基于Cauchy稀疏约束的同时迭代反演反射系数与地震子波的研究
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摘要
在二阶统计量实现地震反褶积基础上,作反射系数为高斯分布的随机序列、子波为最小相位的假设,并在稀疏反演中以Cauchy约束为准则,在规则化过程中,微妙的引入稀疏反褶积的原始问题,作预条件处理,采用预条件共轭梯度法迭代反演同时得到地震子波和反射系数序列。在具体方法实现中,以传统预测反褶积结果作为反射系数的迭代初始值,初始子波用稀疏约束反演方法得到。利用理论模型进行试算,表明该算法精度高、稳定、收敛速度快。
Based on the second order statistics of deconvolution, assuming Gaussian random sequence reflectivity and minimum phase wavelet,in sparse constraint inversion use Cauchy constraint as a criterion. The authors present a subtle construction of the problem prototype based upon the regularization strategy by introducing preconditional conditions and estimate the wavelet and reflectivity simultaneous by preconditional conjugate gradient algorithm. During the procedures, taking traditional predictive deconvolution result as initial reflectivity for iteration inversion and initial wavelet is obtained form Cauchy sparse constraint inversion algorithm. Theoretical model is applied to test the algorithm, the results show that the algorithm is correct and stability,it can also get the same results with real 2-D seismic data. Compared with the direct sparse simultaneous iteration inversion, the preconditional conjugate gradient algorithm is accurate, stable and fast converging speed.
Based on the second order statistics of deconvolution, assuming Gaussian random sequence reflectivity and minimum phase wavelet,in sparse constraint inversion use Cauchy constraint as a criterion. The authors present a subtle construction of the problem prototype based upon the regularization strategy by introducing preconditional conditions and estimate the wavelet and reflectivity simultaneous by preconditional conjugate gradient algorithm. During the procedures, taking traditional predictive deconvolution result as initial reflectivity for iteration inversion and initial wavelet is obtained form Cauchy sparse constraint inversion algorithm. Theoretical model is applied to test the algorithm, the results show that the algorithm is correct and stability,it can also get the same results with real 2-D seismic data. Compared with the direct sparse simultaneous iteration inversion, the preconditional conjugate gradient algorithm is accurate, stable and fast converging speed.
引文
[1]黄绪德.反褶积与地震道反演[M].北京:石油工业出版社,1992.
[2]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.
[3]Robinson E A,TreitelS.Geophysical Signal Analysis[M].PrenticeHall,Inc.1980.
[4]谢桂生,石玉梅,尹成.高阶统计量法子波估计与处理[J].石油物探,2000,39(4):19-25.
[5]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.
[6]刘喜武,刘洪,李幼铭.反射系数与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,2006,28(3):211-215.
[7]Claerbout J F.Fundamentals of Geophysical Data Process ing-With Application to Ptrolum Prospecting[M].New York:Blackwell Scientific Publication,1985.
[8]Baan M V.Time-varying Wavelete Estimation and Decon volution Inverse Problem[J].Expanded Abstracts of72nd Annual Internat SEG Mtg,2002(2):202-205.
[2]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.
[3]Robinson E A,TreitelS.Geophysical Signal Analysis[M].PrenticeHall,Inc.1980.
[4]谢桂生,石玉梅,尹成.高阶统计量法子波估计与处理[J].石油物探,2000,39(4):19-25.
[5]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.
[6]刘喜武,刘洪,李幼铭.反射系数与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,2006,28(3):211-215.
[7]Claerbout J F.Fundamentals of Geophysical Data Process ing-With Application to Ptrolum Prospecting[M].New York:Blackwell Scientific Publication,1985.
[8]Baan M V.Time-varying Wavelete Estimation and Decon volution Inverse Problem[J].Expanded Abstracts of72nd Annual Internat SEG Mtg,2002(2):202-205.
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