海洋磁力测量垂直空间归算中曲面延拓迭代方法的改进
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摘要
海洋磁力测量中,由于受到海流等因素的影响导致磁力仪传感器(拖鱼)的入水深度起伏变化,测得的海洋磁场数据并不在固定的平面上。为了满足不同用户对海洋磁场数据的应用需求,必须采取合理的"曲化平",实现整个测区磁场数据垂直空间上的统一。针对位场曲面延拓积分方程的迭代解中高阶垂向导数对高频噪声的放大问题,尝试引入Tikhonov正则化方法对其进行改进,以抑制高频噪声的影响。仿真分析表明,在选择合适的正则化参数后,改进的延拓方法可将延拓精度提高1.6 nT。实测数据分析表明,采用改进曲面延拓迭代方法,将磁测成果数据归算到曲面最低平面时,归算后交叉点磁异常不符值精度可提高2 nT,进一步验证了海洋磁力测量数据垂直空间归算的必要性。
The constantly changing of depth of towfish into the water often leads to the magnetic data on a curved surface, which is not taken into account during data processing in marine magnetic survey. For the problem that the high frequency noise in the data is easy to be amplified by vertical deriva-tive in continuation iterative solution of integral equation for curved surface, Tikhonov regularization method is introduced to improve the iterative solution, and the regularization parameter is determined by using the L-curve criterion, which makes the continuation method more anti-noise. Theoretical model and actual examples show that the improved method can effectively suppress the influence of high frequency noise, and the precision of continuation is obviously improved, when the survey data is corrected to the lowest plane of curved surface, the magnetic anomaly discrepancy mean square error of the line network intersection is increased 2 nT than before reduction, which verifies the improved method is feasible for vertical space reduction of marine magnetic survey data.
The constantly changing of depth of towfish into the water often leads to the magnetic data on a curved surface, which is not taken into account during data processing in marine magnetic survey. For the problem that the high frequency noise in the data is easy to be amplified by vertical deriva-tive in continuation iterative solution of integral equation for curved surface, Tikhonov regularization method is introduced to improve the iterative solution, and the regularization parameter is determined by using the L-curve criterion, which makes the continuation method more anti-noise. Theoretical model and actual examples show that the improved method can effectively suppress the influence of high frequency noise, and the precision of continuation is obviously improved, when the survey data is corrected to the lowest plane of curved surface, the magnetic anomaly discrepancy mean square error of the line network intersection is increased 2 nT than before reduction, which verifies the improved method is feasible for vertical space reduction of marine magnetic survey data.
引文
[1] Bian Gang, Xia Wei, Jin Shaohua, et al. Marine Magnetic Survey Data Processing and Its Application[M]. Beijing: Surveying and Mapping Press, 2015(边刚, 夏伟, 金绍华, 等. 海洋磁力测量数据处理方法及其应用研究[M]. 北京:测绘出版社, 2015)
[2] Yu Bo, Liu Yanchun, Bian Gang, et al. Correction of Vertical Free-Air in Marine Magnetic Surveying[J]. Geomatics and Information Science of Wuhan University, 2008, 33(9): 926-929(于波,刘雁春, 边刚, 等. 海洋磁力测量垂直空间改正研究[J]. 武汉大学学报\5信息科学版, 2008, 33(9): 926-929)
[3] Yu Bo, Liu Yanchun, Zhai Guojun, et al. Analysis of Vertical Space Variation of Marine Magnetic Field[J]. Chinese J Geophys, 2009, 52(1): 169-175(于波, 刘雁春, 翟国君, 等. 海洋地磁场的垂直空间变化分析[J]. 地球物理学报, 2009, 52(1): 169-175)
[4] Yu Bo, Huang Motao, Zhai Guojun, et al. Application and Determination of Threshold on Free-Air Correction of Marine Magnetic Survey[J]. Geomatics and Information Science of Wuhan University, 2010, 35(2): 172-175(于波, 黄谟涛, 翟国君, 等. 海洋磁力测量空间归算阈值条件确定及其应用[J]. 武汉大学学报\5信息科学版, 2010, 35(2): 172-175)
[5] Bhattacharyya B K, Chan K C. Reduction of Magnetic and Gravity Data on an Arbitrary Surface Acquired in a Region of High Topographic Relief[J]. Geophysics, 1977, 42(7): 1 411-1 430
[6] Wang Wanyin, Pan Zuoshu, Li Jiakang. Continuation Methods for Curved Surface of the Three-Dimensional High-Precision Gravity and Magnetic Potential Field[J]. Geophysical & Geochemical Exploration, 1991, 15(6): 415-422 (王万银, 潘作枢, 李家康. 三维高精度重磁位场曲面延拓方法[J]. 物探与化探, 1991, 15(6): 415-422)
[7] Wang Wanyin, Liu Jinlan, Qiu Zhiyun, et al. The Research of the Frequency Domain Dipole Layer Method for the Processing and Transformation of Potential Field on Curved Surface[J]. Chinese J Geophys, 2009, 52(10): 2 652-2 665(王万银, 刘金兰, 邱之云, 等. 频率域偶层位曲面位场处理和转换方法研究[J]. 地球物理学报, 2009, 52(10): 2 652-2 665)
[8] Chen Zhenyan. Reduction of Magnetic and Gravity Data to a Horizontal Plane by Using Finite Element Method[J]. Geophysical & Geochemical Exploration, 1981, 5(3): 153-158(程振炎. 重磁场的有限元法曲化平[J]. 物探与化探, 1981, 5(3): 153-158)
[9] Xu Shizhe,Lou Yunju. Application of the Boundary Element Method to the Continuation Upward and Transformation of 2-D Potential Field on Relief Topography[J]. Computing Techniques for Geophysical and Geochemical Exploration, 1987, 7(3): 195-199 (徐世浙, 楼云菊. 起伏地形二维位场上延与换算的边界单元法[J]. 物化探计算技术, 1987, 7(3): 195-199)
[10] Liu Jinlan, Wang Wanyin, Yu Changchun. Reduction of Potential Field Data to a Horizontal Plane by a Successive Approximation Procedure [J]. Chinese J Geophys, 2007, 50(5): 1 551-1 557(刘金兰, 王万银, 于长春. 逐步逼近曲化平方法研究[J]. 地球物理学报, 2007, 50(5): 1 551-1 557)
[11] Xu Shizhe, Yu Hailong. The Interpolation-Iteration Method for Potential Field Continuation from Undulating Surface to Plane[J]. Chinese J Geophys, 2007, 50(6): 1 811-1 815(徐世浙, 余海龙. 位场曲化平的插值-迭代法[J]. 地球物理学报, 2007, 50(6): 1 811-1 815)
[12] Chen Shengchang, Lin Chen, Li Pei. An Iteration Approach to Potential Field Continuation from Curved Surface to Plane [J]. Progress in Geophys, 2009, 24(4): 1 320-1 326(陈生昌, 林晨, 李佩. 位场数据曲化平的迭代法[J]. 地球物理学进展, 2009, 24(4): 1 320-1 326)
[13] Yu Bo. The Vertical Space Reduction and the Model Construction of Marine Magnetic Anomaly[D]. Dalian: Dalian Naval Academy, 2009(于波. 海洋磁力测量垂直空间归算与背景场模型构建[D]. 大连: 大连舰艇学院, 2009)
[14] Liu Dongjia, Hong Tianqiu, Liao Xutao, et al. Iterative Solution of Integral Equation for Potential Field Continuation from an Irregular Surface to a Horizontal Plane[J]. Chinese J Geophys, 2012, 55(10): 3 467-3 476(刘东甲, 洪天求, 廖旭涛, 等. 位场曲化平积分方程的迭代解[J]. 地球物理学报, 2012, 55(10): 3 467-3 476)
[15] Guan Zhining. Geomagnetic Field and Magnetic Exploration[M]. Beijing: Geological Publishing House, 2005(管志宁. 地磁场与磁力勘探[M]. 北京: 地质出版社, 2005)
[16] Tikhonov A N,Arsenin V Y.Solutions of Ill-posed Problems [M]. New York: John Wiley and Sons,1977
[17] Gu Yongwei, Gui Qingming, Han Songhui, et al. Regularization by Grouping Correction in Downward Continuation of Airborne Gravity[J]. Geomatics and Information Science of Wuhan University, 2013, 38(6): 720-724(顾勇为, 归庆明, 韩松辉, 等. 航空重力向下延拓分组修正的正则化解法[J]. 武汉大学学报\5信息科学版, 2013, 38(6): 720-724)
[18] GJB 7537-2012. Specifications for Marine Magnetic Survey[S]. Beijing: Standards Press of China, 2012(GJB 7537-2012. 海洋磁力测量要求[S]. 北京: 中国标准出版社,2012)
[2] Yu Bo, Liu Yanchun, Bian Gang, et al. Correction of Vertical Free-Air in Marine Magnetic Surveying[J]. Geomatics and Information Science of Wuhan University, 2008, 33(9): 926-929(于波,刘雁春, 边刚, 等. 海洋磁力测量垂直空间改正研究[J]. 武汉大学学报\5信息科学版, 2008, 33(9): 926-929)
[3] Yu Bo, Liu Yanchun, Zhai Guojun, et al. Analysis of Vertical Space Variation of Marine Magnetic Field[J]. Chinese J Geophys, 2009, 52(1): 169-175(于波, 刘雁春, 翟国君, 等. 海洋地磁场的垂直空间变化分析[J]. 地球物理学报, 2009, 52(1): 169-175)
[4] Yu Bo, Huang Motao, Zhai Guojun, et al. Application and Determination of Threshold on Free-Air Correction of Marine Magnetic Survey[J]. Geomatics and Information Science of Wuhan University, 2010, 35(2): 172-175(于波, 黄谟涛, 翟国君, 等. 海洋磁力测量空间归算阈值条件确定及其应用[J]. 武汉大学学报\5信息科学版, 2010, 35(2): 172-175)
[5] Bhattacharyya B K, Chan K C. Reduction of Magnetic and Gravity Data on an Arbitrary Surface Acquired in a Region of High Topographic Relief[J]. Geophysics, 1977, 42(7): 1 411-1 430
[6] Wang Wanyin, Pan Zuoshu, Li Jiakang. Continuation Methods for Curved Surface of the Three-Dimensional High-Precision Gravity and Magnetic Potential Field[J]. Geophysical & Geochemical Exploration, 1991, 15(6): 415-422 (王万银, 潘作枢, 李家康. 三维高精度重磁位场曲面延拓方法[J]. 物探与化探, 1991, 15(6): 415-422)
[7] Wang Wanyin, Liu Jinlan, Qiu Zhiyun, et al. The Research of the Frequency Domain Dipole Layer Method for the Processing and Transformation of Potential Field on Curved Surface[J]. Chinese J Geophys, 2009, 52(10): 2 652-2 665(王万银, 刘金兰, 邱之云, 等. 频率域偶层位曲面位场处理和转换方法研究[J]. 地球物理学报, 2009, 52(10): 2 652-2 665)
[8] Chen Zhenyan. Reduction of Magnetic and Gravity Data to a Horizontal Plane by Using Finite Element Method[J]. Geophysical & Geochemical Exploration, 1981, 5(3): 153-158(程振炎. 重磁场的有限元法曲化平[J]. 物探与化探, 1981, 5(3): 153-158)
[9] Xu Shizhe,Lou Yunju. Application of the Boundary Element Method to the Continuation Upward and Transformation of 2-D Potential Field on Relief Topography[J]. Computing Techniques for Geophysical and Geochemical Exploration, 1987, 7(3): 195-199 (徐世浙, 楼云菊. 起伏地形二维位场上延与换算的边界单元法[J]. 物化探计算技术, 1987, 7(3): 195-199)
[10] Liu Jinlan, Wang Wanyin, Yu Changchun. Reduction of Potential Field Data to a Horizontal Plane by a Successive Approximation Procedure [J]. Chinese J Geophys, 2007, 50(5): 1 551-1 557(刘金兰, 王万银, 于长春. 逐步逼近曲化平方法研究[J]. 地球物理学报, 2007, 50(5): 1 551-1 557)
[11] Xu Shizhe, Yu Hailong. The Interpolation-Iteration Method for Potential Field Continuation from Undulating Surface to Plane[J]. Chinese J Geophys, 2007, 50(6): 1 811-1 815(徐世浙, 余海龙. 位场曲化平的插值-迭代法[J]. 地球物理学报, 2007, 50(6): 1 811-1 815)
[12] Chen Shengchang, Lin Chen, Li Pei. An Iteration Approach to Potential Field Continuation from Curved Surface to Plane [J]. Progress in Geophys, 2009, 24(4): 1 320-1 326(陈生昌, 林晨, 李佩. 位场数据曲化平的迭代法[J]. 地球物理学进展, 2009, 24(4): 1 320-1 326)
[13] Yu Bo. The Vertical Space Reduction and the Model Construction of Marine Magnetic Anomaly[D]. Dalian: Dalian Naval Academy, 2009(于波. 海洋磁力测量垂直空间归算与背景场模型构建[D]. 大连: 大连舰艇学院, 2009)
[14] Liu Dongjia, Hong Tianqiu, Liao Xutao, et al. Iterative Solution of Integral Equation for Potential Field Continuation from an Irregular Surface to a Horizontal Plane[J]. Chinese J Geophys, 2012, 55(10): 3 467-3 476(刘东甲, 洪天求, 廖旭涛, 等. 位场曲化平积分方程的迭代解[J]. 地球物理学报, 2012, 55(10): 3 467-3 476)
[15] Guan Zhining. Geomagnetic Field and Magnetic Exploration[M]. Beijing: Geological Publishing House, 2005(管志宁. 地磁场与磁力勘探[M]. 北京: 地质出版社, 2005)
[16] Tikhonov A N,Arsenin V Y.Solutions of Ill-posed Problems [M]. New York: John Wiley and Sons,1977
[17] Gu Yongwei, Gui Qingming, Han Songhui, et al. Regularization by Grouping Correction in Downward Continuation of Airborne Gravity[J]. Geomatics and Information Science of Wuhan University, 2013, 38(6): 720-724(顾勇为, 归庆明, 韩松辉, 等. 航空重力向下延拓分组修正的正则化解法[J]. 武汉大学学报\5信息科学版, 2013, 38(6): 720-724)
[18] GJB 7537-2012. Specifications for Marine Magnetic Survey[S]. Beijing: Standards Press of China, 2012(GJB 7537-2012. 海洋磁力测量要求[S]. 北京: 中国标准出版社,2012)