一种用于Occam反演中搜索拉格朗日乘子的方法
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摘要
Occam反演法由于其算法稳定,对初始条件要求不高,反演效果较好,在大地电磁反演中运用较多。不过其每次迭代都需要进行偏导数计算和大量的模型计算,以便搜索到最佳的拉格朗日乘子,这造成了计算量和计算时间的增加。Occam反演在每次迭代寻找最佳模型的过程中需要搜索合适的拉格朗日乘子使拟合差最小,搜索的方法一般使用进退法和扫描法,鲜少使用其他一维搜索方法。本文将牛顿迭代搜索法和二分法组合一起用于拉格朗日乘子的搜索,取得了较好的结果,减少了模型的搜索量,在一定程度上提高了计算速度。
Occam inversion method is widely used in the magnetotelluric inversion because of its algorithm stability,low requirements on the initial conditions and the inversion effect.But in each iteration,partial derivative calculation and a large number of model calculation are required in order to search the optimal Lagrange multiplier,which results in an increase in the amount of calculation and the calculation time.When Occam inversion finds the best model in each iteration,the appropriate Lagrange multiplier is needed to seek the suitable Lagrange multiplier so as to minimize the fitting error.The advance-retreat method and scanning method are generally used.In this paper,the combination of Newton iterative search method and dichotomy used in search of Lagrange multiplier achieve a good result.
Occam inversion method is widely used in the magnetotelluric inversion because of its algorithm stability,low requirements on the initial conditions and the inversion effect.But in each iteration,partial derivative calculation and a large number of model calculation are required in order to search the optimal Lagrange multiplier,which results in an increase in the amount of calculation and the calculation time.When Occam inversion finds the best model in each iteration,the appropriate Lagrange multiplier is needed to seek the suitable Lagrange multiplier so as to minimize the fitting error.The advance-retreat method and scanning method are generally used.In this paper,the combination of Newton iterative search method and dichotomy used in search of Lagrange multiplier achieve a good result.
引文
[1]胡祖志,胡祥云,何展祥.大地电磁非线性共轭梯度反演[J].地球物理学报,2006,49(4):1226～1234.
[2]Siripunvaraporn W,Egbert G.An efficient data-subspace inversion method for 2-D magnetotelluricdata[J].Geophysics,2000,65(3):791～803.
[3]韩波,胡祥云,何展翔,等.大地电磁反演方法的数学分类[J].石油地球物理勘探,2012,47(1):177～187.
[4]吴小平,徐国明.大地电磁数据的occam反演改进[J].地球物理学报,1998,41(4):547～554.
[5]谭捍东,余钦范,Booker,等.大地电磁三维快速松弛反演[J].地球物理学报,2003,46(6):850～855.
[6]刘羽,王家映,孟永良.基于PC机群的大地电磁Oc-cam反演并行计算研究[J].石油物探,2006,45(3):311～315.
[7]刘羽.大地电磁Oceam反演中拉格朗日乘子搜索的并行计算[J].物探化探计算技术,2005,28(4):342～345.
[8]Rodi W L,Mackie R L.Nonlinear conjugate gradientsalgorithm for 2-D magnetotelluric inversion[J].Geo-physics,2001,66(1):174～187.
[9]Constable S C,Parker R L,Constable C G.Occam'sin-version:A practical algorithm for generating smoothmodels from electromagnetic sounding data[J].Geo-physics,1987,52(3):289～300.
[10]柳辉.解非线性方程的牛顿迭代法及其应用[J].重庆工学院学报(自然科学版),2007,21(8):95～98.
[2]Siripunvaraporn W,Egbert G.An efficient data-subspace inversion method for 2-D magnetotelluricdata[J].Geophysics,2000,65(3):791～803.
[3]韩波,胡祥云,何展翔,等.大地电磁反演方法的数学分类[J].石油地球物理勘探,2012,47(1):177～187.
[4]吴小平,徐国明.大地电磁数据的occam反演改进[J].地球物理学报,1998,41(4):547～554.
[5]谭捍东,余钦范,Booker,等.大地电磁三维快速松弛反演[J].地球物理学报,2003,46(6):850～855.
[6]刘羽,王家映,孟永良.基于PC机群的大地电磁Oc-cam反演并行计算研究[J].石油物探,2006,45(3):311～315.
[7]刘羽.大地电磁Oceam反演中拉格朗日乘子搜索的并行计算[J].物探化探计算技术,2005,28(4):342～345.
[8]Rodi W L,Mackie R L.Nonlinear conjugate gradientsalgorithm for 2-D magnetotelluric inversion[J].Geo-physics,2001,66(1):174～187.
[9]Constable S C,Parker R L,Constable C G.Occam'sin-version:A practical algorithm for generating smoothmodels from electromagnetic sounding data[J].Geo-physics,1987,52(3):289～300.
[10]柳辉.解非线性方程的牛顿迭代法及其应用[J].重庆工学院学报(自然科学版),2007,21(8):95～98.