一种基于L_1-L_1范数稀疏表示的地震反演方法
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摘要
高分辨率地震反演面临着:①地震反演是一个不适定问题,存在多解性;②采集和处理流程产生噪声和畸变降低反演算法的稳定性,针对这两个问题,提出一种基于L_1-L_1范数稀疏表示的地震反射系数反演方法。该方法利用L_1范数正则化项降低反演多解性和L_1范数拟合项增加噪声鲁棒性。通过井震联合提取子波构建过完备楔形子波字典,然后用L_1-L_1范数稀疏表示对地震信号进行稀疏分解,实现高分辨率反射系数反演。楔形模型和实际地震资料试算结果表明,该反演算法稳定,具有良好的噪声鲁棒性,通过测井资料标定检验,其反演结果准确可信。
High-resolution seismic inversion is confronted with two problems: First,seismic inversion is an ill-posed problem and has multiplicity of solutions,and second,noise and distortion are generated in the flows of acquisition and processing to reduce the stability of the inversion algorithm.Aimed at solving these two problems,this paper proposes an inversion method of seismic reflectivity based on L_1-L_1-norm sparse representation.Firstly,the L_1-norm regularization term is used to reduce the inversion multiplicity,and then the L_1-norm fitting term is used to enhance the noise robustness.The wavelet is extracted by well logging and seismic data to construct the over-complete wedge wavelet dictionary,and then the seismic signal is sparsely decomposed by the L_1-L_1-norm sparse representation,so as to realize the high-resolution reflectivity inversion.The experimental results of wedge model and actual seismic data show that the inversion algorithm is stable and has good noise robustness,and the inversion results are accurate and credible through logging data calibration.
High-resolution seismic inversion is confronted with two problems: First,seismic inversion is an ill-posed problem and has multiplicity of solutions,and second,noise and distortion are generated in the flows of acquisition and processing to reduce the stability of the inversion algorithm.Aimed at solving these two problems,this paper proposes an inversion method of seismic reflectivity based on L_1-L_1-norm sparse representation.Firstly,the L_1-norm regularization term is used to reduce the inversion multiplicity,and then the L_1-norm fitting term is used to enhance the noise robustness.The wavelet is extracted by well logging and seismic data to construct the over-complete wedge wavelet dictionary,and then the seismic signal is sparsely decomposed by the L_1-L_1-norm sparse representation,so as to realize the high-resolution reflectivity inversion.The experimental results of wedge model and actual seismic data show that the inversion algorithm is stable and has good noise robustness,and the inversion results are accurate and credible through logging data calibration.
引文
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[28]Zhou H.Practical seismic data processing[M].Cambridge University Press,2014.
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[30]Gabay D,Mercier B.A dual algorithm for the solution of nonlinear variational problems via finite element approximation[J].Computers&Mathematics with Applications,1976,2(1):17-40.
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[32]He B,Yuan X.On the O(1/n)convergence rate of the douglasrachford alternating direction method[J].Siam Journal on Numerical Analysis,2012,50(2):700-709.
[33]Chung H,Lawton D C.Frequency characteristics of seismic reflections from thin beds[J].Canadian Journal of Exploration Geophysics,1995,31(1):8-32.
[2]Kallweit R S.The limits of resolution zero-phase wavelets[J].Geophysics,1982,47(7):1035-1046.
[3]Voogd N D,Rooijen H D.Thin-layer response and spectral bandwidth[J].Geophysics,1983,48(1):12-18.
[4]Chung H M,Lawton D C.Amplitude responses of thin beds;sinusoidal approximation versus Ricker approximation[J].Geophysics,1995,60(1):223-230.
[5]Van Riel P.Resolution in seismic trace inversion by parameter estimation[J].Geophysics,1985,50(9):1440-1455.
[6]Russell B H.Introduction to Seismic Inversion Methods[M].Society of Exploration Geophysicists,1988.
[7]Schuster G T.Seismic Inversion[M].Society of Exploration Geophysicists,2017.
[8]Partyka G.Interpretational applications of spectral decomposition in reservoir characterization[J].Leading Edge,1999,18(3):173-184.
[9]Marfurt K J,Kirlin R L.Narrow-band spectral analysis and thinbed tuning[J].Geophysics,2001,66(4):1274-1283.
[10]Puryear C I,Castagna J P.An algorithm for calculation of bed thickness and reflection coefficients from amplitude spectrum[J].SEG Technical Program Expanded Abstracts,2006:1767-1770.
[11]Puryear C I,Castagna J P.Layer-thickness determination and stratigraphic interpretation using spectral inversion:Theory and application[J].Geophysics,2008,73(2):R37-R48.
[12]Puryear C I,Portniaguine O N,Cobos C M,et al.Constrained leastsquares spectral analysis:Application to seismic data[J].Geophysics,2012,77(5):V143-V167.
[13]Nguyen T,Castagna J.High-resolution reflectivity inversion[J].Journal of Seismic Exploration,2010,19(4):303-320.
[14]Zhang R,Castagna J.Seismic sparse-layer reflectivity inversion using basis pursuit decomposition[J].Geophysics,2011,76(6):R147-R158.
[15]Mallat S G,Zhang Z.Matching pursuits with time-frequency dictionaries[J].IEEE Transactions on Signal Processing,1993,41(12):3397-3415.
[16]Chen S S,Donoho D L,Saunders M A.Atomic decomposition by basis pursuit[J].Siam Review,2001,43(1):129-159.
[17]Beck A,Teboulle M.A fast iterative Shrinkage-Thresholding algorithm for linear inverse problems[J].Siam Journal on Imaging Sciences,2009,2(1):183-202.
[18]Becker S,Bobin J,Candès E J.NESTA:A fast and accurate first-order method for sparse recovery[J].Siam Journal on Imaging Sciences,2009,4(1):1-39.
[19]Zhang Z.Integrating globality and locality for robust representation based classification[J].Mathematical Problems in Engineering,2014,2014:1-10.
[20]Tropp J A,Gilbert A C,Strauss M J.Algorithms for simultaneous sparse approximation.Part I:Greedy pursuit[J].Signal Processing,2006,86(3):572-588.
[21]Tropp J A.Algorithms for simultaneous sparse approximation:part II:Convex relaxation[J].Signal Processing,2006,86(3):589-602.
[22]Zhang Z,Xu Y,Yang J,et al.A survey of sparse representation:algorithms and applications[J].IEEE Access,2017,3:490-530.
[23]Fuchs J J.Fast implementation of a l1-l1regularized sparse representations algorithm[C]//IEEE International Conference on A-coustics,Speech and Signal Processing IEEE,2009:3329-3332.
[24]Yang J,Zhang Y.Alternating direction algorithms for l1-problems in compressive sensing[J].Siam Journal on Scientific Computing,2009,33(1):250-278.
[25]Claerbout J F,Muir F.Robust modeling with erratic data[J].Geophysics,1973,38(5):826-844.
[26]Morozov I B.Geometrical attenuation,frequency dependence of Q,and the absorption band problem[J].Geophysical Journal International,2008,175(1):239-252.
[27]Cheng H X,Kennett B L N.Frequency dependence of seismic wave attenuation in the upper mantle beneath the Australian region[J].Geophysical Journal International,2010,150(1):45-57.
[28]Zhou H.Practical seismic data processing[M].Cambridge University Press,2014.
[29]Zhang F,Dai R,Liu H.Seismic inversion based on L1-norm misfit function and total variation regularization[J].Journal of Applied Geophysics,2014,109:111-118.
[30]Gabay D,Mercier B.A dual algorithm for the solution of nonlinear variational problems via finite element approximation[J].Computers&Mathematics with Applications,1976,2(1):17-40.
[31]Boyd S,Parikh N,Chu E,et al.Distributed optimization and statistical learning via the alternating direction method of multipliers[J].Foundations&Trends in Machine Learning,2011,3(1):1-122.
[32]He B,Yuan X.On the O(1/n)convergence rate of the douglasrachford alternating direction method[J].Siam Journal on Numerical Analysis,2012,50(2):700-709.
[33]Chung H,Lawton D C.Frequency characteristics of seismic reflections from thin beds[J].Canadian Journal of Exploration Geophysics,1995,31(1):8-32.
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