基于L1范数的波阻抗反演
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摘要
提出了一种新的波阻抗反演方法,首先根据地下反射系数序列是一个稀疏脉冲序列这一假设,将地震波阻抗反演中的目标函数表示为L1范数约束下的L1范数优化问题,并将L1范数用一个平滑函数来近似,从而使得目标函数函数可微。然后将L1范数约束下的基追踪问题转化为无约束最优化问题,并利用基于导数的局部优化方法求解无约束优化问题,求得反射系数,进而计算得到波阻抗。模型和实际资料计算结果均表明该方法可行。
A new method to inverse seismic reflection data for reflection coefficients is introduced. According to the assumption: the reflectivity is composed of a series of sparse-spike, the inversion is accomplished by first minimizing an objective function which includes a quadratic error term( norm) combined with a sparseness-inducing regularization term( norm). Then the norm is approximated by a smoothing function, so that the penalty becomes differentiable, and then minimization algorithm for continuous functions based on derivative is used to solve the problems. The method was tested on both model data and real field data, and the results show the method is feasible.
A new method to inverse seismic reflection data for reflection coefficients is introduced. According to the assumption: the reflectivity is composed of a series of sparse-spike, the inversion is accomplished by first minimizing an objective function which includes a quadratic error term( norm) combined with a sparseness-inducing regularization term( norm). Then the norm is approximated by a smoothing function, so that the penalty becomes differentiable, and then minimization algorithm for continuous functions based on derivative is used to solve the problems. The method was tested on both model data and real field data, and the results show the method is feasible.
引文
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[6] 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[J].地球物理学报,2012,55(6):2027-2034.WU G N, CAO S Y, SUN N. Matching pursuit method based on complex seismic traces and its application of hydrocarbon exploration[J]. Chinese Journal of Geophysics, 2012,55(6):2027-2034.(In Chinese)
[7] 杨昊,郑晓东,李劲松,等.基于匹配追踪的薄层自动解释方法[J].石油地球物理勘探,2013,48(3):429-435.YANG H, ZHENG X D, LI J S, et al. The method of thin-bed automatic interpretation base on matching pursuit[J]. OGP, 2013,48(3):429-435.(In Chinese)
[8] 李海山,杨午阳,田军,等.匹配追踪煤层强反射分离方法[J].石油地球物理勘探,2014,49(5):866-870.LI H S, YANG W Y, TIAN J, et al. Coal seam strong reflection separation with matching pursuit[J]. OGP, 2014,49(5):866-870.(In Chinese)
[9] 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[J]. 石油地球物理勘探,2014,49(6):1179-1183.ZHOU D Y, WEN X T, HE Z H, et al. Matching pursuit based on dipole decomposition in seismic thin-bed inversion[J]. OGP, 2014,49(6):1179-1183.(In Chinese)
[10] 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[J].石油地球物理勘探,2015,50(5):925-935.LIU X J, YIN X Y, WU G C, et al. Prestack seismic inversion based on orthogonal matching pursuit algorithm[J]. OGP, 2015,50(5):925-935.(In Chinese)
[11] RUI ZHANG, JOHN CASTAGNA. Seismic sparse-layer reflectivity inversion using basis pursuit decomposition[J]. Geophysics, 2011, 76(6): R147-R158.
[2] 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[J].石油地球物理勘探,2010,45(6):850-855.LIU X L, LIU T Y, WANG H, et al. Spectrum imaging technique and its application[J]. OGP, 2010,45(6):850-855.(In Chinese)
[3] 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[J]. 地球物理学报,2012,55(1):277-283.ZHANG F C, LI C H. Seismic signal fast matching pursuit based on the orthogonal time-frequency atom[J]. Chinese of Journal of Geophysics, 2012,55(1):277-283.(In Chinese)
[4] 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[J].石油地球物理勘探,2012,47(1):82-88.ZHANG F C, LI C H, YIN X Y. Delta fringe line recognition based on seismic matching pursuit instantaneous spectral characteristics[J]. OGP, 2012,47(1):82-88.(In Chinese)
[5] 张繁昌,李传辉. 地震信号复数域高效匹配追踪分解[J]. 石油地球物理勘探,2013,48(2):171-175.ZHANG F C, LI C H. Seismic signal complex domain efficient matching pursuit decomposition[J]. OGP, 2013,48(2):171-175.(In Chinese)
[6] 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[J].地球物理学报,2012,55(6):2027-2034.WU G N, CAO S Y, SUN N. Matching pursuit method based on complex seismic traces and its application of hydrocarbon exploration[J]. Chinese Journal of Geophysics, 2012,55(6):2027-2034.(In Chinese)
[7] 杨昊,郑晓东,李劲松,等.基于匹配追踪的薄层自动解释方法[J].石油地球物理勘探,2013,48(3):429-435.YANG H, ZHENG X D, LI J S, et al. The method of thin-bed automatic interpretation base on matching pursuit[J]. OGP, 2013,48(3):429-435.(In Chinese)
[8] 李海山,杨午阳,田军,等.匹配追踪煤层强反射分离方法[J].石油地球物理勘探,2014,49(5):866-870.LI H S, YANG W Y, TIAN J, et al. Coal seam strong reflection separation with matching pursuit[J]. OGP, 2014,49(5):866-870.(In Chinese)
[9] 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[J]. 石油地球物理勘探,2014,49(6):1179-1183.ZHOU D Y, WEN X T, HE Z H, et al. Matching pursuit based on dipole decomposition in seismic thin-bed inversion[J]. OGP, 2014,49(6):1179-1183.(In Chinese)
[10] 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[J].石油地球物理勘探,2015,50(5):925-935.LIU X J, YIN X Y, WU G C, et al. Prestack seismic inversion based on orthogonal matching pursuit algorithm[J]. OGP, 2015,50(5):925-935.(In Chinese)
[11] RUI ZHANG, JOHN CASTAGNA. Seismic sparse-layer reflectivity inversion using basis pursuit decomposition[J]. Geophysics, 2011, 76(6): R147-R158.