Bifactor weight determination method based on direction and distance in geomagnetic data assimilation
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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.
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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 
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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