石油学报,2011,32(4):551-563.Feng Zhiqiang,Sun Guoxi,Meng Qi'an,et al.Beizhong sub-depression in the Hailaer Basin:a successful case for oil exploration in small residual superimposed rift basins[J].Acta Petrolei Sinica,2011,32(4):551-563.
[14]Felix J H.Seismic deconvolution by atomic decomposition:aparametric approach with sparseness constraints[J].Integrated Computer-Aided Engineering,2005,12(1):69-91.
[15]Cand′es E J,Donoho D L.Curvelets:a surprisingly effectivenonadattive representation for objects with edges[G]∥Cohen A,Rabut C,Schumaker L L.Curves and surface fitting.Nashville:Vanderbilt University Press,2000:105-120.
[16]张恒磊,刘天佑,李红巧.Curvelet域面波衰减方法研究[J].中南大学学报:自然科学版,2011,42(8):2372-2378.Zhang Henglei,Liu Tianyou,Li Hongqiao.Attenuation of surface wave in Curvelet domain[J].Journal of Central South University:Science and Technology,2011,42(8):2372-2378.
[17]Cand′es E J,Laurent D L,David D,et al.Fast discrete Curvelet transforms[J].Multiscale Modeling and Simulation,2006,5(3):861-899.
[18]Herrmann F J,Hennenfent G,Non parametric seismic data recovery with Curvelet frames[J].Geophysical Journal International,2008,173(1):233-248.
[19]Wang Deli,Tong Zhongfei,Tang Chen.An iterative Curvelet thresholding algorithm for seismic random noise attenuation[J].Applied Geophysics,2010,7(4):315-324.
[20]刘喜武,刘洪.地震盲反褶积综述[J].地球物理学进展,2003,18(2):203-209.Liu Xiwu,Liu Hong.Survey on seismic blind deconvolution[J].Progress in Geophysics,2003,18(2):203-209.
[21]Danilo R.Stochastic sparse-spike deconvolution[J].Geophysics,2008,73(1):R1-R9.
[22]Elad M,Starck J L,Querre P.Simultaneous cartoon and texture image imprinting using morphological component analysis[J].Applied and Computational Harmonic Analysis,2005,19(3):340-358.
[23]Daubechies I,Defrise M,Demol C.An iterative thresholding algorithm for linear inverse problems with a sparsity constraint[J].Communications on Pure and Applied Mathematics,2004,57(11):1413-1457.
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