Boundary Compensation Approach in Geomagnetic Map Preparation Based on BEMD
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摘要: 针对采用矩谐分析方法构建地磁基准图的边界震荡问题, 提出一种基于二维经验模态分解的区域地磁异常数据边界补偿方法.采用二维经验模态分解方法对区域地磁异常数据进行多尺度分解, 对分解所得小尺度本征模态函数分量, 利用总体Hilbert变换法进行瞬时频率和瞬时幅值特征提取, 通过自采样和特征匹配进行边界补偿; 将大尺度分量之和作为趋势项, 利用三角函数方法建立模型并计算边界之外的大尺度磁异常值.实验证明, 相比当前已有方法, 可以更加有效地抑制对区域地磁异常数据进行矩谐分析的边界震荡问题, 稳定提高构建地磁基准图的准确性.Abstract: A boundary compensation method based on bi-dimensional empirical mode decomposition (BEMD) is proposed in this paper to address the boundary effect in preparation of geomagnetic navigation reference map. The local geomagnetic anomaly data are firstly decomposed into components with different scales with BEMD; then for small scale ones instant amplitude and frequency are computed with total Hilbert transform, and the boundary is compensated with self-sampling and feature-matching; whereas for the large scale ones, trigonometric function model is conducted and used to compute the values outside the boundary. After the compensation of local dataset, rectangular harmonic model is used to prepare geomagnetic map. Experimental results indicate that BEMD method could better compress the boundary effect of rectangular harmonic analysis, and improve the mapping precision steadily in comparison with other existing methods.
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图 4 不同区域矩谐分析边界震荡
Fig. 4. Boundary effect of rectangular harmonic analysis in different areas
图 6 本征模态函数分量及趋势项补偿结果
红色框内为补偿前数据
Fig. 6. Composition results of intrinsic mode functions and tendency item
图 7 实验区域采用不同方法边界补偿后的边界震荡问题对比
Fig. 7. Comparison of experimental areas' boundary effect after compensation with different methods
表 1 不同方法边界补偿效果对比
Table 1. Comparison of different compensation methods
数据编号 A B C 原始边界震荡 37.527 48.425 34.753 Malin et al.(1996)方法 28.639 34.739 26.331 李明明等(2010)方法 25.815 32.121 24.727 乔玉坤等(2010b)方法 36.703 46.308 32.562 本文方法 19.318 24.643 18.248 注：单位为nT. 
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