Ellipsoids (v1.0): 3D Magnetic modelling of ellipsoidal bodies

(2017) Diego Takahashi Tomazella, Vanderlei C. Oliveira Jr.


This article is unpublished and is currently undergoing peer-review.

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Tomazella, D. T. and Oliveira Jr., V. C.: Ellipsoids (v1.0): 3D Magnetic modelling of ellipsoidal bodies, Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2017-44, in review, 2017.

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Ellipsoids are the only bodies for which the self-demagnetization can be treated analytically. This property is particularly useful for modelling compact ore bodies having high susceptibility. Here, we present a review of the magnetic modelling of ellipsoids, propose an alternative way of determining the isotropic susceptibility above which the self-demagnetization must be taken into consideration, as well as provide a set of routines to model the magnetic field produced by ellipsoids.

All the code developed for generating the results presented in the paper, as well as the code developed for generating additional numerical simulations, can be found at the online Github repository.

The paper is under review for the journal Geoscientific Model Development (GMD) and can be freely accessed at the journal website.

Abstract

A considerable amount of literature has been published on the magnetic modelling of uniformly magnetized ellipsoids since the second half of the nineteenth century. Ellipsoids have flexibility to represent a wide range of geometrical forms, are the only known bodies which can be uniformly magnetized in the presence of a uniform inducing field and are the only finite bodies for which the self-demagnetization can be treated analytically. This property makes ellipsoids particularly useful for modelling compact orebodies having high susceptibility. In this case, neglecting the self-demagnetization may strongly mislead the interpretation of these bodies by using magnetic methods. A number of previous studies consider that the self-demagnetization can be neglected for the case in which the geological body has an isotropic susceptibility lower than or equal to 0.1 SI. This limiting value, however, seems to be determined empirically and there has been no discussion about how this value was determined. Besides, the geoscientific community lacks an easy-to-use tool to simulate the magnetic field produced by uniformly magnetized ellipsoids. Here, we present an integrated review of the magnetic modelling of arbitrarily oriented triaxial, prolate and oblate ellipsoids. Our review includes ellipsoids with both induced and remanent magnetization, as well as with isotropic or anisotropic susceptibility. We also discuss the ambiguity between confocal ellipsoids with the same magnetic moment and propose a way of determining the isotropic susceptibility above which the self-demagnetization must be taken into consideration. Tests with synthetic data validate our approach. Finally, we provide a set of routines to model the magnetic field produced by ellipsoids. The routines are written in Python language as part of the Fatiando a Terra, which is an open-source library for modelling and inversion in geophysics.