The magnetic field and magnetic gradient tensor for a right circular cylinder

Abstract

Expressions for the magnetic scalar potential, the magnetic field vector and the magnetic gradient tensor due to a uniformly magnetised semi-infinite right circular vertical cylinder are presented based on an application of Poisson’s relation to the gravity gradient tensor. The superposition principle allows for the theory to be extended to finite length and concentrically zoned right circular cylinders. This formulation provides an accurate and computationally efficient means of modelling the magnetic response of vertical or plunging right circular cylinders or pipes in which the total magnetisation is assumed to be homogeneous. This modelling technique lends itself to inversion applications in magnetic exploration. Furthermore, the theory presented here considers some important special cases including expressions for the magnetic gradient tensor on the axis of a vertical cylinder or pipe. This leads to expressions for estimating the direction of magnetisation within a uniformly magnetised pipe. This theory provides a basis for mapping magnetisation directions over quasi-vertical pipe-like bodies.

KEYWORDS:

• Pipe
• gravity gradient tensor
• magnetic gradient tensor
• magnetisation
• superposition

Acknowledgements

This paper represents a partial contribution towards a Ph.D. in the Department of Earth and Environmental Sciences at Macquarie University under the supervision of Mark Lackie and Craig O’Neill. I should like to thank Clive Foss, David Pratt and David Clark for encouraging me to write this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.