Ratio Method for Calculating the Source Location of Gravity and Magnetic Anomalies Based on Deep Learning
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摘要: 场源中心位置的计算是重磁数据反演的主要任务之一，现主要通过异常与场源位置之间的数学物理方程来估算地质体的位置.为了快速、准确获得地质体的位置信息，提出基于重磁梯度比值的深度学习技术实现场源位置的获取；其利用深度学习技术所建立的重磁梯度比值水平分布与地质体埋深、构造指数的关系，快速实现异常场源位置计算，且提出利用多个值的相互关系来更加准确、稳定地计算出地质体的信息.该方法可以计算复杂地质体的中心位置，且避免了以往线性方程反演方法需对结果进行筛选的复杂过程，对于存在剩磁的磁异常则采用解析信号的深度学习方法来进行位置反演.理论模型试验证明利用梯度比值的深度学习方法可以准确获得地质体的深度，且通过对比更多点的深度学习计算结果发现，采用多个不同比例极值点可以减弱噪声带来的干扰，从而得到更加准确的位置.最后将该方法应用于实测磁异常的反演工作，获得了地下磁性物体的中心位置，且计算结果与欧拉反褶积法相接近，因此该方法具有良好的实用性.Abstract: The location of field source's center is one important purpose in the inversion of gravity and magnetic data, and the location of geological body is estimated mainly through the linear equation between the anomaly and the location of the field source. In order to obtain the location accurately and quickly, a deep learning technique based on the ratio of gravity and magnetic gradient is proposed to achieve the acquisition of the field source location in this paper, which can calculate the field source location quickly by using the deep learning technique to learn the relationship between the horizontal distribution of the gravity and magnetic gradient ratio, the buried depth, and the index. It is also proposed to use the mutual relationship of multiple values to calculate the information of the geological body more accurately and stably. This method can calculate the center location of complex geological bodies, and avoid the complicated process of screening the results of the previous methods, using the deep learning method of analytic signal for magnetic anomaly with remanent magnetism to achieve the location inversion. The application effect of the method is tested by theoretical models, which shows that the proposed method can obtain the depth information of the geological body accurately. Comparing the calculation results of the deep learning of more points, it is found that the use of multiple extreme points of different proportions can reduce the interference by noise and can get a location more accurately, so the method has good practicability.
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Key words:
- gravity magnetic source /
- center location /
- ratio /
- deep learning /
- geophysics
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图 3 深度学习方法与传统方法水平结果对比
a. 原始重力异常；b. 梯度比值计算原始重力异常的水平位置；c. 欧拉反褶积(N=2)计算原始重力异常的水平位置；d. 含有0.5 mGal的背景场的原始重力异常；e. 梯度比值计算原始重力异常的水平位置；f. 欧拉反褶积(N=2)计算原始重力异常的水平位置. 图b、c、e、f中▼代表理论位置，●代表计算位置
Fig. 3. Comparison of the horizontal position calculated by deep learning methods and traditional methods
图 4 不同组合梯度比值极值点的深度学习法与传统欧拉反褶积法水平结果对比
a. 叠加20%高斯白噪声的重力异常；b. 叠加50%高斯白噪声的重力异常；c. 叠加70%高斯白噪声的重力异常；d. 1/2、1/3极值点联合计算叠加20%高斯白噪声的重力异常的水平位置；e. 1/2、1/3极值点联合计算叠加50%高斯白噪声的重力异常的水平位置；f. 1/2、1/3极值点联合计算叠加70%高斯白噪声的重力异常的水平位置；g. 1/2、1/10极值点联合计算叠加20%高斯白噪声的重力异常的水平位置；h. 1/2、1/10极值点联合计算叠加50%高斯白噪声的重力异常的水平位置；i. 1/2、1/10极值点联合计算叠加70%高斯白噪声的重力异常的水平位置；j. 欧拉反褶积计算叠加20%高斯白噪声的重力异常的水平位置；k. 欧拉反褶积计算叠加50%高斯白噪声的重力异常的水平位置；l. 欧拉反褶积计算叠加70%高斯白噪声的重力异常的水平位置. 图d~l中▼代表计算理论位置，●代表计算位置
Fig. 4. Comparison of the horizontal position calculated by different combination of gradient ratio's deep learning methods and traditional methods
图 5 不同组合梯度比值极值点的深度学习法计算结果
a. 1/2、1/5、1/10极值点联合计算叠加20%高斯白噪声的重力异常的水平位置；b. 1/2、1/5、1/10极值点联合计算叠加50%高斯白噪声的重力异常的水平位置；c. 1/2、1/5、1/10极值点联合计算叠加70%高斯白噪声的重力异常的水平位置；d. 1/2、1/3、1/5、1/10极值点联合计算叠加20%高斯白噪声的重力异常的水平位置；e. 1/2、1/3、1/5、1/10极值点联合计算叠加50%高斯白噪声的重力异常的水平位置；f. 1/2、1/3、1/5、1/10极值点联合计算叠加70%高斯白噪声的重力异常的水平位置；g. 不同噪声、不同极值点组合深度学习计算理论深度为3m的地质体的深度；h. 不同噪声、不同极值点组合深度学习计算理论深度为8 m的地质体的深度；i. 不同噪声、不同极值点组合深度学习计算的构造指数. 图a~f中▼代表理论位置，●代表计算位置
Fig. 5. The deep learning's results calculated by combination of gradient ratio's different extreme value point
图 6 深度学习方法计算结果
a. 原始磁异常；b. 异常的解析信号；c. 原始磁异常化极后，基于梯度比值的1/2、1/5、1/10极值点联合计算结果的水平位置；d. 对原始磁异常化极，基于梯度比值的1/2、1/5、1/10极值点联合计算结果的深度；e. 对于解析信号，基于梯度比值的1/2、1/5、1/10极值点联合计算结果的水平位置；f. 对于解析信号，基于梯度比值的1/2、1/5、1/10极值点联合计算结果的深度. 图c~f中▼代表理论位置，●代表计算位置
Fig. 6. The deep learning's results
图 7 磁测区域的磁异常等值线与异常解析信号的等值线
a. 该地区磁测异常等值线；b. 该地区磁异常的解析信号的等值线
Fig. 7. The contour of magnetic anomaly and magnetic anomaly's analytical signal
图 8 多极值点深度学习与传统欧拉反褶积对比
a. 梯度比值的1/2、1/5和1/10比例极值点深度学习法计算的炸弹水平位置；b. 欧拉反褶积法计算结果；c. 欧拉反褶积与多极值联合法计算得到的深度，■代表欧拉反褶积的计算结果，▲代表多极值联合法计算的结果
Fig. 8. Comparison of the result calculated by deep learning methods and traditional methods
表 1 不同深度下，深度学习在有无剩磁的埋深计算对比
Table 1. Depth calculated by deep learning at different theoretical depth
地质体理论埋深(m) 化极后计算深度(m) 解析信号计算深度(m) 5.0(1)、7.0(2) 5.1(1)、7.2(2) 5.3(1)、7.4(2) 5.5(1)、7.5(2) 5.6(1)、7.7(2) 5.2(1)、7.9(2) 6.0(1)、8.0(2) 6.3(1)、8.2(2) 6.4(1)、8.4(2) 6.5(1)、8.5(2) 6.8(1)、8.3(2) 6.9(1)、8.9(2) 注：括号中数字代表不同地质体的序号. 
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表 2 深度学习模型与欧拉反褶积法识别炸弹的深度
Table 2. Bomb depth calculated by deep learning model and Euler deconvolution
序号 比值深度学习计算深度(m) 欧拉反褶积计算埋深(m) 构造指数 1 5.1 5.8 2.7 2 2.9 3.5 2.8 3 3.1 2.6 3.1 4 3.5 3.0 3.2 5 3.2 2.6 4.3 6 4.5 4.0 3.0 7 2.9 3.0 2.8 8 3.3 3.3 3.6 9 5.1 5.3 3.5 10 4.5 4.7 3.6 11 2.5 3.9 2.9 12 4.4 4.0 4.0 13 3.7 2.7 4.0 14 3.5 3.3 3.1
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