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The research of the regularization method in the ratio methods of edge recognition by potential field |
Tao HE1,2,3, Wan-Yin WANG1,2,3, Jin-Ming HUANG4, Ming-Hua ZHANG4, Min YANG1,2,3,5 |
1. Gravity & Magnetic Institute of Chang’an University,Xi’an 710054,China; 2. College of Geology Engineering and Geomatics,Chang’an University,Xi’an 710054,China; 3. Key Laboratory of Western China’s Mineral Resources and Geological Engineering,Ministry of Education,Chang’an University,Xi’an 710054,China; 4. China Geological Survey Development Research Center, Beijing 100037, China 5. Department of Earth Sciences, Memorial University of Newfoundland, St. Johns, NF, Canada |
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Abstract The ratio methods are one sort of edge recognition methods by using potential field, which contains the Normalized Standard Deviation method (NSTD), Tilt Angle method (Ta) and Theta Map (cosθ). If the denominator of ratio method closes or even equals to zero in the process of calculation, the result obtaining from ratio methods is unstable and may even bear little resemblance to the true geology. In order to relief this problem, a regularization factor, which is greater than zero, is added in the denominator of the ratio methods’ formula, which not only enhances the numerical stability of the ratio methods but also improves the accuracy of some ratio edge recognition methods. The stability, accuracy and effectiveness of the new method is verified by testing synthetic models and calculating real data. Also, the introduction of the regularization factor also can improve the effect of recognizing edge by the second-derivative edge recognition methods, which is based on the ratio methods, such as the Total Horizontal Derivative of the Tilt Angle (Ta-THDR). The idea of regularization can not only solve the numerical calculation problem of the ratio methods of edge recognition for potential field, but also solve the numerical calculation problem of all ratio methods.
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Received: 03 December 2018
Published: 15 April 2019
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| 模型类别 | 形体个数 | 长/m | 宽/m | 埋深/m | 间隔/m | 模型设计目的 | 模型A | 重力模型 | 1 | 160 | 80 | 10~50 | | 测试比值类方法加入正则 化因子后的适用性 | 模型B | 重力模型 | 2 | 160 | 90 | 10~50 | | | 20 | 测试比值类方法加入正则化 因子后,对于横向分辨率 的影响 | 160 | 90 | 10~50 | | 模型C | 重力模型 | 3 | 160 | 40 | 10~50 | | | 90 | 测试比值类方法加入正则 化因子后,对于不同埋深地 质体边缘识别的影响 | 160 | 40 | 25~65 | | | 160 | 40 | 40~80 | | | 模型D | 磁力模型 | 1 | 160 | 80 | 10~50 | | 测试比值类方法加入正则化因子 后,对于磁力异常的适用性 | 模型E | 加噪(1%) 重力模型 | 1 | 160 | 80 | 10~50 | | 测试比值类方法加入正则 化因子后的稳定性 |
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The parameters of models
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Gravity anomaly of model A
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The ratio methods edge recognition results comparison map based on model A a—Ta(α=0);b—R-Ta(α=0.2);c—R-Ta(α=0.5);d—cosθ(α=0);e—R-cosθ(α=0.2);f—R-cosθ(α=0.5);g—NSTD(α=0);h—R-NSTD(α=0.2);i—R-NSTD(α=0.5)
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The Ta-THDR method edge recognition results comparison map based on model A a—Ta-THDR(α=0);b—R-Ta-THDR(α=0.2);c—R-Ta-THDR(α=0.5)
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Gravity anomaly of model B
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The ratio methods edge recognition results comparison map based on model B a—Ta;b—R-Ta;c—cosθ;d—R-cosθ;e—NSTD;f—R-NSTD
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The Ta-THDR method edge recognition results comparison map based on model B a—Ta-THDR;b—R-Ta-THDR
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Gravity anomaly of model C
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The ratio methods edge recognition results comparison map based on model C a—Ta;b—R-Ta;c—cosθ;d—R-cosθ;e—NSTD;f—R-NSTD
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The Ta-THDR method edge recognition results comparison map based on model C a—Ta-THDR;b—R-Ta-THDR
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Magnetic anomaly and RTP magnetic anomaly map a—magnetic anomaly map;b—RTP magnetic anomaly map
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The ratio methods edge recognition results comparison map based on model D a—Ta;b—R-Ta;c—cosθ;d—R-cosθ;e—NSTD;f—R-NSTD
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The Ta-THDR method edge recognition results comparison map based on model D a—Ta-THDR;b—R-Ta-THDR
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Gravity anomaly of model E
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The ratio methods edge recognition results comparison map based on model E a—Ta;b—R-Ta;c—cosθ;d—R-cosθ;e—NSTD;f—R-NSTD
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The Ta-THDR method edge recognition results comparison map based on model E a—Ta-THDR;b—R-Ta-THDR
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Real gravity anomaly map
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The ratio methods edge recognition results comparison map based on real dataa—Ta;b—R-Ta;c—cosθ;d—R-cosθ;e—NSTD;f—R-NSTD
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The Ta-THDR method edge recognition results comparison map based on real dataa—Ta-THDR;b—R-Ta-THDR
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