基于基追踪的时变子波提取与地震反射率反演
|
摘要
由于噪声和衰减的影响,地震数据不平稳,即地震信号的频谱从浅到深是逐渐变化的。为了研究地震数据的非平稳性质,基于基追踪谱分解方法进行高分辨率时频分解,通过点谱模拟提取广义地震子波,继而构建时变子波核矩阵和时变子波字典,最终实现非平稳基追踪地震反演。实际资料测试表明,基追踪谱分解广义时变子波提取方法能实现高效井震标定,基于时变子波的非平稳基追踪地震反演结果分辨率更高、地质连续性更强、地质细节展示更详细。
Seismic data are nonstationary because of noise contamination and energy attenuation during wave propagation,which means that the frequency spectrum of seismic signals changes from shallow to deep formations.In order to capture the non-stationary of seismic data,a time-variant wavelet extraction method is proposed using basis pursuit spectral decomposition and generalized seismic wavelet,in which basis pursuit spectral decomposition would supply high resolution time-frequency spectrum for better time-variant wavelet extraction.Based on time-variant wavelets,wavelet kernel matrix and wave dictionary are constructed,and basis pursuit seismic inversion is executed at last.Field data test shows that the proposed scheme achieves better data resolution,more effective wellto-seismic calibration,better geological continuity,and clearer geological details.
Seismic data are nonstationary because of noise contamination and energy attenuation during wave propagation,which means that the frequency spectrum of seismic signals changes from shallow to deep formations.In order to capture the non-stationary of seismic data,a time-variant wavelet extraction method is proposed using basis pursuit spectral decomposition and generalized seismic wavelet,in which basis pursuit spectral decomposition would supply high resolution time-frequency spectrum for better time-variant wavelet extraction.Based on time-variant wavelets,wavelet kernel matrix and wave dictionary are constructed,and basis pursuit seismic inversion is executed at last.Field data test shows that the proposed scheme achieves better data resolution,more effective wellto-seismic calibration,better geological continuity,and clearer geological details.
引文
[1] Van der Baan M.Time-varying wavelet estimation and deconvolution by kurtosis maximization[J].Geophy-sics,2008,73(2):V11-V18.
[2] Van der Baan M,Fomel S.Nonstationary phase estimation using regularized local kurtosis maximization[J].Geophysics,2009,74(6):A75-A80.
[3] Margrave G F,Lamoureux M P,Henley D C.Gabor deconvolution: Estimating reflectivity by nonstationa-ry deconvolution of seismic data[J].Geophysics,2011,76(3):W15-W30.
[4] Dai Y S,Wang R R,Li C,et al.A time-varying wavelet extraction using local similarity[J].Geophysics,2016,81(1):V55-V68.
[5] 王蓉蓉,戴永寿,李闯,等.时频分析与自适应分段相结合的时变子波提取方法[J].石油地球物理勘探,2016,51(5):850-862.WANG Rongrong,DAI Yongshou,LI Chuang,et al.Time-varying wavelet extraction based on time-frequency analysis and adaptive segmentation[J].Oil Geophysical Prospecting,2016,51(5):850-862.
[6] 孔德辉,彭真明.利用改进的在线字典学习估计时变子波[J].石油地球物理勘探,2016,51(5):901-908.KONG Dehui,PENG Zhenming.Time-varying wavelet estimation based on improved online dictionary learning[J].Oil Geophysical Prospecting,2016,51(5):901-908.
[7] Zhang R,Fomel S.Time-variant wavelet extraction with a local-attribute-based time-frequency decomposition for seismic inversion[J].Interpretation,2017,5(1):SC9-SC16.
[8] Wang Y H.Generalized seismic wavelets[J].Geo-physical Journal International,2015,203(2):1172-1178.
[9] Allen J.Short term spectral analysis,synthesis,and modification by discrete Fourier transform[J].IEEE Transactions on Acoustics,Speech and Signal Processing,1977,25(3):235-238.
[10] Chakraborty A,Okaya D.Frequency-time decomposition of seismic data using wavelet-based method[J].Geophysics,1995,60(6):1906-1916.
[11] Sinha S,Routh P S,Anno P D,et al.Spectral decomposition of seismic data with continuous-wavelet transform[J].Geophysics,2005,70(7):P19-P25.
[12] Liu J,Marfurt K J.Instantaneous spectral attributes to detect channels.Geophysics,2007,72(2):P23-P31.
[13] Wang Y H.Seismic time-frequency spectral decomposition by matching pursuit[J].Geophysics,2007,72(1):V13-V20.
[14] Liu G,Fomel S,Chen X.Time-frequency analysis of seismic data using local attributes[J].Geophysics,2011,76(6):P23-P34.
[15] Liu Y,Fomel S.Seismic data analysis using local time-frequency decomposition[J].Geophysical Prospecting,2013,61(3):516-525.
[16] Stockwell R G,Mansinha L,Lowe R P.Localization of the complex spectrum: The S transform[J].IEEE Transactions on Signal Processing,1996,44(4):998-1001.
[17] Fomel S.Shaping regularization in geophysical-esti-mation problems[J].Geophysics,2005,24(1):R29-R36.
[18] Cai Y H,Fomel S,Zeng H L.Automated spectral recomposition with application in stratigraphic interpretation[J].Interpretation,2013,1(1):SA109-SA116.
[19] Huang N E,Shen Z,Long S R,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J].Proceeding of the Royal Society of London Series,1998,454(1971):903-995.
[20] Tary J B,Herrera R H,Han J,et al.Spectral estimation: What is new? What is next?[J].Reviews of Geophysics,2014,52(4):723-749.
[21] Daubechies I,Lu J,Wu H T.Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool[J].Applied and Computational Harmonic Analysis,2011,30(2):243-261.
[22] 刘晗,张建中,黄忠来.基于同步挤压S变换的地震信号时频分析[J].石油地球物理勘探,2017,52(4):689-695.LIU Han,ZHANG Jianzhong,HUANG Zhonglai.Time-frequency analysis of seismic data using synchro-squeezing S transform[J].Oil Geophysical Prospecting,2017,52(4):689-695.
[23] Chen S S,Donoho D L,Saunders M A.Atomic decomposition by basis pursuit[J].Siam Review,2001,43(1):129-159.
[24] Bonar D C,Sacchi M D.Complex spectral decomposition via inversion strategies[J].SEG Technical Program Expanded Abstracts,2010,29(1):1408-1412.
[25] Vera Rodriguez I,Bonar D,Sacchi M D.Microseismic data denoising using a 3C group sparsity constrained time-frequency transform[J].Geophysics,2012,77(2):V21-V29.
[26] Figueiredo M,Nowak R D,Wright S J.Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems[J].IEEE Journal of Selected Topics in Signal Processing,2007,1(4):568-598.
[27] Van den B,Friedlander M P.Probing the Pareto frontier for basis pursuit solutions[J].Siam Journal on Scientific Computing,2008,31(2):890-912.
[28] Beck A,Teboulle M.A fast iterative shrinkage-thre-sholding algorithm for linear inverse problems[J].SIAM Journal on Imaging Science,2009,2(1):183-202.
[29] Rubinstein R,Bruckstein A M,Elad M.Dictionaries for sparse representation modeling[J].Proceedings of the IEEE,2010,98(6):1045-1057.
[30] Graham RL,Knuth D E,Patashnik O.Concrete Mathe-matics: A Foundation for Computer Science[M].Addison-Wesley Professional,Massachusetts,1994.
[31] Oldenburg D W,Scheuer T,Levy S.Recovery of the acoustic impedance from reflection seismograms[J].Geophysics,1983,48(10):1318-1337.
[32] White R E,O’Brien P.Estimation of the primary seismic pulse[J].Geophysical Prospecting,1974,22(4):627-651.
[33] Bednar J B.Applications of median filtering to deconvolution,pulse estimation,and statistical editing of seismic data[J].Geophysics,1983,48(2):1598-1610.
[34] Walden A,White R.Seismic wavelet estimation: A frequency domain solution to a geophysical noisy input-output problem[J].IEEE Transactions on Geoscience and Remote Sensing,1998,36(1):287-297.
[35] Sacchi M D,Ulrych T J.Nonminimum-phase wavelet estimation using higher order statistics[J].The Lea-ding Edge,2000,19(1):80-83.
[36] Misra S,Chopra S.Mixed-phase wavelet estimation:A case study[J].CSEG Recorder,2011,36(1):33-35.
[37] Danielsen V,Karlsson T V.Extraction of signatures from seismic and well data[J].First Break,1984,2(4):15-21.
[38] Lines L R,Treitel S.Wavelets,well logs and Wiener filters[J].First Break,1985,3(8):9-14.
[39] Zhang R,Castagna J.Seismic sparse-layer reflectivity inversion using basis pursuit decomposition[J].Geophysics,2011,76(6):R147-R158.
[40] Yuan S,Wang S.Spectral sparse Bayesian learning reflectivity inversion[J].Geophysical Prospecting,2013,61(4):735-746.
[41] Zhang R,Sen M K,Srinivasan S.A prestack basis pursuit seismic inversion[J].Geophysics,2013,78(1):R1-R11.
[42] 刘晓晶,印兴耀,吴国忱,等.基于基追踪弹性阻抗反演的深部储层流体识别方法[J].地球物理学报,2016,59(1):277-286.LIU Xiaojing,YIN Xingyao,WU Guochen,et al.Identification of deep reservoir fluids based on basis pursuit inversion for elastic impedance[J].Chinese Journal of Geophysics,2016,59(1):277-286.
[43] 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[J].石油地球物理勘探,2017,52(4):770-782.ZHANG Fengqi,JIN Zhijun,SHENG Xiujie,et al.AVA sparse layer inversion with the soft-low frequency constraint[J].Oil Geophysical Prospecting,2017,52(4):770-782.
[2] Van der Baan M,Fomel S.Nonstationary phase estimation using regularized local kurtosis maximization[J].Geophysics,2009,74(6):A75-A80.
[3] Margrave G F,Lamoureux M P,Henley D C.Gabor deconvolution: Estimating reflectivity by nonstationa-ry deconvolution of seismic data[J].Geophysics,2011,76(3):W15-W30.
[4] Dai Y S,Wang R R,Li C,et al.A time-varying wavelet extraction using local similarity[J].Geophysics,2016,81(1):V55-V68.
[5] 王蓉蓉,戴永寿,李闯,等.时频分析与自适应分段相结合的时变子波提取方法[J].石油地球物理勘探,2016,51(5):850-862.WANG Rongrong,DAI Yongshou,LI Chuang,et al.Time-varying wavelet extraction based on time-frequency analysis and adaptive segmentation[J].Oil Geophysical Prospecting,2016,51(5):850-862.
[6] 孔德辉,彭真明.利用改进的在线字典学习估计时变子波[J].石油地球物理勘探,2016,51(5):901-908.KONG Dehui,PENG Zhenming.Time-varying wavelet estimation based on improved online dictionary learning[J].Oil Geophysical Prospecting,2016,51(5):901-908.
[7] Zhang R,Fomel S.Time-variant wavelet extraction with a local-attribute-based time-frequency decomposition for seismic inversion[J].Interpretation,2017,5(1):SC9-SC16.
[8] Wang Y H.Generalized seismic wavelets[J].Geo-physical Journal International,2015,203(2):1172-1178.
[9] Allen J.Short term spectral analysis,synthesis,and modification by discrete Fourier transform[J].IEEE Transactions on Acoustics,Speech and Signal Processing,1977,25(3):235-238.
[10] Chakraborty A,Okaya D.Frequency-time decomposition of seismic data using wavelet-based method[J].Geophysics,1995,60(6):1906-1916.
[11] Sinha S,Routh P S,Anno P D,et al.Spectral decomposition of seismic data with continuous-wavelet transform[J].Geophysics,2005,70(7):P19-P25.
[12] Liu J,Marfurt K J.Instantaneous spectral attributes to detect channels.Geophysics,2007,72(2):P23-P31.
[13] Wang Y H.Seismic time-frequency spectral decomposition by matching pursuit[J].Geophysics,2007,72(1):V13-V20.
[14] Liu G,Fomel S,Chen X.Time-frequency analysis of seismic data using local attributes[J].Geophysics,2011,76(6):P23-P34.
[15] Liu Y,Fomel S.Seismic data analysis using local time-frequency decomposition[J].Geophysical Prospecting,2013,61(3):516-525.
[16] Stockwell R G,Mansinha L,Lowe R P.Localization of the complex spectrum: The S transform[J].IEEE Transactions on Signal Processing,1996,44(4):998-1001.
[17] Fomel S.Shaping regularization in geophysical-esti-mation problems[J].Geophysics,2005,24(1):R29-R36.
[18] Cai Y H,Fomel S,Zeng H L.Automated spectral recomposition with application in stratigraphic interpretation[J].Interpretation,2013,1(1):SA109-SA116.
[19] Huang N E,Shen Z,Long S R,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J].Proceeding of the Royal Society of London Series,1998,454(1971):903-995.
[20] Tary J B,Herrera R H,Han J,et al.Spectral estimation: What is new? What is next?[J].Reviews of Geophysics,2014,52(4):723-749.
[21] Daubechies I,Lu J,Wu H T.Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool[J].Applied and Computational Harmonic Analysis,2011,30(2):243-261.
[22] 刘晗,张建中,黄忠来.基于同步挤压S变换的地震信号时频分析[J].石油地球物理勘探,2017,52(4):689-695.LIU Han,ZHANG Jianzhong,HUANG Zhonglai.Time-frequency analysis of seismic data using synchro-squeezing S transform[J].Oil Geophysical Prospecting,2017,52(4):689-695.
[23] Chen S S,Donoho D L,Saunders M A.Atomic decomposition by basis pursuit[J].Siam Review,2001,43(1):129-159.
[24] Bonar D C,Sacchi M D.Complex spectral decomposition via inversion strategies[J].SEG Technical Program Expanded Abstracts,2010,29(1):1408-1412.
[25] Vera Rodriguez I,Bonar D,Sacchi M D.Microseismic data denoising using a 3C group sparsity constrained time-frequency transform[J].Geophysics,2012,77(2):V21-V29.
[26] Figueiredo M,Nowak R D,Wright S J.Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems[J].IEEE Journal of Selected Topics in Signal Processing,2007,1(4):568-598.
[27] Van den B,Friedlander M P.Probing the Pareto frontier for basis pursuit solutions[J].Siam Journal on Scientific Computing,2008,31(2):890-912.
[28] Beck A,Teboulle M.A fast iterative shrinkage-thre-sholding algorithm for linear inverse problems[J].SIAM Journal on Imaging Science,2009,2(1):183-202.
[29] Rubinstein R,Bruckstein A M,Elad M.Dictionaries for sparse representation modeling[J].Proceedings of the IEEE,2010,98(6):1045-1057.
[30] Graham RL,Knuth D E,Patashnik O.Concrete Mathe-matics: A Foundation for Computer Science[M].Addison-Wesley Professional,Massachusetts,1994.
[31] Oldenburg D W,Scheuer T,Levy S.Recovery of the acoustic impedance from reflection seismograms[J].Geophysics,1983,48(10):1318-1337.
[32] White R E,O’Brien P.Estimation of the primary seismic pulse[J].Geophysical Prospecting,1974,22(4):627-651.
[33] Bednar J B.Applications of median filtering to deconvolution,pulse estimation,and statistical editing of seismic data[J].Geophysics,1983,48(2):1598-1610.
[34] Walden A,White R.Seismic wavelet estimation: A frequency domain solution to a geophysical noisy input-output problem[J].IEEE Transactions on Geoscience and Remote Sensing,1998,36(1):287-297.
[35] Sacchi M D,Ulrych T J.Nonminimum-phase wavelet estimation using higher order statistics[J].The Lea-ding Edge,2000,19(1):80-83.
[36] Misra S,Chopra S.Mixed-phase wavelet estimation:A case study[J].CSEG Recorder,2011,36(1):33-35.
[37] Danielsen V,Karlsson T V.Extraction of signatures from seismic and well data[J].First Break,1984,2(4):15-21.
[38] Lines L R,Treitel S.Wavelets,well logs and Wiener filters[J].First Break,1985,3(8):9-14.
[39] Zhang R,Castagna J.Seismic sparse-layer reflectivity inversion using basis pursuit decomposition[J].Geophysics,2011,76(6):R147-R158.
[40] Yuan S,Wang S.Spectral sparse Bayesian learning reflectivity inversion[J].Geophysical Prospecting,2013,61(4):735-746.
[41] Zhang R,Sen M K,Srinivasan S.A prestack basis pursuit seismic inversion[J].Geophysics,2013,78(1):R1-R11.
[42] 刘晓晶,印兴耀,吴国忱,等.基于基追踪弹性阻抗反演的深部储层流体识别方法[J].地球物理学报,2016,59(1):277-286.LIU Xiaojing,YIN Xingyao,WU Guochen,et al.Identification of deep reservoir fluids based on basis pursuit inversion for elastic impedance[J].Chinese Journal of Geophysics,2016,59(1):277-286.
[43] 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[J].石油地球物理勘探,2017,52(4):770-782.ZHANG Fengqi,JIN Zhijun,SHENG Xiujie,et al.AVA sparse layer inversion with the soft-low frequency constraint[J].Oil Geophysical Prospecting,2017,52(4):770-782.