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

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