利用微分进化法确定海洋磁场向下延拓中的最优参数
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摘要
位场的解析延拓是实现不同高度海洋地磁场相互转换的主要途径,是构建海洋三维磁空间背景场模型的关键技术.针对位场向下延拓迭代法中最优正则化参数及最佳迭代次数难以确定问题,尝试引入微分进化法,以正则化参数及迭代次数为种群变量,以延拓结果的熵值为目标函数,以目标函数最小化为搜索准则,实现两种参数的并行全局寻优.采用实测数据对微分进化法在几种常用的迭代法中最优正则化参数及最佳迭代次数的确定进行了分析,与传统L-曲线准则确定的最优正则化参数及多次试验确定的最佳迭代次数进行对比,结果表明:微分进化法确定的最优参数能使三种迭代法取得最佳迭代效果,延拓结果与真实地磁场最为接近,并且该法计算稳定、自适应强,建议在海洋磁场数据向下延拓中应用.
The analytic continuation of potential fields is the main approach to realize the conversion of marine geomagnetic field at different altitudes,which is a key technique to construct the 3D marine geomagnetic field model.Focusing on the determination of the optimal regularization parameters and the number of iterations,the differential evolution algorithm(DE)is adopted in iterative downward continuation.Moreover,two kinds of optimum parameters can be selected effectively according to the minimum objective function by taking the entropy value of continuation results as the objective function,and the regularization parameter and times of iteration as individual species.Furthermore,the DE method has been applied to determine optimal parameters in several commonly used iteration methods with observed data.Compared with the optimum regularization parameters determined by the L-curve rule and the best number of iterations determined through multiple experiments,the optimum parameters determined bythe DE method can achieve the best effect of continuation in different iterative methods,and the continuation results are closer to the real geomagnetic field.Hence,the DE method is recommended to be applied in downward continuation of the marine geomagnetic field.
The analytic continuation of potential fields is the main approach to realize the conversion of marine geomagnetic field at different altitudes,which is a key technique to construct the 3D marine geomagnetic field model.Focusing on the determination of the optimal regularization parameters and the number of iterations,the differential evolution algorithm(DE)is adopted in iterative downward continuation.Moreover,two kinds of optimum parameters can be selected effectively according to the minimum objective function by taking the entropy value of continuation results as the objective function,and the regularization parameter and times of iteration as individual species.Furthermore,the DE method has been applied to determine optimal parameters in several commonly used iteration methods with observed data.Compared with the optimum regularization parameters determined by the L-curve rule and the best number of iterations determined through multiple experiments,the optimum parameters determined bythe DE method can achieve the best effect of continuation in different iterative methods,and the continuation results are closer to the real geomagnetic field.Hence,the DE method is recommended to be applied in downward continuation of the marine geomagnetic field.
引文
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Liu D J,Hong T Q,Jia Z H,et al.2009.Wave number domainiteration method for downward continuation of potential fields and its convergence.Chinese J.Geophys.(in Chinese),52(6):1599-1605,doi:10.3969/j.issn.0001-5733.2009.06.022.
Liu X G,Li Y C,Xiao Y,et al.2014.Optimal regularization parameter determination method in downward continuation of gravimetric and geomagnetic data.Acta Geodaetica et Cartographica Sinica(in Chinese),43(9):881-887.
Ma T,Chen L W,Wu M P,et al.2013.The selection of regularization parameter in downward continuation of potential field based on L-curve method.Progress in Geophys.(in Chinese),28(5):2485-2494,doi:10.6038/pg20130527.
Ministry of Land and Resources of the People′s Republic of China.2010.DZ/T 0142-2010.Criterion of aeromagnetic survey(in Chinese).Beijing:China Standard Publishing House.
Song W Q,Gao Y K,Zhu H W.2013.The differential evolution inversion method based on Bayesian theory for micro-seismic data.Chinese J.Geophys.(in Chinese),56(4):1331-1339,doi:10.6038/cjg20130427.
Storn R,Price K.1996.Minimizing the real functions of the ICEC′96contest by differential evolution.∥Proceeding of the IEEEConference on Evolutionary Computation.Nagoya,Japan:IEEE,842-844.
Sun W,Wu X P,Wang Q B,et al.2014.Wave number domain iterative Tikhonov regularization method for downward continuation of airborne gravity data.Acta Geodaetica et Cartographica Sinica(in Chinese),43(6):566-574.
Wang T Y,Yang J,Yan T J,et al.2014.The differential evolution algorithm in geophysical inversion.Geology and Exploration(in Chinese),50(5):971-975.
Wang W J.2010.Regularization algorithms for solving ill-posed matrix equations arising from geophysical inversions[Ph.D.thesis](in Chinese).Chengdu:Chengdu University of Technology.
Wang Y F.2007.Computational Methods for Inverse Problems and Their Applications(in Chinese).Beijing:Higher Education Press,76-84.
Wang Y G,Zhang F X,Wang Z W,et al.2011.Taylor series iteration for downward continuation of potential field.OGP(in Chinese),46(4):657-662.
Xu S Z.2006.The integral-iteration method for continuation of potential fields.Chinese J.Geophys.(in Chinese),49(4):1176-1182.
Xu X S,Zhang Y Q.2008.Application of modified terrain entropy algorithm in terrain aided navigation.Journal of Chinese Inertial Technology(in Chinese),16(5):595-598.
Yao C L,Li H W,Zheng Y M,et al.2012.Research on iteration method using in potential field transformations.Chinese J.Geophys.(in Chinese),55(6):2062-2078,doi:10.6038/j.issn.0001-5733.2012.06.028.
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Zeng X N,Li X H,Niu C,et al.2013.Regularization-integral iteration in wave number domain for downward continuation of potential fields.OGP(in Chinese),48(4):643-650.
陈龙伟,张辉,郑志强等.2007.水下地磁辅助导航中地磁场延拓方法.中国惯性技术学报,15(6):693-697.
刘东甲,洪天求,贾志海等.2009.位场向下延拓的波数域迭代法及其收敛性.地球物理学报,52(6):1599-1605,doi:10.3969/j.issn.0001-5733.2009.06.022.
刘晓刚,李迎春,肖云等.2014.重力与磁力测量数据向下延拓中最优正则化参数确定方法.测绘学报,43(9):881-887.
马涛,陈龙伟,吴美平等.2013.基于L曲线法的位场向下延拓正则化参数选择.地球物理学进展,28(5):2485-2494,doi:10.6038/pg20130527.
宋维琪,高艳珂,朱海伟.2013.微地震资料贝叶斯理论差分进化反演方法.地球物理学报,56(4):1331-1339,doi:10.6038/cjg20130427.
孙文,吴晓平,王庆宾等.2014.航空重力数据向下延拓的波数域迭代Tikhonov正则化方法.测绘学报,43(6):566-574.
王天意,杨进,颜廷杰等.2014.地球物理反演中的差分进化算法.地质与勘探,50(5):971-975.
王文娟.2010.地球物理反演中病态矩阵方程正则化解算方法研究[博士论文].成都:成都理工大学.
王彦飞.2007.反演问题的计算方法及其应用.北京:高等教育出版社,76-84.
王彦国,张风旭,王祝文等.2011.位场向下延拓的泰勒级数迭代法.石油地球物理勘探,46(4):657-662.
徐世浙.2006.位场延拓的积分-迭代法.地球物理学报,49(4):1176-1182.
徐晓苏,张逸群.2008.改进的地形熵算法在地形辅助导航中的应用.中国惯性技术学报,16(5):595-598.
姚长利,李宏伟,郑元满等.2012.重磁位场转换计算中迭代法的综合分析与研究.地球物理学报,55(6):2062-2078,doi:10.6038/j.issn.0001-5733.2012.06.028.
曾小牛,李夕海,韩绍卿等.2011.位场向下延拓三种迭代方法之比较.地球物理学进展,26(3):908-915,doi:10.3969/j.issn.1004-2903.2011.03.016.
曾小牛,李夕海,牛超等.2013.位场向下延拓的波数域正则-积分迭代法.石油地球物理勘探,48(4):643-650.
中华人民共和国国土资源部.2010.DZ/T 0142-2010.航空磁测技术规范.北京:中国标准出版社.
Liu D J,Hong T Q,Jia Z H,et al.2009.Wave number domainiteration method for downward continuation of potential fields and its convergence.Chinese J.Geophys.(in Chinese),52(6):1599-1605,doi:10.3969/j.issn.0001-5733.2009.06.022.
Liu X G,Li Y C,Xiao Y,et al.2014.Optimal regularization parameter determination method in downward continuation of gravimetric and geomagnetic data.Acta Geodaetica et Cartographica Sinica(in Chinese),43(9):881-887.
Ma T,Chen L W,Wu M P,et al.2013.The selection of regularization parameter in downward continuation of potential field based on L-curve method.Progress in Geophys.(in Chinese),28(5):2485-2494,doi:10.6038/pg20130527.
Ministry of Land and Resources of the People′s Republic of China.2010.DZ/T 0142-2010.Criterion of aeromagnetic survey(in Chinese).Beijing:China Standard Publishing House.
Song W Q,Gao Y K,Zhu H W.2013.The differential evolution inversion method based on Bayesian theory for micro-seismic data.Chinese J.Geophys.(in Chinese),56(4):1331-1339,doi:10.6038/cjg20130427.
Storn R,Price K.1996.Minimizing the real functions of the ICEC′96contest by differential evolution.∥Proceeding of the IEEEConference on Evolutionary Computation.Nagoya,Japan:IEEE,842-844.
Sun W,Wu X P,Wang Q B,et al.2014.Wave number domain iterative Tikhonov regularization method for downward continuation of airborne gravity data.Acta Geodaetica et Cartographica Sinica(in Chinese),43(6):566-574.
Wang T Y,Yang J,Yan T J,et al.2014.The differential evolution algorithm in geophysical inversion.Geology and Exploration(in Chinese),50(5):971-975.
Wang W J.2010.Regularization algorithms for solving ill-posed matrix equations arising from geophysical inversions[Ph.D.thesis](in Chinese).Chengdu:Chengdu University of Technology.
Wang Y F.2007.Computational Methods for Inverse Problems and Their Applications(in Chinese).Beijing:Higher Education Press,76-84.
Wang Y G,Zhang F X,Wang Z W,et al.2011.Taylor series iteration for downward continuation of potential field.OGP(in Chinese),46(4):657-662.
Xu S Z.2006.The integral-iteration method for continuation of potential fields.Chinese J.Geophys.(in Chinese),49(4):1176-1182.
Xu X S,Zhang Y Q.2008.Application of modified terrain entropy algorithm in terrain aided navigation.Journal of Chinese Inertial Technology(in Chinese),16(5):595-598.
Yao C L,Li H W,Zheng Y M,et al.2012.Research on iteration method using in potential field transformations.Chinese J.Geophys.(in Chinese),55(6):2062-2078,doi:10.6038/j.issn.0001-5733.2012.06.028.
Zeng X N,Li X H,Han S Q,et al.2011.A comparison of three iteration methods for downward continuation of potential fields.Progress in Geophys.(in Chinese),26(3):908-915,doi:10.3969/j.issn.1004-2903.2011.03.016.
Zeng X N,Li X H,Niu C,et al.2013.Regularization-integral iteration in wave number domain for downward continuation of potential fields.OGP(in Chinese),48(4):643-650.
陈龙伟,张辉,郑志强等.2007.水下地磁辅助导航中地磁场延拓方法.中国惯性技术学报,15(6):693-697.
刘东甲,洪天求,贾志海等.2009.位场向下延拓的波数域迭代法及其收敛性.地球物理学报,52(6):1599-1605,doi:10.3969/j.issn.0001-5733.2009.06.022.
刘晓刚,李迎春,肖云等.2014.重力与磁力测量数据向下延拓中最优正则化参数确定方法.测绘学报,43(9):881-887.
马涛,陈龙伟,吴美平等.2013.基于L曲线法的位场向下延拓正则化参数选择.地球物理学进展,28(5):2485-2494,doi:10.6038/pg20130527.
宋维琪,高艳珂,朱海伟.2013.微地震资料贝叶斯理论差分进化反演方法.地球物理学报,56(4):1331-1339,doi:10.6038/cjg20130427.
孙文,吴晓平,王庆宾等.2014.航空重力数据向下延拓的波数域迭代Tikhonov正则化方法.测绘学报,43(6):566-574.
王天意,杨进,颜廷杰等.2014.地球物理反演中的差分进化算法.地质与勘探,50(5):971-975.
王文娟.2010.地球物理反演中病态矩阵方程正则化解算方法研究[博士论文].成都:成都理工大学.
王彦飞.2007.反演问题的计算方法及其应用.北京:高等教育出版社,76-84.
王彦国,张风旭,王祝文等.2011.位场向下延拓的泰勒级数迭代法.石油地球物理勘探,46(4):657-662.
徐世浙.2006.位场延拓的积分-迭代法.地球物理学报,49(4):1176-1182.
徐晓苏,张逸群.2008.改进的地形熵算法在地形辅助导航中的应用.中国惯性技术学报,16(5):595-598.
姚长利,李宏伟,郑元满等.2012.重磁位场转换计算中迭代法的综合分析与研究.地球物理学报,55(6):2062-2078,doi:10.6038/j.issn.0001-5733.2012.06.028.
曾小牛,李夕海,韩绍卿等.2011.位场向下延拓三种迭代方法之比较.地球物理学进展,26(3):908-915,doi:10.3969/j.issn.1004-2903.2011.03.016.
曾小牛,李夕海,牛超等.2013.位场向下延拓的波数域正则-积分迭代法.石油地球物理勘探,48(4):643-650.
中华人民共和国国土资源部.2010.DZ/T 0142-2010.航空磁测技术规范.北京:中国标准出版社.