Forward modeling formulae without analytic singularities for third-order magnetic gradient tensor of uniformly magnetized vertical cuboid
WANG Zhen1, DU Jinsong1,2,3, QIAN Bohao1, YUAN Changqing1, HU Zhengwang1,2
1. School of Geophysics and Geomatics, China University of Geosciences, Wuhan, Hubei 430074, China; 2. Hubei Subsurface Multiscale Imaging Key Laboratory, China University of Geosciences(Wuhan), Wuhan, Hubei 430074, China; 3. State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences(Wuhan), Wuhan, Hubei 430074, China
Abstract：As one of the most basic and most commonly used source models, the uniformly magnetized vertical cuboid is usually adopted for forward modeling and three-dimensional inversion of magnetic anomalies. Thus, its forward modeling formulae are of great importance both in theory and practice. The third-order magnetic gradient tensor (MGT) is a newly proposed concept and may be an important development direction of satellite magnetic and aeromagnetic surveys. Furthermore, many magnetic transforms for anomaly interpretation involve the forward modeling of several elements of the third-order MGT. Therefore, given the previous studies, the forward modeling formulae without analytic singularities for third-order MGT of the uniformly magnetized vertical cuboid are derived. Then, the correctness of the derived formulae is verified. Finally, the corresponding formulae are applied to the forward modeling of the analytic signal (AS) of the first-order vertical derivatives of total magnetic intensity (TMI) anomalies, first-order derivatives of the invariants of second-order MGT, and the first-order derivatives of normalized source strength (NSS). With high accuracy and high efficiency, the analytic formulae for forward modeling lay the foundation for future magnetic exploration utilizing the third-order MGT and the magnetic anomaly interpretation by magnetic transforms.
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