修正柯西约束地震盲反褶积方法
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摘要
文中从贝叶斯稀疏反演理论出发,结合Canadas提出的地震盲反褶积数学框架,采用修正的柯西准则建立反射系数稀疏约束进行地震盲反褶积处理,不仅能较好地恢复反射系数序列的稀疏性,同时能在提高地震资料的分辨率和减小对弱反射信息的压制之间达到一个平衡,并采用松弛交替迭代求解方案同时求取反射系数和混合相位的地震子波。在有井资料或其他地质资料可用的情况下,引入波阻抗作为反射系数的先验约束,降低了反演问题的多解性,增加了反演结果的精度和可信度。数值模拟和实例分析表明,文中算法收敛快、精度高,具有实际应用价值。
Starting from Bayes sparse inversion theory, the paper adopted modified Cauchy criterion to build up reflectivity sparse constraint and carry out seismic blind deconvolution processing in combination with math frame of seismic blind deconvolution presented by Mr. Canadas, which can better restore the sparse property of reflectivity sequence, and reach a balance between improving the resolution of seismic data and reducing suppressing weak reflection information at the same time, and using relaxation alternative iteration solving plan to simultaneously obtain reflectivity and mixed phase seismic wavelet. In a situation of available well data or other geologic data, the wave impedance can be introduced as prior constraint of reflectivity, which reduces multi-solution of inverse problem and increases the precision and confidence level of inverse result. The numeric simulation and real cases showed that the algorithm in the paper is characterized by rapid convergence and high precision, which has practical application value.
Starting from Bayes sparse inversion theory, the paper adopted modified Cauchy criterion to build up reflectivity sparse constraint and carry out seismic blind deconvolution processing in combination with math frame of seismic blind deconvolution presented by Mr. Canadas, which can better restore the sparse property of reflectivity sequence, and reach a balance between improving the resolution of seismic data and reducing suppressing weak reflection information at the same time, and using relaxation alternative iteration solving plan to simultaneously obtain reflectivity and mixed phase seismic wavelet. In a situation of available well data or other geologic data, the wave impedance can be introduced as prior constraint of reflectivity, which reduces multi-solution of inverse problem and increases the precision and confidence level of inverse result. The numeric simulation and real cases showed that the algorithm in the paper is characterized by rapid convergence and high precision, which has practical application value.
引文
[1]刘喜武等.地震盲反褶积综述.地球物理学进展,2003,18(2):203~209
[2]Walden A T.Non-Gaussian reflectivity,entropy,and deconvolution.Geophysics,1985,50(12):2862~2888
[3]Canadas G.A mathematical framework for blind de-convolution inversion problems.Expanded Abstracts of72nd SEG Mtg,2002,10
[4]朱振宇等.基于预条件共轭梯度法的盲反褶积方法.勘探地球物理进展,2004,27(3):174~176
[5]孟小红等.盲源反褶积方法与应用研究.石油地球物理勘探,2005,40(6):642~645
[6]Sacchi M D.Statistical and Transform Methods in Geophysical Signal Processing.Depart ment of Phys-ics University of Alberta,2002
[7]印兴耀等.一种基于负熵的Bussgang地震盲反褶积方法.石油地球物理勘探,2007,42(5):499~505
[8]王锐等.有限熵反褶积.石油地球物理勘探,2005,40(6):637~641
[9]Youzwishen C F.Non-linear sparse andblock constraints for seismic inversion problems.Master's thesis.Uni-versity of Albert,2001,9
[2]Walden A T.Non-Gaussian reflectivity,entropy,and deconvolution.Geophysics,1985,50(12):2862~2888
[3]Canadas G.A mathematical framework for blind de-convolution inversion problems.Expanded Abstracts of72nd SEG Mtg,2002,10
[4]朱振宇等.基于预条件共轭梯度法的盲反褶积方法.勘探地球物理进展,2004,27(3):174~176
[5]孟小红等.盲源反褶积方法与应用研究.石油地球物理勘探,2005,40(6):642~645
[6]Sacchi M D.Statistical and Transform Methods in Geophysical Signal Processing.Depart ment of Phys-ics University of Alberta,2002
[7]印兴耀等.一种基于负熵的Bussgang地震盲反褶积方法.石油地球物理勘探,2007,42(5):499~505
[8]王锐等.有限熵反褶积.石油地球物理勘探,2005,40(6):637~641
[9]Youzwishen C F.Non-linear sparse andblock constraints for seismic inversion problems.Master's thesis.Uni-versity of Albert,2001,9
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