Characteristics and Applications of Variogram for Gravity and Magnetic Fields
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摘要: 用变差函数研究重磁场的区域变化特征.变差函数的变程反映重磁场的相干范围, 块金效应反映随机干扰, 基台值反映变异程度.重磁场的理论模拟说明: 重力场的相干范围大于磁场, 重磁场变程主要取决于场源深度, 浅源重磁场变差函数近似为球状模型或指数模型, 深源重磁场近似为连续性更好的高斯模型.磁场场源深度近似等于变程的一半, 重力场场源深度近似等于变程的四分之一.湖北大冶铁矿垂直分量磁异常具有几何各向异性, 北西-南东走向, 变差函数推测磁铁矿平均深度为250m.磁异常小波多尺度分解细节和逼近部分磁场具有协调几何各向异性, 变差函数的各阶场源深度估计结果与功率谱估计结果吻合.Abstract: The variogram is used to investigate the regional variation characteristics of gravity and magnetic fields in this study. The range of variogram reflects the coherent area; the nugget effect represents the random disturbance; and the sill means the variation degree. The theoretical simulations involving gravity and magnetic fields show that the coherent range of gravity field is larger than that of magnetic field. The range of potential gravity and magnetic field is mainly determined by the depth of field sources. The variogram for shallow sources is approximate to be a spherical or exponential model, while with the increase of the depth, it nearly becomes a more continuously Gaussian model. The depth of magnetic source is approximately equal to the half of the range, whereas the depth of gravity source is approximately equal to one quarter of the range. The real example of the vertical component magnetic anomaly of the Daye iron-ore deposit in Hubei has geometric anisotropy striking northwest-southeast direction. The variogram reveals that the average depth of magnetite orebodies is about 250m. The decomposed details and approximations of magnetic anomaly using wavelet transform have the coordinate geometric anisotropy. And the estimated depths using variogram ranges are in agreement with those gained by power spectrum method.
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Key words:
- gravity and magnetic fields /
- variogram /
- range /
- nugget effect /
- sill /
- Daye iron-ore deposit /
- geostatistics
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图 1 变差函数示意(a)及3种常见的变差函数模型(b)
Fig. 1. The diagram of variogram (a) and three popular variogram models (b)
图 2 直立长方体模型的磁场及其变差曲线
Fig. 2. The magnetic fields of cuboid model and the variogram curves
图 3 含噪声磁场的变差函数
a.高斯噪声；b.含高斯噪声的磁场；c.高斯噪声的变差函数；d.含高斯噪声的磁场的变差函数
Fig. 3. Variogram of magnetic field containing gaussian noise
图 4 不同深度球体模型的磁场的变差函数
a.深度=100m；b.深度=200m；c.深度=300m；d.深度=400m；e.深度=500m；f.深度=600m
Fig. 4. Variograms of magnetic fields of sphere models located at different depths
图 5 不同深度球体模型的重力场的变差函数
a.深度=100m；b.深度=200m；c.深度=300m；d.深度=400m；e.深度=500m；f.深度=600m
Fig. 5. Variograms of gravity fields of sphere models located at different depths
图 6 湖北大冶铁矿ΔZ磁异常(a)及其变差函数(b)
Fig. 6. ΔZ magnetic anomaly (a) and its variogram (b) of the Daye iron-ore deposit, Hubei
图 7 湖北大冶铁矿ΔZ磁异常小波多尺度分解
a.一阶细节；b.二阶细节；c.三阶细节；d.四阶细节；e.五阶细节；f.五阶逼近
Fig. 7. Wavelet multi-scale decomposition of ΔZ magnetic anomaly of the Daye iron-ore deposit, Hubei
图 8 湖北大冶铁矿地面ΔZ磁异常小波多尺度分解细节和逼近部分的变差函数
Fig. 8. Variograms of the details and approximations of the ΔZ magnetic anomaly using wavelet multi-scale decomposition of the Daye iron-ore deposit, Hubei
图 9 湖北大冶铁矿ΔZ磁异常小波多尺度分解各阶细节在各个方向的变差函数变程
Fig. 9. Variogram ranges at different directions of the details of the ΔZ magnetic anomalies using wavelet multi-scale decomposition of the Daye iron-ore deposit, Hubei
表 1 磁场与重力场变差函数变程估计场源的深度结果
Table 1. Estimated depths of field sources using variogram ranges of gravity and magnetic fields
真实深度(m) 100 200 300 400 500 600 磁场估计深度(m)(I=45°) 110.0 199.8 294.4 416.0 525.0 572.1 磁场估计深度(m)(I=90°) 110.0 199.8 294.4 430.4 534.0 574.2 重力场估计深度(m) 99.5 208.0 277.5 395.0 508.0 548.8 
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表 2 变差函数估计的场源深度与功率谱估计的场源深度结果对比
Table 2. Comparisons of estimated depths using variogram and power spectrum
小波分解 D1 D2 D3 D4 D5 A5 功率谱估计深度(m) 26 144 235 488 912 912 变差函数估计深度(m) 60.7 155.5 250.7 432.0 917.3 ＞1000
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表 3 ΔZ磁异常小波分解细节和逼近在不同方向的变差函数变程
Table 3. Variogram ranges at different directions of the details and approximations of ΔZ magnetic anomalies using wavelet multi-scale decomposition
小波分解 东-西 北东-南西 南-北 北西-南东 D1 160 160 180 200 D2 340 260 280 400 D3 520 460 480 520 D4 920 820 780 820 D5 1880 1600 1720 1880 A5 - - - -
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