基于贝叶斯理论的薄层反演方法
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摘要
大量实验表明,地球物理数据符合或近似符合高斯分布,因此可将高斯分布和贝叶斯原理结合并应用于地球物理反演。本文在无噪假设条件下推导出具有明确物理意义的迭代反演算法,基于贝叶斯原理重新推导了迭代反演公式。经3层和12层砂泥岩互层层状介质模型试算与实际应用,其结果均表明,将基于贝叶斯理论的波阻抗反演算法与多道反演思路相结合,具有反演精度高和稳定性好的特点,可明显降低噪声影响,而且运算简单,可有效识别薄层。
Numerous tests indicate that geophysical data conform to or approximately conform to Gaussian distribution,so it is feasible to combine Gaussian distribution with Bayes theory and apply to geophysical inversion.An iterative inversion algorithm with definite physical significance is derived on the assumption of no noise,and an iterative inversion formula is newly derived based on Bayes theory in this paper.Through test results of 3-layer and 12-layer sand shale interbed models with layered medium and actual applied results,it is found that combining wave impedance inversion algorithm based on Bayes theory with multi-trace inversion idea has features of high precision and improved stability,and that influence of noise can be reduced obviously.The calculation is simple and thin beds can be identified effectively based on inversion results.
Numerous tests indicate that geophysical data conform to or approximately conform to Gaussian distribution,so it is feasible to combine Gaussian distribution with Bayes theory and apply to geophysical inversion.An iterative inversion algorithm with definite physical significance is derived on the assumption of no noise,and an iterative inversion formula is newly derived based on Bayes theory in this paper.Through test results of 3-layer and 12-layer sand shale interbed models with layered medium and actual applied results,it is found that combining wave impedance inversion algorithm based on Bayes theory with multi-trace inversion idea has features of high precision and improved stability,and that influence of noise can be reduced obviously.The calculation is simple and thin beds can be identified effectively based on inversion results.
引文
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[9]胡光岷,贺振华,黄德济.广义非线性反演及其应用.石油物探,2000,39(2):44～51Hu Guang-min,He Zhen-hua and Huang De-ji.Gen-eralized nonlinear inversion and its application.GPP,2000,39(2):44～51
[10]Yuan San-yi,Wang Shang-xu and Tian Nan.Swarmintelligence optimization and its application in geo-physical data inversion.Applied Geophysics,2009,6(2):166～174
[11]杨文采.地球物理反演的遗传算法.石油物探,1995,34(1):116～122Yang Wen-cai.Genetic algorithm for the geophysicalinversion.GPP,1995,34(1):116～122
[12]陈双全,王尚旭,季敏,张永刚.地震波阻抗反演的蚁群算法实现.石油物探,2005,44(6):551～553Chen Shuang-quan,Wang Shang-xu,Ji Min and ZhangYong-gang.The ant colony optimization for the seis-mic impedance inversion.GPP,2005,44(6):551～553
[13]黄捍东,张如伟,于茜.基于蚁群算法的层速度反演方法.石油地球物理勘探,2008,43(4):422～424Huang Han-dong,Zhang Ru-wei and Yu Qian.Inver-sion method of interval velocity based on ant colonyalgorithm.OGP,2008,43(4):422～424
[14]姚姚.地球物理非线性反演模拟退火法的改进.地球物理学报,1995,38(5):643～650Yao Yao.Improvement on simulated annealing algo-rithm of geophysical nonlinear inversion.ChineseJournal of Geophysics,1995,38(5):643～650
[15]李庆忠.走向精确勘探的道路.北京:石油工业出版社,1993
[2]邹振桓,杨文采.地震道的广义线性反演.石油地球物理勘探,1987,22(4):363～375Zou Zhen-huan and Yang Wen-cai.Generalized linearinversion of seismic traces.OGP,1987,22(4):363～375
[3]杨文采.地震道的非线性混沌反演(Ⅰ).地球物理学报,1993,36(2):222～232Yang Wen-cai.Nonlinear chaotic inversion of seismictraces(Ⅰ).Chinese Journal of Geophysics,1993,36(2):222～232
[4]杨文采.地震道的非线性混沌反演(Ⅱ).地球物理学报,1993,36(3):376～387Yang Wen-cai.Nonlinear chaotic inversion of seismictraces(Ⅱ).Chinese Journal of Geophysics,1993,36(3):376～387
[5]Debeye H W J and Van Riel P.Lp-norm deconvolu-tion.Geophysical Prospecting,1990,38:381～404
[6]李宏兵.具有剔除噪音功能的多道广义线性反演.石油物探,1996,35(4):11～17Li Hong-bing.Generalized multi-trace linear inversionwith the removal of noise.GPP,1996,35(4):11～17
[7]林小竹,杨慧珠,汤磊.无井多道反演.石油地球物理勘探,1998,33(4):448～452Lin Xiao-zhu,Yang Hui-zhu and Tang Lei.Multi-trace inversion without borehole data.OGP,1998,33(4):448～452
[8]林小竹,杨慧珠.有井多道反演.石油物探,1999,38(4):44～50Lin Xiao-zhu and Yang Hui-zhu.Multi-trace brand-hand constrained inversion.GPP,1999,38(4):44～50
[9]胡光岷,贺振华,黄德济.广义非线性反演及其应用.石油物探,2000,39(2):44～51Hu Guang-min,He Zhen-hua and Huang De-ji.Gen-eralized nonlinear inversion and its application.GPP,2000,39(2):44～51
[10]Yuan San-yi,Wang Shang-xu and Tian Nan.Swarmintelligence optimization and its application in geo-physical data inversion.Applied Geophysics,2009,6(2):166～174
[11]杨文采.地球物理反演的遗传算法.石油物探,1995,34(1):116～122Yang Wen-cai.Genetic algorithm for the geophysicalinversion.GPP,1995,34(1):116～122
[12]陈双全,王尚旭,季敏,张永刚.地震波阻抗反演的蚁群算法实现.石油物探,2005,44(6):551～553Chen Shuang-quan,Wang Shang-xu,Ji Min and ZhangYong-gang.The ant colony optimization for the seis-mic impedance inversion.GPP,2005,44(6):551～553
[13]黄捍东,张如伟,于茜.基于蚁群算法的层速度反演方法.石油地球物理勘探,2008,43(4):422～424Huang Han-dong,Zhang Ru-wei and Yu Qian.Inver-sion method of interval velocity based on ant colonyalgorithm.OGP,2008,43(4):422～424
[14]姚姚.地球物理非线性反演模拟退火法的改进.地球物理学报,1995,38(5):643～650Yao Yao.Improvement on simulated annealing algo-rithm of geophysical nonlinear inversion.ChineseJournal of Geophysics,1995,38(5):643～650
[15]李庆忠.走向精确勘探的道路.北京:石油工业出版社,1993
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