基于快速匹配追踪的混合域地震稀疏反演方法
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摘要
匹配追踪稀疏地震反演是基于模型参数L0范数稀疏性度量的高分辨率反射系数反演方法。针对经典匹配追踪反演策略抗噪能力强但计算效率低的问题,通过控制多原子迭代次数和迭代阈值搜索模型最优解,提出基于快速匹配追踪算法的混合域地震稀疏反演方法。首先,在相对纵波阻抗低频模型约束下,构建混合域褶积模型正演算子和正则化方程,低频背景的引入将有效缩小模型参数的搜索空间;然后,在多原子快速匹配追踪反演框架推导混合域稀疏反演目标泛函,提高地层反射系数的恢复效率和收敛精度;最后,利用数据测试及实际地震资料对该方法的预测精度和可靠性进行试验分析,该方法相比常规时间域反演有助于选择高信噪比的频率分量提高算法的抗噪能力,而且在改善反演分辨率的同时避免了匹配追踪算法存在的计算效率低和局部极值的问题。
Seismic inversion utilizing matching pursuit algorithm(FMP-SI) is one of the most effective sparse inversion methods with superior resolution by considering the sparse characteristic on model reflectivity.Considering the excellent antinoise property and the low computational efficiency of traditional matching pursuit algorithms,we proposed a novel mixed-domain sparse inversion utilizing the fast matching pursuit algorithm to improve the inversion efficiency.Sparse optimal solution of the subsurface reflectivity can be achieved by controlling the number of iterations and iteration s threshold.Firstly,the mixed-domain modeling operator and regularization equation are established by jointing the mixed-domain convolution with the low-frequency constraint,which can reduce the search space of model parameters effectively.In addition,the object function in the mixed-frequency domain can be deduced by a polyatomic fast matching pursuit algorithm.The recovery efficiency and convergence precision of model parameters can be improved.Finally,the feasibility and excellent stability are illustrated by several synthetic simulations and a field case.From the results,we conclude that the proposed method can achieve superior resolution and high anti-noise ability compared with the conventional time domain inversions.Furthermore,the problem of local extremum in single-atom matching pursuit algorithms can be avoided effectively.
Seismic inversion utilizing matching pursuit algorithm(FMP-SI) is one of the most effective sparse inversion methods with superior resolution by considering the sparse characteristic on model reflectivity.Considering the excellent antinoise property and the low computational efficiency of traditional matching pursuit algorithms,we proposed a novel mixed-domain sparse inversion utilizing the fast matching pursuit algorithm to improve the inversion efficiency.Sparse optimal solution of the subsurface reflectivity can be achieved by controlling the number of iterations and iteration s threshold.Firstly,the mixed-domain modeling operator and regularization equation are established by jointing the mixed-domain convolution with the low-frequency constraint,which can reduce the search space of model parameters effectively.In addition,the object function in the mixed-frequency domain can be deduced by a polyatomic fast matching pursuit algorithm.The recovery efficiency and convergence precision of model parameters can be improved.Finally,the feasibility and excellent stability are illustrated by several synthetic simulations and a field case.From the results,we conclude that the proposed method can achieve superior resolution and high anti-noise ability compared with the conventional time domain inversions.Furthermore,the problem of local extremum in single-atom matching pursuit algorithms can be avoided effectively.
引文
[1]李坤,印兴耀,宗兆云.利用平滑模型约束的频率域多尺度地震反演[J].石油地球物理勘探,2016,51(4):760-768.LI Kun,YIN Xingyao,ZONG Zhaoyun.Seismic multiscale inversion in the frequency domain based on smooth model constraint[J].Oil Geophysical Prospecting,2016,51(4):760-768.
[2]TARANTOLA A.Inverse problem theory and methods for model parameter estimation[J].Soc Ind Appl Math,2005,9(5):1597-1620.
[3]TIKHONOV A.Solution of incorrectly formulated problems and the regularization method[J].Sov Math Dokl,1963,5:1035-1038.
[4]ALEMIE W,SACCHI M.High-resolution three-term AVO inversion by means of a Trivariate Cauchy probability distribution[J].Geophysics,2011,76(3):R43-R55.
[5]ZONG Zhaoyun,YIN Xingyao,WU Guochen.Geofluid discrimination incorporating poroelasticity and seismic reflection inversion[J].Surveys in Geophysics,2015,36(5):659-681.
[6]YIN Xingyao,ZHANG Shixin.Bayesian inversion for effective pore-fluid bulk modulus based on fluid-matrix decoupled amplitude variation with offset approximation[J].Geophysics,2014,79(5):R221-R232.
[7]印兴耀,刘倩.致密储层各向异性地震岩石物理建模及应用[J].中国石油大学学报(自然科学版),2016,40(2):52-58.YIN Xingyao,LIU Qian.Anisotropic rock physics modeling of tight sandstone and applications[J].Journal of China University of Petroleun(Edition of Natural Science),2016,40(2):52-58.
[8]吴飞,范宜仁,邓少贵,等.储层岩石T2-G实验采集参数自动匹配技术研究[J].中国石油大学学报(自然科学版),2014,38(4):50-56.WU Fei,FAN Yiren,DENG Shaogui,et al.Automatic matching technology for determining acquisition parameters of formation rock T2-G experiment[J].Journal of China University of Petroleun(Edition of Natural Science),2014,38(4):50-56.
[9]NGUYEN T,CASTAGNA J.High resolution seismic reflectivity inversion[J].Journal of Seismic Exploration,2010,19(4):303-320.
[10]WANG Y.Seismic time-frequency spectral decomposition by matching pursuit[J].Geophysics,2006,72(1):V13-V20.
[11]WANG Y.Multichannel matching pursuit for seismic trace decomposition[J].Geophysics,2010,75(4):V61-V66.
[12]MALLAT S,ZHANG Z.Matching pursuits with timefrequency dictionaries[J].IEEE Transactions on Signal Processing,1993,41(12):3397-3415.
[13]张繁昌,李传辉,印兴耀.基于动态匹配子波库的地震数据快速匹配追踪[J].石油地球物理勘探,2010,45(5):667-673.ZHANG Fanchang,LI Chuanhui,YIN Xingyao.Seismic data fast matching pursuit based on dynamic matching wavelet library[J].Oil Geophysical Prospecting,2010,45(5):667-673.
[14]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 Fanchang,LI Chuanhui,YIN Xingyao.Delta fringe line recognition based on seismic matching pursuit instantaneous spectral characteristics[J].Oil Geophysical Prospecting,2012,47(1):82-88.
[15]李坤,印兴耀,宗兆云.基于匹配追踪谱分解的时频域FAVO流体识别方法[J].石油学报,2016,37(6):777-786.LI Kun,YIN Xingyao,ZONG Zhaoyun.Time frequency domain FAVO fluid discrimination method based on matching pursuit spectrum decomposition[J].Acta Petrolei Sinica,2016,37(6):777-786.
[16]OZBEK A,OZDEMIR A,VASSALLO M.Interpolation by matching pursuit[C/OL]//2009 SEG Annual Meeting,Houston City,October25-30,2009:SEG Technical Program Expanded Abstracts[2014-10-09].http://library.seg.org/doi/abs/10.1190/1.3255534.
[17]CHOI J,BYUN J,SEOL S J,et al.Wavelet based interpolation by matching pursuit and multicomponent streamer data[C/OL]//2014 SEG Annual Meeting,Denver City,October 26-31,2014:SEG Technical Program Expanded Abstracts[2015-12-10].http://library.seg.org/doi/abs/10.1190/segam2014-1492.1.
[18]SCHONEWILLE M,YAN Z,BAYLY M,et al.Matching pursuit Fourier interpolation using priors derived from a second data set[C/OL]//2013 SEG Annual Meeting,Houston City,September 22-27,2013:SEG Technical Program Expanded Abstracts[2016-02-08].http://library.seg.org/doi/abs/10.1190/segam2013-0956.1.
[19]VASSALLO M,OZBEK A J,OZDEMIR K,et al.Crossline wavefield reconstruction from multi-component streamer data:multichannel interpolation by matching pursuit[C/OL]//2010 SEG Annual Meeting,Denver City,October 17-28,2010:SEG Technical Program Expanded Abstracts[2015-05-10].http://library.seg.org/doi/abs/10.1190/1.3513597.
[20]WEN X,ZHANG B,PENNINGTON W,et al.Relative P-impedance estimation using a dipole-based matching pursuit decomposition strategy[J].Interpretation,2015,3(4):T197-T206.
[21]FENG F,LEI G,ZHANG Y,et al.Matching pursuit inversion modeling based on true depth calibration and its applications[C/OL]//2015 SEG Annual Meeting,New Orleans City,October 18-22,2015:SEG Technical Program Expanded Abstracts[2015-09-08].http://library.seg.org/doi/abs/10.1190/segam2015-5841552.1.
[22]RODRIGUEZ I,SACCHI M,GU Y.Continuous hypocenter and source mechanism inversion via a Greens function-based matching pursuit algorithm[J].The Leading Edge,2010,29(3):334-337.
[23]刘杰,张忠涛,刘道理,等.强反射背景下沉积体边界检测及流体识别方法[J].石油物探,2016,55(1):142-149.LIU Jie,ZHANG Zhongtao,LIU Daoli,et al.Sediment boundary identification and fluid detection for the seismic data with strong background reflections[J].Geophysical Prospecting for Petroleum,2016,55(1):142-149.
[24]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 Haishan,YANG Wuyang,TIAN Jun,et al.Coal seam strong reflection separation with matching pursuit[J].Oil Geophysical Prospecting,2014,49(5):866-870.
[25]朱博华,向雪梅,张卫华,等.匹配追踪强反射层分离方法及应用[J].石油物探,2016,55(2):280-287.ZHU Bohua,XIANG Xuemei,ZHANG Weihua,et al.Strong reflection horizons separation based on matching pursuit algorithm and its application[J].Geophysical Prospecting for Petroleum,2016,55(2):280-287.
[26]陈胜,欧阳永林,曾庆才,等.匹配追踪子波分解重构技术在气层检测中的应用[J].岩性油气藏,2014,26(6):111-114.CHEN Sheng,OUYANG Yonglin,ZENG Qingcai,et al.Application of matching pursuit wavelet decomposition and reconstruction technique to reservoir prediction and gas detection[J].Geophysical Prospecting for Petroleum,2014,26(6):111-114.
[27]赵天姿,宋炜,王尚旭.基于匹配追踪算法的时频滤波去噪方法[J].石油物探,2008,47(4):367-371.ZHAO Tianzi,SONG Wei,WANG Shangxu.Time-frequency filtering de-noise method based on matching pursuit algorithm[J].Geophysical Prospecting for Petroleum,2008,47(4):367-371.
[28]HU H,LIU Y,OSEN A,et al.Compression of local slant stacks by the estimation of multiple local slopes and the matching pursuit decomposition[J].Geophysics,2015,80(6):WD175-WD187.
[29]WANG B,PANN K.Kirchhoff migration of seismic data compressed by matching pursuit decomposition[C/OL]//1996 SEG Annual Meeting,Denver City,November 10-15,1996:SEG Technical Program Expanded Abstracts[2014-03-18].http://library.seg.org/doi/abs/10.1190/1.1826441.
[30]MARGRAVE G.Theory of nonstationary linear filtering in the Fourier domain with application to time-variant filtering[J].Geophysics,1998,63(1):244-259.
[31]YIN Xingyao,LI Kun,ZONG Zhaoyun.Resolution enhancement of robust Bayesian pre-stack inversion in the frequency domain[J].Journal of Geophysics and Engineering,2016,13(5):646-656.
[2]TARANTOLA A.Inverse problem theory and methods for model parameter estimation[J].Soc Ind Appl Math,2005,9(5):1597-1620.
[3]TIKHONOV A.Solution of incorrectly formulated problems and the regularization method[J].Sov Math Dokl,1963,5:1035-1038.
[4]ALEMIE W,SACCHI M.High-resolution three-term AVO inversion by means of a Trivariate Cauchy probability distribution[J].Geophysics,2011,76(3):R43-R55.
[5]ZONG Zhaoyun,YIN Xingyao,WU Guochen.Geofluid discrimination incorporating poroelasticity and seismic reflection inversion[J].Surveys in Geophysics,2015,36(5):659-681.
[6]YIN Xingyao,ZHANG Shixin.Bayesian inversion for effective pore-fluid bulk modulus based on fluid-matrix decoupled amplitude variation with offset approximation[J].Geophysics,2014,79(5):R221-R232.
[7]印兴耀,刘倩.致密储层各向异性地震岩石物理建模及应用[J].中国石油大学学报(自然科学版),2016,40(2):52-58.YIN Xingyao,LIU Qian.Anisotropic rock physics modeling of tight sandstone and applications[J].Journal of China University of Petroleun(Edition of Natural Science),2016,40(2):52-58.
[8]吴飞,范宜仁,邓少贵,等.储层岩石T2-G实验采集参数自动匹配技术研究[J].中国石油大学学报(自然科学版),2014,38(4):50-56.WU Fei,FAN Yiren,DENG Shaogui,et al.Automatic matching technology for determining acquisition parameters of formation rock T2-G experiment[J].Journal of China University of Petroleun(Edition of Natural Science),2014,38(4):50-56.
[9]NGUYEN T,CASTAGNA J.High resolution seismic reflectivity inversion[J].Journal of Seismic Exploration,2010,19(4):303-320.
[10]WANG Y.Seismic time-frequency spectral decomposition by matching pursuit[J].Geophysics,2006,72(1):V13-V20.
[11]WANG Y.Multichannel matching pursuit for seismic trace decomposition[J].Geophysics,2010,75(4):V61-V66.
[12]MALLAT S,ZHANG Z.Matching pursuits with timefrequency dictionaries[J].IEEE Transactions on Signal Processing,1993,41(12):3397-3415.
[13]张繁昌,李传辉,印兴耀.基于动态匹配子波库的地震数据快速匹配追踪[J].石油地球物理勘探,2010,45(5):667-673.ZHANG Fanchang,LI Chuanhui,YIN Xingyao.Seismic data fast matching pursuit based on dynamic matching wavelet library[J].Oil Geophysical Prospecting,2010,45(5):667-673.
[14]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 Fanchang,LI Chuanhui,YIN Xingyao.Delta fringe line recognition based on seismic matching pursuit instantaneous spectral characteristics[J].Oil Geophysical Prospecting,2012,47(1):82-88.
[15]李坤,印兴耀,宗兆云.基于匹配追踪谱分解的时频域FAVO流体识别方法[J].石油学报,2016,37(6):777-786.LI Kun,YIN Xingyao,ZONG Zhaoyun.Time frequency domain FAVO fluid discrimination method based on matching pursuit spectrum decomposition[J].Acta Petrolei Sinica,2016,37(6):777-786.
[16]OZBEK A,OZDEMIR A,VASSALLO M.Interpolation by matching pursuit[C/OL]//2009 SEG Annual Meeting,Houston City,October25-30,2009:SEG Technical Program Expanded Abstracts[2014-10-09].http://library.seg.org/doi/abs/10.1190/1.3255534.
[17]CHOI J,BYUN J,SEOL S J,et al.Wavelet based interpolation by matching pursuit and multicomponent streamer data[C/OL]//2014 SEG Annual Meeting,Denver City,October 26-31,2014:SEG Technical Program Expanded Abstracts[2015-12-10].http://library.seg.org/doi/abs/10.1190/segam2014-1492.1.
[18]SCHONEWILLE M,YAN Z,BAYLY M,et al.Matching pursuit Fourier interpolation using priors derived from a second data set[C/OL]//2013 SEG Annual Meeting,Houston City,September 22-27,2013:SEG Technical Program Expanded Abstracts[2016-02-08].http://library.seg.org/doi/abs/10.1190/segam2013-0956.1.
[19]VASSALLO M,OZBEK A J,OZDEMIR K,et al.Crossline wavefield reconstruction from multi-component streamer data:multichannel interpolation by matching pursuit[C/OL]//2010 SEG Annual Meeting,Denver City,October 17-28,2010:SEG Technical Program Expanded Abstracts[2015-05-10].http://library.seg.org/doi/abs/10.1190/1.3513597.
[20]WEN X,ZHANG B,PENNINGTON W,et al.Relative P-impedance estimation using a dipole-based matching pursuit decomposition strategy[J].Interpretation,2015,3(4):T197-T206.
[21]FENG F,LEI G,ZHANG Y,et al.Matching pursuit inversion modeling based on true depth calibration and its applications[C/OL]//2015 SEG Annual Meeting,New Orleans City,October 18-22,2015:SEG Technical Program Expanded Abstracts[2015-09-08].http://library.seg.org/doi/abs/10.1190/segam2015-5841552.1.
[22]RODRIGUEZ I,SACCHI M,GU Y.Continuous hypocenter and source mechanism inversion via a Greens function-based matching pursuit algorithm[J].The Leading Edge,2010,29(3):334-337.
[23]刘杰,张忠涛,刘道理,等.强反射背景下沉积体边界检测及流体识别方法[J].石油物探,2016,55(1):142-149.LIU Jie,ZHANG Zhongtao,LIU Daoli,et al.Sediment boundary identification and fluid detection for the seismic data with strong background reflections[J].Geophysical Prospecting for Petroleum,2016,55(1):142-149.
[24]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 Haishan,YANG Wuyang,TIAN Jun,et al.Coal seam strong reflection separation with matching pursuit[J].Oil Geophysical Prospecting,2014,49(5):866-870.
[25]朱博华,向雪梅,张卫华,等.匹配追踪强反射层分离方法及应用[J].石油物探,2016,55(2):280-287.ZHU Bohua,XIANG Xuemei,ZHANG Weihua,et al.Strong reflection horizons separation based on matching pursuit algorithm and its application[J].Geophysical Prospecting for Petroleum,2016,55(2):280-287.
[26]陈胜,欧阳永林,曾庆才,等.匹配追踪子波分解重构技术在气层检测中的应用[J].岩性油气藏,2014,26(6):111-114.CHEN Sheng,OUYANG Yonglin,ZENG Qingcai,et al.Application of matching pursuit wavelet decomposition and reconstruction technique to reservoir prediction and gas detection[J].Geophysical Prospecting for Petroleum,2014,26(6):111-114.
[27]赵天姿,宋炜,王尚旭.基于匹配追踪算法的时频滤波去噪方法[J].石油物探,2008,47(4):367-371.ZHAO Tianzi,SONG Wei,WANG Shangxu.Time-frequency filtering de-noise method based on matching pursuit algorithm[J].Geophysical Prospecting for Petroleum,2008,47(4):367-371.
[28]HU H,LIU Y,OSEN A,et al.Compression of local slant stacks by the estimation of multiple local slopes and the matching pursuit decomposition[J].Geophysics,2015,80(6):WD175-WD187.
[29]WANG B,PANN K.Kirchhoff migration of seismic data compressed by matching pursuit decomposition[C/OL]//1996 SEG Annual Meeting,Denver City,November 10-15,1996:SEG Technical Program Expanded Abstracts[2014-03-18].http://library.seg.org/doi/abs/10.1190/1.1826441.
[30]MARGRAVE G.Theory of nonstationary linear filtering in the Fourier domain with application to time-variant filtering[J].Geophysics,1998,63(1):244-259.
[31]YIN Xingyao,LI Kun,ZONG Zhaoyun.Resolution enhancement of robust Bayesian pre-stack inversion in the frequency domain[J].Journal of Geophysics and Engineering,2016,13(5):646-656.