重力数据三维共轭梯度聚焦反演及应用
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摘要
基于共轭梯度算法对欠定线性目标函数进行求解。为改善目标函数的多解性、消除多余构造信息影响,引入粗糙度系数矩阵;为克服"趋肤效应",更好地反映地质体的真实形态,在模型目标函数中引入深度加权函数;为更好的反映地质体的某些尖锐构造和边界,本文对目标函数添加了基于最小支撑泛函的聚焦反演约束。通过对多种模型的计算,验证了该方法具有较好的有效性和稳定性,并将该方法应用于实际重力资料地下密度反演中去,得到了较好的反演结果。
We solve underdetermined linear objective function based on conjugate gradient algorithm.In order to improve the multiplicity results of the objective function,and eliminate the influence of redundant structure information,the roughness has been introduced.In order to overcome the"skin effect",the depth weighting function has also been added in the model objective function,and the minimum support function was also added in the objective function to better reflect the sharp features and tectonic boundary.Calculation of several models indicates that this method has good validity and stability.The proposed method was applied to the practical gravity data processing for inversion of 3Dcrust density,and obtained a good precision inversion results.
We solve underdetermined linear objective function based on conjugate gradient algorithm.In order to improve the multiplicity results of the objective function,and eliminate the influence of redundant structure information,the roughness has been introduced.In order to overcome the"skin effect",the depth weighting function has also been added in the model objective function,and the minimum support function was also added in the objective function to better reflect the sharp features and tectonic boundary.Calculation of several models indicates that this method has good validity and stability.The proposed method was applied to the practical gravity data processing for inversion of 3Dcrust density,and obtained a good precision inversion results.
引文
[1]姚姚.地球物理反演基本理论与应用方法[M].武汉:中国地质大学出版社,2002:51-71.
[2]刘天佑.位场勘探数据处理新方法[M].北京:科学出版社,2007:88-113.
[3]Last B J,K Kubik.Compact gravity inversion[J].Geophysics,1983,48(6):713-721.
[4]Constable S C,Parker K L,Constable C G.Occam’s inversion a practical algorithm for generating smooth models from EM sounding data[J].Geophysics,1987,52:289-300.
[5]Li Y G,Oldenburg D W.3Dinversion of gravity data[J].Geophysics,1996,61(2):394-408.
[6]Li Y G,Oldenburg D W.3Dinversion of magnetic data[J].Geophysics,1998,63(1):109-119.
[7]Zhdanov Michael S,Robert G Ellis,Souvik Mukherjee,et al.Regularized focusing inversion of 3-D gravity tensor data[A].SEG Int'l Exposition and 72nd Annual Meeting,2002.
[8]王逸宸.重力等维聚焦反演研究[D].北京:中国地质大学,2014.
[9]陈少华,朱自强,鲁光银,等.重力梯度张量的预条件共轭梯度法反演[J].中南大学学报:自然科学版,2013,44(2):619-625.
[10]陈闫,李桐林,范翠松,等.重力梯度全张量数据三维共轭梯度聚焦反演[J].地球物理学进展,2014,29(3):1 133-1 142.
[11]聂慧梓.重力梯度张量三维聚焦反演方法研究[D].北京:中国地质大学,2014.
[12]刘小军.大地电磁聚焦反演成像方法研究[D].上海:同济大学,2007.
[13]Scales J A.Tomographic inversion via the conjugate gradient methods Geophysics[J].1987,52:179-185.
[14]吴小平,江彤彤.利用共轭梯度方法的电阻率三维反演若干问题研究[J].地震地质,2001,23(2):321-324.
[15]王浩然,陈超,杜劲松.重力梯度张量数据的三维反演方法与应用[J].石油地球物理勘探,2013,48(3):474-481.
[16]陈昭曦,孟小红,郭良辉.重磁数据三维物性反演方法进展[J].地球物理学进展,2012,27(2):503-511.
[17]李媛,牛安福,刘希康,等.汶川Ms8.0地震震前近震源区地壳形变机制探究[J].地震地质,2015,37(6):959-972.
[2]刘天佑.位场勘探数据处理新方法[M].北京:科学出版社,2007:88-113.
[3]Last B J,K Kubik.Compact gravity inversion[J].Geophysics,1983,48(6):713-721.
[4]Constable S C,Parker K L,Constable C G.Occam’s inversion a practical algorithm for generating smooth models from EM sounding data[J].Geophysics,1987,52:289-300.
[5]Li Y G,Oldenburg D W.3Dinversion of gravity data[J].Geophysics,1996,61(2):394-408.
[6]Li Y G,Oldenburg D W.3Dinversion of magnetic data[J].Geophysics,1998,63(1):109-119.
[7]Zhdanov Michael S,Robert G Ellis,Souvik Mukherjee,et al.Regularized focusing inversion of 3-D gravity tensor data[A].SEG Int'l Exposition and 72nd Annual Meeting,2002.
[8]王逸宸.重力等维聚焦反演研究[D].北京:中国地质大学,2014.
[9]陈少华,朱自强,鲁光银,等.重力梯度张量的预条件共轭梯度法反演[J].中南大学学报:自然科学版,2013,44(2):619-625.
[10]陈闫,李桐林,范翠松,等.重力梯度全张量数据三维共轭梯度聚焦反演[J].地球物理学进展,2014,29(3):1 133-1 142.
[11]聂慧梓.重力梯度张量三维聚焦反演方法研究[D].北京:中国地质大学,2014.
[12]刘小军.大地电磁聚焦反演成像方法研究[D].上海:同济大学,2007.
[13]Scales J A.Tomographic inversion via the conjugate gradient methods Geophysics[J].1987,52:179-185.
[14]吴小平,江彤彤.利用共轭梯度方法的电阻率三维反演若干问题研究[J].地震地质,2001,23(2):321-324.
[15]王浩然,陈超,杜劲松.重力梯度张量数据的三维反演方法与应用[J].石油地球物理勘探,2013,48(3):474-481.
[16]陈昭曦,孟小红,郭良辉.重磁数据三维物性反演方法进展[J].地球物理学进展,2012,27(2):503-511.
[17]李媛,牛安福,刘希康,等.汶川Ms8.0地震震前近震源区地壳形变机制探究[J].地震地质,2015,37(6):959-972.