Cauchy稀疏约束Bayesian估计地震盲反褶积框架与算法研究
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摘要
以二阶统计学方法为基础,从Canadas等提出的非最小相位子波和非白噪反射系数地震盲反褶积框架出发,给出了Cauchy稀疏约束Bayesian估计地震盲反褶积框架。基于反射系数与子波相互独立(或弱相关)的假设,分别构建了反射系数和子波最优估计方程,并采用预条件共轭梯度法迭代反演实现反射系数和子波的同时估计。在方法具体实现时,以传统脉冲反褶积结果作为迭代初值,通过迭代得到反射系数和任意相位子波;然后再对子波进行最小相位化,通过反演得到反子波;最后将反子波与地震道褶积,得到反褶积结果。利用理论模型和实际数据对算法进行了试算,结果表明,给出的地震盲反褶积理论框架是正确的;与直接(共轭梯度求解正则方程)稀疏同时迭代反演法的对比显示,预条件共轭梯度算法稳定,精度高,收敛快。
Based on second order statistics,starting from the seismic blind deconvolution frame proposed by Canadas for non-minimum phase wavelet and non-white reflectivity,the Cauchy sparseness constrained Bayesian estimation based seismic blind deconvolution frame was proposed.Assuming the independence(or the weak-correlation) between the reflectivity and wavelet,the optimal estimation equations for the wavelet and reflectivity were derived respectively. Furthermore,pre-conditional conjugate gradient algorithm iteration inversion was applied to realize the simultaneous estima- tion of reflectivity and wavelet.During the procedures,taking traditional impulse devonvolution result as initials for iteration inversion, the reflectivity and wavelet with arbitrary phase was obtained from iteration.Then,the minimum phase of wavelet was achieved, and reversed wavelet was obtained by inversion.Finally,reversed wavelet was carried out convolution with seismic traces to get deconvolution results.Theoretical model and real 2-D seismic data were applied to test the algorithm.The results show that the proposed deconvolution theoretical frame is correct.Compared the above method to direct sparse simultaneous iteration inversion(solving canonical equation by conjugate gradient),the results indicate that pre-conditional conjugate gradient algorithm is stable,with high accuracy and fast converging speed.
Based on second order statistics,starting from the seismic blind deconvolution frame proposed by Canadas for non-minimum phase wavelet and non-white reflectivity,the Cauchy sparseness constrained Bayesian estimation based seismic blind deconvolution frame was proposed.Assuming the independence(or the weak-correlation) between the reflectivity and wavelet,the optimal estimation equations for the wavelet and reflectivity were derived respectively. Furthermore,pre-conditional conjugate gradient algorithm iteration inversion was applied to realize the simultaneous estima- tion of reflectivity and wavelet.During the procedures,taking traditional impulse devonvolution result as initials for iteration inversion, the reflectivity and wavelet with arbitrary phase was obtained from iteration.Then,the minimum phase of wavelet was achieved, and reversed wavelet was obtained by inversion.Finally,reversed wavelet was carried out convolution with seismic traces to get deconvolution results.Theoretical model and real 2-D seismic data were applied to test the algorithm.The results show that the proposed deconvolution theoretical frame is correct.Compared the above method to direct sparse simultaneous iteration inversion(solving canonical equation by conjugate gradient),the results indicate that pre-conditional conjugate gradient algorithm is stable,with high accuracy and fast converging speed.
引文
1刘喜武,刘洪.地震盲反褶积综述[J].地球物理学进展,2003,18(2):203-209
2李春峰.从多尺度反射系数的角度评估反褶积模型的适用性[J].勘探地球物理进展,2005,28(4):250-257
3刘喜武,刘洪.实现稀疏反褶积的预条件共轭梯度法[J].物探化探计算技术,2003,18(3):215-219
4刘喜武,刘洪,李幼铭.反射系数和子波同时迭代反演的预条件共轭梯度法[J].物探化探计算技术,2006,21 (3):211-215
5孟小红,吴何珍,刘国峰.盲源反褶积方法与应用研究[J].石油地球物理勘探,2005,40(6):642-645
6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):391-396
7曾锐,刘洪,陈世军,等.柯西约束盲反褶积技术在井间地震的应用[J].地球物理学进展,2004,19(1):66- 172
8朱振宇,刘洪,李幼铭,等.基于预条件共轭梯度法的盲反褶积方法[J].勘探地球物理进展,2004,27(3): 174-176
9印兴耀,刘杰,杨培杰.一种基于负熵的Bussgang地震盲反褶积方法[J].石油地球物理勘探,2007,42(5): 499-505
10刘喜武,高伟,张宁,等.基于带状混合矩阵ICA实现地震盲反褶积[J].地球物理学进展,2007,22(3): 1 153-1 163
11刘财,谢金娥,郭全仕,等.一种基于自然梯度的地震盲反褶积方法[J].石油物探,2008,47(5):439-443
12彭春翌,朱孝龙,张贤达.基于斜投影的卷积信道盲信号分离[J].清华大学学报(自然科学版),2005,45(4): 517-520
13 Baan M V,Pham D T.Robust wavelet estimation and blind deconvolution of noisy surface seismics[J].Geophysics, 2008,73(5):V37 - V46
14 Baan M V.Time-varying wavelet estimation and deconvolution by kurtosis maximization[J].Geophysics, 2008,73(2):V11-V18
15 Guy C.A mathematical framework for blind deconvolution inverse problem[J].Expanded Abstracts of 72~(nd) Annual Internat SEG Mtg,2002,2 202-2 205
2李春峰.从多尺度反射系数的角度评估反褶积模型的适用性[J].勘探地球物理进展,2005,28(4):250-257
3刘喜武,刘洪.实现稀疏反褶积的预条件共轭梯度法[J].物探化探计算技术,2003,18(3):215-219
4刘喜武,刘洪,李幼铭.反射系数和子波同时迭代反演的预条件共轭梯度法[J].物探化探计算技术,2006,21 (3):211-215
5孟小红,吴何珍,刘国峰.盲源反褶积方法与应用研究[J].石油地球物理勘探,2005,40(6):642-645
6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):391-396
7曾锐,刘洪,陈世军,等.柯西约束盲反褶积技术在井间地震的应用[J].地球物理学进展,2004,19(1):66- 172
8朱振宇,刘洪,李幼铭,等.基于预条件共轭梯度法的盲反褶积方法[J].勘探地球物理进展,2004,27(3): 174-176
9印兴耀,刘杰,杨培杰.一种基于负熵的Bussgang地震盲反褶积方法[J].石油地球物理勘探,2007,42(5): 499-505
10刘喜武,高伟,张宁,等.基于带状混合矩阵ICA实现地震盲反褶积[J].地球物理学进展,2007,22(3): 1 153-1 163
11刘财,谢金娥,郭全仕,等.一种基于自然梯度的地震盲反褶积方法[J].石油物探,2008,47(5):439-443
12彭春翌,朱孝龙,张贤达.基于斜投影的卷积信道盲信号分离[J].清华大学学报(自然科学版),2005,45(4): 517-520
13 Baan M V,Pham D T.Robust wavelet estimation and blind deconvolution of noisy surface seismics[J].Geophysics, 2008,73(5):V37 - V46
14 Baan M V.Time-varying wavelet estimation and deconvolution by kurtosis maximization[J].Geophysics, 2008,73(2):V11-V18
15 Guy C.A mathematical framework for blind deconvolution inverse problem[J].Expanded Abstracts of 72~(nd) Annual Internat SEG Mtg,2002,2 202-2 205
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