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通过数据拟合建立区域地磁场模型时,一般都存在截断阶数的选取与边界效应的控制问题。针对常用的Taylor多项式模型和Legendre多项式模型,结合中国地区1960、1970、1990和2000年的实测地磁数据,分别研究了两种问题的解决方案。首先计算模型的均方根偏差(RMSE)可初步确定截断阶数的选取范围,再计算AKAIKE信息标准值(AIC)与标准均方根偏差(NRMSE)并进行比较,可确定合适的截断阶数。通过异常区域添加法(首次提出)与均匀添加法逐次添加境外补充点,发现随着补充点的增加,境外磁异常极值点强度逐步减少并趋于稳定。均匀添加法能够更好地控制中国地区的边界效应,而异常区域添加法更适合处理小尺度地区的边界效应。根据结果,提出了三步法以确定截断阶数,还提出了两个准则以基本确定补充点的数量,从而可较好地控制边界效应。
When using the data fitting to establish the regional geomagnetic field model, the selection of truncation order and the control of boundary effect generally exist. For the commonly used Taylor polynomial model and Legendre polynomial model, combined with the measured geomagnetic data of China in 1960, 1970, 1990 and 2000, the solutions to the two problems were studied respectively. First calculate the root mean square deviation (RMSE) of the model to initially determine the selection of truncation order, and then calculate and compare the AKAIKE information standard value (AIC) with the standard root mean square deviation (NRMSE) to determine the appropriate truncation order . Through the addition of abnormal region (first proposed) and uniform addition method, the overseas supplementary points were added one after another. It was found that with the increase of supplementary points, the intensity of extreme magnetic anomalies abroad gradually decreased and stabilized. The uniform addition method can better control the boundary effect in China, while the abnormal area addition method is more suitable to deal with the boundary effect in the small-scale area. According to the results, a three-step method is proposed to determine the truncation order. Two criteria are also proposed to basically determine the number of complementary points so that the boundary effect can be controlled well.