探索性GPS全球电离层TEC数据分析
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中国科技论文在线
探索性 GPS 全球电离层 TEC 数据分析
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秦昆，彭军还
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基金项目：科技部 863 项目（2012AA121303）；国家自然科学基金（41074009, 40674015）；教育部博士
点学科基金（20100022110008）；国家自然科学基金青年科学基金（41304012，41104025）；大地测量与
地球动力学国家重点实验室基金（SKLGED2013-4-8-E）；国家基础测绘（201305）
作者简介：秦昆（1987-），女，博士研究生，主要研究方向：空间数据挖掘与分析
通信联系人：彭军还（1964-），男，教授，主要研究方向：空间数据处理. E-mail: pengjunhuan@163.com
（中国地质大学（北京）土地科学技术学院，北京 100083）
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摘要：本文应用空间统计学方法对 IGS 中心发布的全球电离层 TEC 数据进行挖掘并做出分
析。通过分析全球 TEC 数据的三维图、频率直方图、半变异函数并计算均值、中位数、偏
度、峰度等统计量，揭示 TEC 数据的空间分布呈非平稳性；其全局趋势用球谐函数描述，
采用最小二乘拟合，根据残差的统计特征确定 9 次球谐函数为最适合的全局趋势；对去掉趋
势后的残差，通过半变异函数进行结构分析，变异函数并不满足平稳性。通过经度方向一次10
差分、纬度方向二次差分后的残差分析，呈现几乎无空间相关性的独立噪声空间过程，说明
局部变化呈现非平稳的三阶偏随机游动。差分后的误差标准差从 9.221TECU 降低至
1.175TECU。同时，用基于 Delaunay 三角网的自然邻域方法对 TEC 数据进行空间异常（斑
点噪声）探测，并分析其空间分布，得出 TEC 数据的斑点噪声呈单调下降趋势。对不同历
元的 TEC 数据，可由同样的混合模型描述，即电离层 TEC 呈现由球谐函数描述的全局趋势，15
局部（或小尺度）变化呈现 3 阶非平稳偏随机游动，并受服从单点下降的斑点噪声扰动。
关键词：地图制图学与地理信息工程；GPS TEC；变异函数；球谐函数；偏随机游动；空间
异常
中图分类号：P352.7
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Exploratory GPS Global Ionospheric TEC analysis
QIN Kun, PENG Junhuan
(School of Land Science and Technology,China University of Geoscience(Beijing),Beijing
100083)
Abstract: In this paper we apply spatial statistics for mining and analyzing global ionospheric 25
TEC data published by IGS center. The spatial non-stationary property of the global TEC is
discovered by analyzing three-dimensional map, histogram, semivariogram and counting the
statistics such as mean, median, skewness, kurtosis, etc. The global trend surface of TEC can be
modeled by the Spherical Harmonics and 9-order is the most suitable by comparing residuals’
statistical characteristics after least-squares fitting. After removing the trend, the semivarigram of 30
the residuals doesn’t show stationary character. After doing second-order difference in
longitudinal direction and then doing first-order difference in latitudinal direction, the residual
result shows the white noise property, and which indicates the local and/or small scale of variation
is a three order of partial random walking spatial process. And after three order’s difference,
error’s standard deviation decreased from 9.221TECU to1.175TECU .At the same time, spatial 35
outliers (speckle noises) are detected on TEC data by using the nearest neighbor method based on
the Delaunay triangulation and its spatial statistical distribution is found obeying monotonic
decreasing. For the TEC data obtained at different epoch, its spatial distribution can be describe
with the fore-mentioned mixed model including global trend, local variation and abnomaly, that
is, the TEC global trend surface can be fitted by the Spherical Harmonics, and the local (small 40
scale)change can be described with the three-order of partial random walk process, also disturbed
by speckle noises obeying monotonic decreasing.
Key words: Cartography and Geographic Information Engineering;
GPS-TEC;Semivariogram;Spherical Harmonics;Partial random walk;Spatial outlier
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