稳健稀疏反褶积方法研究
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摘要
地震勘探数字信号处理领域中一个重要而基本的方法是地震信号的反褶积方法.在地震数据的采集过程中往往会遇到异常点的干扰,这种干扰严重影响了利用反褶积方法对真实反射系数与地震子波的重构效果.本文在Canadas等人提出的针对高斯噪声的贝叶斯反褶积数学框架的基础之上,提出一种能够克服异常点干扰的稳健稀疏反褶积方法.新方法针对具有重尾分布的异常点噪声与稀疏的反射系数建模,并使用交替迭代与线性规划的算法求解.最后,通过实验证明该方法在克服异常点噪声的基础上,能实现对地震子波与反射系数的同步估计,所得到的估计有效地消除了重尾分布异常点噪声的影响,提高了地震信号反褶积处理的精度.这也能证明所提算法是收敛的,并且模型是有效的.
A fundamental and important approach in the field of seismic signal processing is the deconvolution of seismic signals. However, seismic signal acquisition can be contaminated by outliers, and the outliers affect the performance of deconvolution results. In this paper, we follow the Bayesian deconvolution framework, which was proposed by Canadas, and propose a new robust sparse deconvolution method for overcoming the influence of outliers. The new approach properly models the heavy-tail outliers and sparse reflection coefficients simultaneously. For solving the approach, we derive a type of alternative algorithm. Finally, we demonstrate the performance of the algorithm by a series of simulations, which show that the new approach can eliminate the influence of heavy-tail outliers and recover the reflection coefficients. This further indicates the approach is valid and the algorithm is convergent.
A fundamental and important approach in the field of seismic signal processing is the deconvolution of seismic signals. However, seismic signal acquisition can be contaminated by outliers, and the outliers affect the performance of deconvolution results. In this paper, we follow the Bayesian deconvolution framework, which was proposed by Canadas, and propose a new robust sparse deconvolution method for overcoming the influence of outliers. The new approach properly models the heavy-tail outliers and sparse reflection coefficients simultaneously. For solving the approach, we derive a type of alternative algorithm. Finally, we demonstrate the performance of the algorithm by a series of simulations, which show that the new approach can eliminate the influence of heavy-tail outliers and recover the reflection coefficients. This further indicates the approach is valid and the algorithm is convergent.
引文
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[7]张繁昌,刘杰,印兴耀,等.修正柯西约束地震盲反褶积方法[J].石油地球物理勘探,2008,43(4):391-396Zhang F C,Liu J,Yin X Y,et al.Fixed seismic blind deconvolution method Cauchy constraints[J].Oil Geophysical Prospecting,2008,43(4):391-396
[8]刘喜武,宁俊瑞,张改兰.Cauchy稀疏约束Bayesian估计地震盲反褶积框架与算法研究[J].石油物探,2009,48(5):459-464Liu X W,Ning J R,Zhang G L.Cauchy sparse Bayesian estimation and algorithm constrained seismic blind deconvolution framework[J].Petroleum Exploration,2009,48(5):459-464
[9]Saggaf M M,Robinson E A.A unified framework for the deconvolution of traces of nonwhite reflectivity[J].Geophysics,2000,65(5):1660-1676
[10]Painter S,Beresford G,Paterson L.On the distribution of seismic reflection coefficients and seismic amplitudes[J].Geophysics,1995,60(4):1187-1194
[11]Walden A T,Hosken J J.The nature of the non-Gaussianity of primary reflection coefficients and its significance for deconvolution[J].Geophysical Prospecting,1986,34(7):1038-1066
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[15]Chang X Y,Xu Z B,Zhang H,et al.Robust regularization theory based on?q(0 [16]Tibshirani R J.Regression shrinkage and selection via the LASSO[J].Journal of the Royal Statistical Society,Series B(Statistical Methodology),1996,58(5):267-288
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[18]Tseng P.Convergence of a block coordinate descent method for nondifferentiable minimization[J].Journal of Optimization Theory and Applications,2001,109(3):475-494
[2]Wiener N E.Interpolation,and Smoothing of Stationary Time Series[M].New York:Wiley,1949
[3]Peacock K L,Treitel S.Predictive deconvolution:theory and practice[J].Geophysics,1969,34(2):155-169
[4]Mendel J M.Optimal Seismic Deconvolution:An Estimation-Based Approach[M].New York:Academic Press,1983
[5]Wiggins R A.Minimum entropy deconvolution[J].Geoexploration,1978,16(1):21-35
[6]Canadas G.A mathematical framework for blind deconvolution inverse problems[C]//Expanded Abstracts of the 72th Society of Exploration Geophysicists Annual Meeting,2002
[7]张繁昌,刘杰,印兴耀,等.修正柯西约束地震盲反褶积方法[J].石油地球物理勘探,2008,43(4):391-396Zhang F C,Liu J,Yin X Y,et al.Fixed seismic blind deconvolution method Cauchy constraints[J].Oil Geophysical Prospecting,2008,43(4):391-396
[8]刘喜武,宁俊瑞,张改兰.Cauchy稀疏约束Bayesian估计地震盲反褶积框架与算法研究[J].石油物探,2009,48(5):459-464Liu X W,Ning J R,Zhang G L.Cauchy sparse Bayesian estimation and algorithm constrained seismic blind deconvolution framework[J].Petroleum Exploration,2009,48(5):459-464
[9]Saggaf M M,Robinson E A.A unified framework for the deconvolution of traces of nonwhite reflectivity[J].Geophysics,2000,65(5):1660-1676
[10]Painter S,Beresford G,Paterson L.On the distribution of seismic reflection coefficients and seismic amplitudes[J].Geophysics,1995,60(4):1187-1194
[11]Walden A T,Hosken J J.The nature of the non-Gaussianity of primary reflection coefficients and its significance for deconvolution[J].Geophysical Prospecting,1986,34(7):1038-1066
[12]Tukey J W.Exploratory Data Analysis[M].New York:Wiley,1977
[13]Huber P J.Robust Statistics[M].Berlin Heidelberg:Springer,2011
[14]Wang H,Li G,Jiang G.Robust regression shrinkage and consistent variable selection through the ladLasso[J].Journal of Business and Economic Statistics,2007,25(6):347-355
[15]Chang X Y,Xu Z B,Zhang H,et al.Robust regularization theory based on?q(0
[17]Charnes A,Cooper W W,Ferguson O R.Optimal estimation of executive compensation by linear programming[J].Management Sciences,1955,1(2):138-151
[18]Tseng P.Convergence of a block coordinate descent method for nondifferentiable minimization[J].Journal of Optimization Theory and Applications,2001,109(3):475-494
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