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http://dx.doi.org/10.7582/GGE.2022.25.1.38

Closed-form Expressions of Magnetic Field and Magnetic Gradient Tensor due to a Circular Disk  

Rim, Hyoungrea (Department of Earth Science Education, Pusan National University)
Publication Information
Geophysics and Geophysical Exploration / v.25, no.1, 2022 , pp. 38-43 More about this Journal
Abstract
In case axial symmetrical bodies with varying cross sections such as volcanic conduits and unexploded ordnance (UXO), it is efficient to approximate them by adding the response of thin disks perpendicular to the axis of symmetry. To compute the vector magnetic and magnetic gradient tensor respones by such bodies, it is necessary to derive an analytical expression of the circular disk. Therefore, in this study, we drive closed-form expressions of the vector magnetic and magnetic gradient tensor due to a circular disk. First, the vector magnetic field is obtained from the existing gravity gradient tensor using Poisson's relation where the gravity gradient tensor due to the same disk with a constant density can be transformed into a magnetic field. Then, the magnetic gradient tensor is derived by differentiating the vector magnetic field with respect to the cylindrical coordinates converted from the Cartesian coordinate system. Finally, both the vector magnetic and magnetic gradient tensors are derived using Lipschitz-Hankel type integrals based on the axial symmetry of the circular disk.
Keywords
magnetic field; magnetic gradient tensor; circular disk; Liptschitz-Hankel integral;
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Times Cited By KSCI : 5  (Citation Analysis)
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