Bifactor weight determination method based on direction and distance in geomagnetic data assimilation
-
摘要:
针对地磁数据通化处理中传统使用的直接平均法、反距离加权平均法和纬度差加权平均法在定权时存在的缺陷，并根据地磁场强度与纬度变化关系密切这一特点，提出了基于方向和距离的双因子定权方法，即在定权时不仅考虑了地磁台站之间的距离在权值中的贡献，而且在权值分配中加入了地磁台站在纬度和经度方向的影响，从而改进了通化结果的精度，为卫星、航空和海洋磁力测量数据提供更加准确的日变改正值。采用Intermagnet网站提供的地磁台站测量数据对所提定权方法的有效性进行了测试。实验结果表明：所提定权方法计算结果精度优于传统定权方法，为实施地面磁力测量存在困难地区的地磁数据日变改正提供了一种更优的定权方法，具有较好的应用前景。
Abstract:In the geomagnetic data assimilation, we analyze the weight determination weakness of the direct average method, reverse distance weighting average method and latitude difference weighting average method which are widely used in the previous work. Considering the geomagnetic field strength has a close relationship with the changing of latitude, we propose a bifactor weight determination method based on the direction and distance. Concretely, it not only utilizes the distances among the geomagnetic observatories but also takes into account the changes from the latitude and longitude directions simultaneously, which assigns the different weights to the above three factors to improve the precision of geomagnetic data assimilation and obtain the more precise diurnal variation correction for the satellitic, airborne and seaborne geomagnetic measurement data. Furthermore, we use the geomagnetic observatory data supplied by Intermagnet website to validate the proposed method. The experimental results demonstrate that the proposed method is superior to the existing methods in the accuracy of calculation result. Thus, this paper proposes a novel and reliable weight determination method which has a potential application in the diurnal variation correction of geomagnetic measurement data in the regions where the ground survey is implemented difficultly.
-
图 1 地磁北向分量X计算结果
Figure 1. Calculated results of northern component X of geomagnetic field
图 2 地磁东向分量Y计算结果
Figure 2. Calculated results of eastern component Y of geomagnetic field
图 3 地磁垂直分量Z计算结果
Figure 3. Calculated results of vertical component Z of geomagnetic field
图 5 地磁水平分量H计算结果
Figure 5. Calculated results of horizontal component H of geomagnetic field
图 8 不同方法得到的计算结果的相关性系数
Figure 8. Correlation coefficients of calculated results by different methods
表 1 地磁台站基本信息
Table 1. Basic information of geomagnetic observatories
台站代号 台站名 国家 纬度/(°) 经度/(°) BDV Budkov 捷克 49.08 14.02 BEL Belsk 波兰 51.84 20.79 BFO Black Forest 德国 48.331 8.325 FUR Furstenfeldbruck 德国 48.17 11.28 HLP Hel 波兰 54.61 18.82 HRB Hurbanovo 斯洛伐克 47.86 18.19 LON Lonjsko Polje 克罗地亚 45.408 1 16.659 2 NCK Nagycenk 匈牙利 47.63 16.72 PAG Panagjurishte 保加利亚 42.5 24.2 SUA Surlari 罗马尼亚 44.68 26.25 THY Tihany 匈牙利 46.9 17.89 WIC Conrad Observatory 奥地利 47.930 5 15.865 7 WNG Wingst 德国 53.74 9.07 
下载: 导出CSV
表 2 直接平均法计算结果精度统计
Table 2. Precision statistics of calculated results by direct average method
地磁要素 最大值 最小值 平均值 标准差 均方根误差 X/nT 2.61 -9.97 -1.18 3.14 3.35 Y/nT 2.43 -2.24 -0.35 0.93 1.00 Z/nT 2.30 -0.69 0.65 0.74 0.99 F/nT 2.89 -3.17 0.20 1.26 1.27 H/nT 2.37 -9.77 -1.21 3.05 3.28 D/(′) 0.49 -0.37 -0.03 0.19 0.19 I/(′) 0.68 -0.10 0.10 0.20 0.23
下载: 导出CSV
表 3 直接平均法计算结果的相关性系数统计
Table 3. Correlation coefficient statistics of calculated results by direct average method
地磁要素 X Y Z F H D I 相关性系数 0.879 69 0.997 13 0.995 47 0.986 77 0.848 31 0.996 93 0.937 53
下载: 导出CSV
表 4 反距离加权平均法计算结果精度统计
Table 4. Precision statistics of calculated results by reverse distance weighting average method
地磁要素 最大值 最小值 平均值 标准差 均方根误差 X/nT 3.53 -5.60 -0.40 2.17 2.21 Y/nT 2.41 -2.11 -0.43 0.92 1.01 Z/nT 0.80 -0.85 -0.11 0.29 0.31 F/nT 2.07 -1.77 -0.11 0.87 0.88 H/nT 3.39 -5.54 -0.43 2.13 2.17 D/(′) 0.39 -0.33 -0.05 0.16 0.17 I/(′) 0.36 -0.21 0.02 0.14 0.14
下载: 导出CSV
表 5 反距离加权平均法计算结果的相关性系数统计
Table 5. Correlation coefficient statistics of calculated results by reverse distance weighting average method
地磁要素 X Y Z F H D I 相关性系数 0.956 75 0.997 34 0.998 69 0.992 94 0.937 28 0.997 69 0.985 44
下载: 导出CSV
表 6 纬度差加权平均法计算结果精度统计
Table 6. Precision statistics of calculated results by latitude difference weighting average method
地磁要素 最大值 最小值 平均值 标准差 均方根误差 X/nT 3.70 -6.40 -0.48 2.44 2.49 Y/nT 0.73 -2.69 -0.73 0.70 1.01 Z/nT 0.99 -1.21 -0.17 0.40 0.44 F/nT 2.06 -3.73 -0.32 1.18 1.23 H/nT 3.60 -6.65 -0.59 2.48 2.54 D/(′) 0.11 -0.36 -0.10 0.10 0.14 I/(′) 0.41 -0.23 0.03 0.16 0.16
下载: 导出CSV
表 7 纬度差加权平均法计算结果的相关性系数统计
Table 7. Correlation coefficient statistics of calculated results by latitude difference weighting average method
地磁要素 X Y Z F H D I 相关性系数 0.940 16 0.998 68 0.998 07 0.991 34 0.907 08 0.998 72 0.977 54
下载: 导出CSV
表 8 基于方向和距离的双因子定权方法计算结果精度统计(DD1)
Table 8. Precision statistics of calculated results by bifactor weight determination method based on direction and distance (DD1)
地磁要素 最大值 最小值 平均值 标准差 均方根误差 X/nT 4.55 -1.15 0.67 1.34 1.50 Y/nT 2.35 -1.88 -0.46 0.94 1.05 Z/nT 0.60 -0.86 -0.14 0.26 0.29 F/nT 2.34 -1.06 0.15 0.79 0.81 H/nT 4.49 -1.17 0.62 1.35 1.49 D/(′) 0.38 -0.33 -0.05 0.15 0.19 I/(′) 0.08 -0.29 -0.03 0.08 0.09
下载: 导出CSV
表 9 基于方向和距离的双因子定权方法计算结果精度统计(DD2)
Table 9. Precision statistics of calculated results by bifactor weight determination method based on direction and distance (DD2)
地磁要素 最大值 最小值 平均值 标准差 均方根误差 X/nT 4.54 -1.14 0.66 1.34 1.50 Y/nT 0.73 -2.69 -0.73 0.70 1.01 Z/nT 0.50 -0.86 -0.16 0.25 0.30 F/nT 2.34 -1.06 0.15 0.79 0.81 H/nT 4.47 -1.18 0.61 1.35 1.48 D/(′) 0.11 -0.36 -0.10 0.10 0.14 I/(′) 0.08 -0.29 -0.03 0.08 0.09
下载: 导出CSV
表 10 基于方向和距离的双因子定权法计算结果精度统计(DD3)
Table 10. Precision statistics of calculated results by bifactor weight determination method based on direction and distance (DD3)
地磁要素 最大值 最小值 平均值 标准差 均方根误差 X/nT 4.08 -2.86 0.21 1.59 1.61 Y/nT 2.71 -2.03 -0.57 1.08 1.23 Z/nT 0.87 -0.83 -0.10 0.31 0.33 F/nT 2.34 -1.06 0.16 0.79 0.81 H/nT 4.02 -2.76 0.17 1.56 1.57 D/(′) 0.42 -0.34 -0.06 0.17 0.19 I/(′) 0.19 -0.26 -0.01 0.10 0.10
下载: 导出CSV
表 11 基于方向和距离的双因子定权方法计算结果精度统计(DD4)
Table 11. Precision statistics of calculated results by bifactor weight determination method based on direction and distance (DD4)
地磁要素 最大值 最小值 平均值 标准差 均方根误差 X/nT 4.57 -1.11 0.69 1.34 1.51 Y/nT 0.72 -2.69 -0.73 0.70 1.01 Z/nT 0.50 -0.86 -0.16 0.25 0.30 F/nT 2.35 -1.06 0.16 0.79 0.81 H/nT 4.51 -1.14 0.64 1.35 1.49 D/(′) 0.11 -0.36 -0.10 0.10 0.14 I/(′) 0.07 -0.30 -0.03 0.08 0.09
下载: 导出CSV
表 12 基于方向和距离的双因子定权方法计算结果的相关性系数统计
Table 12. Correlation coefficient statistics of calculated results by bifactor weight determination method based on direction and distance
模型 X Y Z F H D I DD1 0.985 24 0.997 61 0.998 76 0.992 92 0.979 06 0.997 72 0.988 66 DD2 0.985 32 0.998 68 0.998 79 0.992 93 0.979 30 0.998 73 0.988 75 DD3 0.982 45 0.997 12 0.998 55 0.992 93 0.973 96 0.997 39 0.991 33 DD4 0.985 08 0.998 68 0.998 79 0.992 95 0.978 86 0.998 73 0.988 46
下载: 导出CSV
表 13 不同方法权因子统计
Table 13. Statistics of weight factors for different methods
方法 X Y Z F H D I 反距离加权平均法 2.35 0.49 3.88 2.21 2.33 1.74 2.39 纬度差加权平均法 25.0 6.13 2.15 4.0 5.73 7.56 1.54 基于方向和距离的双因子定权法 DD1 0/50 1.42/1×10-4 3.29/1×10-4 2.17/1.07 0/50 1.57/1×10-4 0/50 DD2 0/0 0/6.14 7.82/9.98 2.14/1.0 0/0.14 1.53/9.96 0/0 DD3 0/1×10-4 1.43/1×10-4 3.82/1×10-4 1.33/1×10-4 0/1×10-4 1.33/1×10-4 0/1×10-4 DD4 0/0 0/7.87 6.62/9.80 1.19/1.05 0/0 0.45/10.07 0/0
下载: 导出CSV
-
[1] 徐文耀.地磁学[M].北京:地震出版社, 2003.XU W Y.Geomagnetisim[M].Beijing:Seismological Press, 2003(in Chinese). [2] 管志宁.地磁场与磁力勘探[M].北京:地质出版社, 2005.GUAN Z N.Geomagnetic field and magnetic exploration[M].Beijing:Geological Press, 2005(in Chinese). [3] 刘晓刚, 李迎春, 肖云, 等.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[J].测绘学报, 2014, 43(9):881-887. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=chxb201409002LIU X G, LI Y C, XIAO Y, et al.Optimal regularization parameter determination method in downward continuation of gravimetric and geomagnetic data[J].Acta Geodaetica et Cartographica Sinica, 2014, 43(9):881-887(in Chinese). http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=chxb201409002 [4] LIU X G, LI Y C, XIAO Y, et al.Downward continuation of airborne magnetic data based on two iterative regularization methods in frequency domain[J].Geodesy and Geodynamics, 2015, 6(1):34-40. [5] 刘晓刚, 吴娟, 王凯, 等.地磁场空间变化及相关性分析[J].测绘科学与工程, 2018, 38(1):1-7. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=0120181102976606LIU X G, WU J, WANG K, et al.Space changing and correlation analysis of the geomagnetic field[J].Geomatics Science and Engineering, 2018, 38(1):1-7(in Chinese). http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=0120181102976606 [6] 边刚, 刘雁春, 卞光浪, 等.海洋磁力测量中多站地磁日变改正值计算方法研究[J].地球物理学报, 2009, 52(10):1284-1289. http://d.old.wanfangdata.com.cn/Periodical/dqwlxb200910021BIAN G, LIU Y C, BIAN G L, et al.Research on computation method of multi-station diurnal variation correction in marine magnetic surveys[J].Chinese Journal of Geophysics, 2009, 52(10):1284-1289(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/dqwlxb200910021 [7] 边刚, 夏伟, 金绍华, 等.利用最小二乘拟合法进行多站地磁日变基值归算[J].地球物理学报, 2015, 58(4):2613-2618. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=dqwlxb201504016BIAN G, XIA W, JIN S H, et al.Datum reduction with the least squares fitting method in correction of multi-station geomagnetic diurnal variations[J].Chinese Journal of Geophysics, 2015, 58(4):2613-2618(in Chinese). http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=dqwlxb201504016 [8] 卞光浪, 翟国君, 刘雁春, 等.海洋磁力测量中地磁日变站有效控制范围确定[J].地球物理学进展, 2010, 25(3):817-822. doi: 10.3969/j.issn.1004-2903.2010.03.012BIAN G L, ZHAI G J, LIU Y C, et al.Effective operating range of base stations in marine geomagnetic survey[J].Progress in Geophysics, 2010, 25(3):817-822(in Chinese). doi: 10.3969/j.issn.1004-2903.2010.03.012 [9] 刘晓刚, 李晓燕, 吴娟, 等.郑州嵩山地磁台站建站可行性分析[J].测绘科学与工程, 2017, 37(5):21-27. http://www.cqvip.com/QK/93330B/201705/673962255.htmlLIU X G, LI X Y, WU J, et al.Feasibility analysis of the construction of Songshan mountain geomagnetic station in Zhengzhou[J].Geomatics Science and Engineering, 2017, 37(5):21-27(in Chinese). http://www.cqvip.com/QK/93330B/201705/673962255.html [10] 顾春雷, 张毅, 徐如刚, 等.基于虚拟日变台进行地磁矢量数据日变通化方法[J].地球物理学报, 2013, 56(3):834-841. http://d.old.wanfangdata.com.cn/Periodical/dqwlxb201303012GU C L, ZHANG Y, XU R G, et al.The method of geomagnetic diurnal correction to vector geomagnetic data by virtual diurnal variation station[J].Chinese Journal of Geophysics, 2013, 56(3):834-841(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/dqwlxb201303012 [11] 郭建华, 薛典军.多台站磁日变校正方法研究及应用[J].地球学报, 1999, 20(增刊):932-937. http://d.old.wanfangdata.com.cn/Conference/42572GUO J H, XUE D J.The application and method research of magnetic diurnal calibration based on multi-station[J].Acta Geoscientia Sinica, 1999, 20(Sup.):932-937(in Chinese). http://d.old.wanfangdata.com.cn/Conference/42572 [12] 边刚, 刘雁春, 翟国君.一种确定地磁日变改正基值的方法[J].海洋测绘, 2003, 23(5):9-11. doi: 10.3969/j.issn.1671-3044.2003.05.003BIAN G, LIU Y C, ZHAI G J.A method to determine the correction datum of the geomagnetic diurnal variation[J].Hydrographic Surveying and Charting, 2003, 23(5):9-11(in Chinese). doi: 10.3969/j.issn.1671-3044.2003.05.003 [13] 卞光浪, 刘雁春, 翟国君, 等.海洋磁力测量中多站地磁日变改正基值归算[J].海洋测绘, 2009, 29(6):5-8. doi: 10.3969/j.issn.1671-3044.2009.06.002BIAN G L, LIU Y C, ZHAI G J, et al.Base value reduction methods with multi-station diurnal variation correction in marine magnetic survey[J].Hydrographic Surveying and Charting, 2009, 29(6):5-8(in Chinese). doi: 10.3969/j.issn.1671-3044.2009.06.002 [14] YANG Y X, SONG L J, XU T H.Robust estimator for correlated observations based on bifactor equivalent weights[J].Journal of Geodesy, 2002, 76(6-7):353-358. doi: 10.1007/s00190-002-0256-7 [15] 黄维彬.近代平差理论及其应用[M].北京:解放军出版社, 1992.HUANG W B.Modern adjustment theory and its application[M].Beijing:PLA Press, 1992(in Chinese). [16] 隋立芬, 宋力杰.误差理论与测量平差基础[M].北京:解放军出版社, 2004.SUI L F, SONG L J.Basis of error theory and observation adjustment[M].Beijing:PLA Press, 2004(in Chinese). [17] 盛骤, 谢式千, 潘承毅.概率论与数理统计[M].北京:高等教育出版社, 1979.SHENG Z, XIE S Q, PAN C Y.Probability and mathematical statistics[M].Beijing:Higher Education Press, 1979(in Chinese). [18] 吴翊, 李永乐, 胡庆军.应用数理统计[M].长沙:国防科技大学出版社, 1995.WU Y, LI Y L, HU Q J.Application mathematical statistics[M].Changsha:National University of Defense Technology Press, 1995(in Chinese). -
下载:
点击查看大图
计量
- 文章访问数: 556
- HTML全文浏览量: 29
- PDF下载量: 374
- 被引次数: 0
