Prestack data attenuation compensation based on L1-norm regularization constraint
CHENG Wanli1,2,3, WANG Shoudong1,2,3, MENG Jinyu4, WANG Zixu1,2,3, ZHANG Junjie1,2,3
1. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum(Beijing), Beijing 102249, China; 2. CNPC Key Laboratory of Geophysical Exploration, China University of Petroleum(Beijing), Beijing 102249, China; 3. National Engineering Laboratory for Offshore Oil Exploration, China University of Petroleum(Beijing), Beijing 102249, China; 4. State Key Laboratory of Marine Geology, Tongji University, Shanghai 200092, China
Abstract:Due to the absorption of the subsurface medium, seismic waves experience energy attenuation, waveform distortion, and frequency band narrowing during propagation, which severely reduces the resolution of seismic data. Meanwhile, the absorption effect of formations changes with the propagation path for prestack seismic wave, which distorts the amplitude variation with angle (AVA) reflection characteristics of the seismic data. Therefore, this paper considers the influence of the ray path on the attenuation compensation and proposes an attenuation compensation method for prestack data. Firstly, the forward modeling formula of prestack gathers in the attenuation medium is deduced on the assumption of a horizontally stratified medium. Then, the attenuation compensation is simplified to an inverse problem, and the L1-norm regularization constraint is imposed. Finally, the optimal solution is obtained by the alternating direction method of multipliers (ADMM) to achieve the attenua-tion compensation for prestack data. Numerical tests show that the proposed method can compensate for the amplitude and phase and recover the AVA reflection characteristics of prestack gathers. The comparison with the poststack compensation and the conventional prestack inverse-Q filtering method shows that the proposed method has higher precision, stronger stability, and more remarkable noise immunity. The Q-sensitivity analysis experiments illustrate that the method can also maintain high compensation precision with the help of the low-frequency Q model, and it is insensitive to the Q model. The processing results of measured data also reveal that the proposed method can improve the resolution of prestack gathers and effectively restore their AVA reflection characteristics, which provides a basis for high-precision prestack seismic inversion.
FUTTERMAN W I.Dispersive body waves[J].Journal of Geophysical Research,1962,67(13):5279-5291.
[2]
HALE D.An inverse Q-filter[J].Stanford Exploration Project,1981,28(1):289-298.
[3]
白桦,李鲲鹏.基于时频分析的地层吸收补偿[J].石油地球物理勘探,1999,34(6):642-648.BAI Hua,LI Kunpeng.Stratigraphic absorption compensation based on time-frequency analysis[J].Oil Geophysical Prospecting,1999,34(6):642-648.
[4]
WANG Y.A stable and efficient approach of inverse Q filtering[J].Geophysics,2002,67(2):657-663.
[5]
WANG Y.Inverse Q-filter for seismic resolution enhancement[J].Geophysics,2006,71(3):V51-V60.
[6]
严红勇,刘洋,赵前华,等.一种提高VSP分辨率的反Q滤波方法[J].石油地球物理勘探,2011,46(6):873-880.YAN Hongyong,LIU Yang,ZHAO Qianhua,et al.A method for improving VSP resolution by inverse Q filtering[J].Oil Geophysical Prospecting,2011,46(6):873-880.
[7]
ZHANG C,ULRYCH T J.Seismic absorption compensation:a least squares inverse scheme[J].Geophysics,2007,72(6):R109-R114.
[8]
WANG S.Attenuation compensation method based on inversion[J].Applied Geophysics,2011,8(2):150-157.
[9]
WANG S,SONG H,YANG D.Seismic attenuation compensation by Bayesian inversion[J].Journal of Applied Geophysics,2014,111:356-363.
[10]
WANG S,CHEN X.Absorption-compensation me-thod by l1-norm regularization[J].Geophysics,2014,79(3):V107-V114.
[11]
王本锋,陈小宏,李景叶,等.基于反演的稳定高效衰减补偿方法[J].地球物理学报,2014,57(4):1265-1274.WANG Benfeng,CHEN Xiaohong,LI Jingye,et al.A stable and efficient attenuation compensation method based on inversion[J].Chinese Journal of Geophy-sics,2014,57(4):1265-1274.
[12]
MA X,LI G,LI H,et al.Multichannel absorption compensation with a data-driven structural regularization[J].Geophysics,2020,85(1):V71-V80.
[13]
刘金涛,王孝,王小卫,等.全局约束反演多道吸收补偿方法[J].石油地球物理勘探,2021,56(2):273-282.LIU Jintao,WANG Xiao,WANG Xiaowei,et al.Multi-channel absorption compensation method based on global constrained inversion[J].Oil Geophysical Prospecting,2021,56(2):273-282.
[14]
LAZARATOS S,FINN C.Deterministic spectral ba-lancing for high-fidelity AVO[C].SEG Technical Program Expanded Abstracts,2004,23:219-223.
[15]
任浩然,王华忠,张立彬.沿射线路径的波动方程延拓吸收与衰减补偿方法[J].石油物探,2007,46(6):557-561.REN Haoran,WANG Huazhong,ZHANG Libin.Compensation for absorption and attenuation using wave equation continuation along ray path[J].Geophysical Prospecting for Petroleum,2007,46(6):557-561.
[16]
BANSAL R,KHARE V,JENKINSON T,et al.Correction for NMO stretch and differential attenuation in converted-wave data:a key enabling technology for prestack joint inversion of PP and PS data[J].The Leading Edge,2009,28(10):1182-1190.
[17]
YAN H,LIU Y.Estimation of Q and inverse Q filtering for prestack reflected PP- and converted PS-waves[J].Applied Geophysics,2009,6(1):59-69.
[18]
李国发,张小明,彭更新,等.与炮检距有关的地层吸收对AVO分析的影响及其补偿方法[J].石油地球物理勘探,2014,49(1):89-94.LI Guofa,ZHANG Xiaoming,PENG Gengxin,et al.Influence of offset-related absorption on AVO analysis and its compensation[J].Oil Geophysical Prospecting,2014,49(1):89-94.
[19]
CHAI X,WANG S,WEI X,et al.High resolution prestack nonstationary AVA inversion:Part 1-Theory[C].SEG Technical Program Expanded Abstracts,2014,33:553-558.
[20]
张生强,张志军,郭军,等.时频空间域低频约束AVO响应校正方法[J].石油地球物理勘探,2021,56(1):137-145.ZHANG Shengqiang,ZHANG Zhijun,GUO Jun,et al.AVO response correction constrained by low-frequency components in time-frequency-space domain[J].Oil Geophysical Prospecting,2021,56(1):137-145.
[21]
LI G,LIU Y,ZHENG H,et al.Absorption decomposition and compensation via a two-step scheme[J].Geophysics,2015,80(6):V145-V155.
[22]
AHARCHAOU M,NEUMANN E.Prestack Q compensation with sparse tau-p operators[J].Geophy-sics,2019,84(5):V295-V305.
[23]
CHENG W,WANG S,ZHOU C,et al.Prestack data attenuation compensation based on inversion[C].82nd EAGE Annual Conference & Exhibition,2021,1-5.
[24]
BOYD S,PARIKH N,CHU E,et al.Distributed optimization and statistical learning via the alternating direction method of multipliers[J].Foundations and Trends in Machine Learning,2011,3(1):1-122.
[25]
MARGRAVE G F.Theory of nonstationary linear filtering in the Fourier domain with application to time-variant filtering[J].Geophysics,1998,63(1):244-259.
[26]
CHENG W,WANG S,ZHOU C,et al.Q estimation based on the logarithmic spectral area double diffe-rence[J].Geophysics,2022,87(2):V155-V167.
[27]
LINES L R,ULRYCH T J.The old and the new in seismic deconvolution and wavelet estimation[J].Geo-physical Prospecting,1977,25(3):512-540.
[28]
LAZEAR G D.Mixed-phase wavelet estimation using fourth-order cumulants[J].Geophysics,1993,58(7):1042-1051.