A multiple level-set method for 3D boundary inversion of magnetic data
XIAO Xiao1,2,3,4, DUAN Ya-ting3, HU Shuanggui3, TANG Jingtian1,2,3,4, XIE Yong5, LIU Changsheng5
1. Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring (Central South University), Ministry of Education, Changsha, Hunan 410083, China; 2. Hunan Key Laboratory of Nonferrous Resources and Geological Hazards Exploration, Changsha, Hunan 410083, China; 3. School of Geosciences and Info-physics, Central South University, Changsha, Hunan 410083, China; 4. Technical Innovation Center of Coverage Area Deep Resources Exploration, Ministry of Natural Resources, Changsha, Hunan 410083, China; 5. Changsha Aeronautical Vocational and Technical College, Changsha, Hunan 410124, China
Abstract：Present algorithms for inverting the boundaries of magnetic targets use only two level sets. There are usually multiple magnetic geological bodies with different susceptibility in actual exploration. This paper proposes a new multiple level-set inversion algorithm for 3D inverting the position and geometry of magnetic targets with known susceptibility. First, based on the principle of multiple level sets, an objective function based on a multiple level sets function is established. Then, during the inversion process, an arbitrary tetrahedron element magnetic analytical solution algorithm is used for high-precision forward calculation, and the physical property mapping between forward and inverse grids is used to realize the independent operation of the forward grids and the inverse grids. The weighted essentially non-oscillatory scheme (WENO) is introduced to update and reinitialize the level set function, thereby improving the reliability and efficiency of the inversion. Finally, the effectiveness of the algorithm is verified by theoretical models with various numbers of level sets. The results show that the inversion based on the multiple level-set method has strong flexibility, and can automatically merge and separate regions in the model, thereby changing the model's topology with no need to manually reparameterize it. The accuracy of the inversion results is improved, and the boundary of the anomalous body obtained from the inversion accords well with the true boundary.
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