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
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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Tao HE, Wan-Yin WANG, Jin-Ming HUANG, Ming-Hua ZHANG, Min YANG. The research of the regularization method in the ratio methods of edge recognition by potential field. Geophysical and Geochemical Exploration, 2019, 43(2): 308-319.
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