Fusion of Ground and Airborne Magnetic Data Using Multi-Layer Equivalent Source Method
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摘要: 随着地磁场观测数据的不断积累，高效利用观测数据成为亟待解决的问题.以往研究表明，仅对单一观测手段获得的实测数据进行分析与解释，往往很难达到目前解决相关地质问题的精度要求.因为各观测方法获得的地磁场数据集通常在分辨率、精度、高程及覆盖范围方面存在局限性和差异性，造成单一数据集仅能有效表征地磁场某一频段信息的问题.而解决该问题的一种有效途径是数据间的融合.为此，基于等效源方法，提出一种多层等效源技术方案，应用于航空和地面磁测数据融合，提高地面数据插值补空、扩边及航空数据下延的精度.该方法针对观测信息的频谱特征，采用3个位于不同深度的等效源层模拟实测数据；较传统的单层等效源方法，减少了等效源设置的盲目性，增强了观测信息在等效源模型中分配的有序性和结构性.理论实验表明，多层等效源模型设置具有更高的计算精度，航空与地面磁测数据融合可以起到显著的相互丰富及改善的作用.最后，将该方法应用于湖北金牛火山岩盆地航空与地面磁测数据融合，获得了丰富的、平面上规则分布的地磁场数据.Abstract: With the accumulation of measured magnetic data, it is becoming urgent to use these data efficiently. Previous studies have shown that it is difficult to meet the accuracy requirement for solving geological problems by using the measured data from a single observation method. Because of the limitations and differences in resolution, accuracy, elevation and range of magnetic data obtained by various methods, single dataset can only effectively reflect the information over a certain range of wavelength of magnetic field. An effective way to solve this problem is the fusion of data. Therefore, based on the equivalent source method, a multi-layer equivalent source technology is proposed in this paper, which can be applied to the fusion of ground and airborne magnetic data to improve the accuracy of interpolation, continuation, extension, transformation, et al. According to the spectral characteristics of observation data, three-layer equivalent sources at different depths are used to fit the measured data. Compared with the traditional single-layer equivalent source method, it can reduce the blindness for setting equivalent sources, and improve the ordering and structural performance for allotting observation information into equivalent sources. Synthetic experiment shows that the three-layer model has higher computational accuracy, and data fusion can significantly improve each dataset. Finally, the method is applied to the fusion of ground and airborne magnetic data in Jinniu basin, Hubei, and abundant magnetic data with regular distribution on a plane are obtained.
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Key words:
- data fusion /
- multi-layer equivalent source /
- interpolation /
- extension /
- data transformation /
- geophysics
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图 1 三层等效源模型示意图
RLPS表示径向对数功率谱估算；zf, zs, zt分别表示3个等效源层中心埋深
Fig. 1. Three-layer equivalent source model
图 2 理论模型及其地面上观测ΔT磁异常
a.组合模型；b.地形高程（红框为地面观测范围）；c.模拟地面观测ΔT磁异常
Fig. 2. Synthetic models and their theoretical ΔT anomaly on ground
图 3 不同高度正演ΔT磁异常(a~c)和磁异常梯度正演结果(d~i)以及磁场分量正演结果(j~o)
a，b，c分别为地面、350 m和500 m高度平面上ΔT计算结果；d~f为地面上磁异常梯度计算结果；g~i为350 m高度平面上相应计算结果；j~l为地面上磁场三分量计算结果；m~o为350 m高度平面上相应计算结果
Fig. 3. Theoretical ΔT anomaly at different elevations (a-c), theoretical magnetic gradients (d-i) and theoretical components (j-o) on ground and plane at 350 m
图 4 理论模拟地面与航空磁异常对数功率谱曲线
图中红色与蓝色直线为对数功率谱曲线分段拟合线；a，b分别为地面与航空磁测数据计算曲线
Fig. 4. Radial logarithmic power spectrum of observed magnetic data
图 5 等效源单元磁场响应随埋深变化的衰减曲线
a.对应200 m×200 m×600 m等效源单元；b.对应2 000 m×2 000 m×6 000 m等效源单元
Fig. 5. Magnetic attenuation with depths of equivalent source cells
图 6 三种方法计算ΔT磁异常与理论值绝对误差
a~c分别为单层、三层等效源方法与傅里叶‒克里金方法在地面上的计算结果与理论值差值；d~f分别为350 m高度平面上对应差值
Fig. 6. Distribution of absolute errors between the computational ΔT and theoretical values
图 7 单层与三层等效源方法计算磁异常梯度与理论值绝对误差
a~c与d~f分别为单层与三层等效源方法在地面上计算（ΔTx, ΔTy, ΔTz）与理论值差值；g~i与j~l分别是单层和三层等效源方法在350 m高度平面上对应差值
Fig. 7. Distribution of absolute errors between the computational magnetic gradients and theoretical values
图 8 单层与三层等效源方法计算磁场分量与理论值绝对误差
a~c与d~f分别为单层与三层等效源方法在地面上计算（Hax, Hay, Za）与理论值差值；g~i与j~l分别是单层和三层等效源方法在350 m高度平面上对应差值
Fig. 8. Distribution of absolute errors between the computational components and theoretical values
图 9 实测地面及航空ΔT磁异常
a.地形高程；b.地面实测ΔT磁异常；c.航空测量ΔT磁异常
Fig. 9. Measured ΔT anomaly and elevation
图 10 实测地面与航空磁异常对数功率谱曲线
图中红色与蓝色直线为对数功率谱曲线分段拟合线；a，b分别为地面与航空磁测数据计算曲线
Fig. 10. Radial logarithmic power spectrum of observed magnetic data
图 11 计算结果与观测数据拟合差以及288 m高度平面上ΔT计算结果
a.恢复地面磁测数据拟合差；b.恢复航空磁测数据拟合差；c.计算ΔT
Fig. 11. Difference between calculation ΔT and observation values and computational ΔT on the plane at 288 m
图 12 288 m高度平面上磁异常梯度及磁场分量转换结果
a~c分别为转换ΔTx，ΔTy与ΔTz；d~f分别为转换Hax，Hay与Za
Fig. 12. Transformations on the plane at 288 m
表 1 理论模型参数
Table 1. Parameters of synthetic models
模型体 中心埋深
(m)磁化强度
A·m-1）磁化方向 1 1 000 1.5 倾角I=45°
偏角A=5°2 900 2 3 1 600 2.5 4 4 000 4 5 5 500 3 6 6 500 5 
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表 2 理论模型试验等效源层参数
Table 2. Parameters of equivalent source layers of the theoretical model
层号 单元体几何参数
(长×宽×高)(m)等效层顶面深度 展布形态 1 200×200×200 距地表600 m 随地形起伏 2 200×200×600 距0 m平面2 500 m 水平 3 2 000×2 000×6 000 距0 m平面5 500 m 水平
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表 3 实测数据应用等效源层参数
Table 3. Parameters of equivalent source layers of the actual application
层号 单元体几何参数
(长×宽×高)(m)等效层顶面深度 展布形态 1 200×200×200 距地表200 m 随地形起伏 2 200×200×600 距0 m平面2 600 m 水平 3 2 000×2 000×6 000 距0 m平面6 000 m 水平
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