反距离权重插值与克里金插值在冀鲁豫交界区地磁场数据分布中的对比研究

Comparison of Inverse Distance Weighting and Kriging Interpolation in the Distribution of Geomagnetic Field Data in Juncture Area of Hebei, Shandong and Henan

摘要: 为提升冀鲁豫交界地区(35.5˚N~37.5˚N, 113.5˚~116.5˚E)地磁场总强度空间分布的刻画精度，本文基于2025年4月35个地磁测点的总强度日变通化数据，系统对比了克里金插值(Kriging)与反距离权重插值(IDW)的空间建模性能。通过交叉验证法计算残差，结合平均绝对误差(MAE)、均方根误差(RMSE)和确定系数(R²)定量评估精度。结果表明：两种方法均呈现地磁场强度西北高、东南低的趋势，但IDW对局部极值(如孤立峰谷)表现更突出，而Kriging结果更平滑；Kriging的MAE (80.66 nT)、RMSE (94.65 nT)显著低于IDW (MAE = 127.30 nT, RMSE = 159.27 nT)，且R²更高(0.90 > 0.71)，表明其模型拟合度更优；IDW残差离散性强(−357.68~388.93 nT)，存在明显区域偏移；Kriging残差分布集中(−200~200 nT)，近似正态分布，验证其更有效捕捉空间相关性。综上，在冀鲁豫地区地磁场建模中，克里金插值精度与可靠性优于反距离权重插值，可为区域磁异常识别和深部构造研究提供更可靠的数据基础。未来需进一步优化插值参数并拓展多方法对比。

Abstract: To improve the precision of spatial distribution characterization of the geomagnetic total intensity in the juncture area of Hebei, Shandong and Henan (35.5˚N~37.5˚N, 113.5˚E~116.5˚E), this study systematically compares the spatial modeling performance of Kriging interpolation and Inverse Distance Weighting (IDW) interpolation based on the total intensity diurnal variation data from 35 geomagnetic measurement points in April 2025. Cross-validation is used to calculate residuals, and the accuracy is quantitatively evaluated using Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Coefficient of Determination (R²). The results show that both methods exhibit a trend of higher geomagnetic intensity in the northwest and lower in the southeast. However, IDW highlights the local extrema better (e.g., isolated peaks and valleys), while Kriging results are smoother. Kriging has significantly lower MAE (80.66 nT) and RMSE (94.65 nT) compared to IDW (MAE = 127.30 nT, RMSE = 159.27 nT), with a higher R² (0.90 > 0.71), indicating better model fitting. IDW residuals show strong dispersion (−357.68~388.93 nT) with obvious regional shifts, whereas Kriging residuals are concentrated (−200~200 nT) and approximately normally distributed, validating its better capture of spatial correlation. In conclusion, Kriging interpolation demonstrates higher precision and reliability than IDW for geomagnetic modeling in the juncture area of Hebei, Shandong and Henan, providing a more reliable data foundation for regional magnetic anomaly identification and deep structural studies. Future work should focus on optimizing interpolation parameters and expanding multi-method comparisons.