Iterative Forward Magnetic Modelling with Corrections for Self-Demagnetisation

Abstract

Self-demagnetisation is commonly ignored in magnetic modelling of geometrically complex mineral exploration targets. With conventional methods the level of accepted mismatch between the observed magnetic field and the calculated magnetic field governs the degree of modelled complexity. Where the target bodies possess low magnetic susceptibilities, the effect of self-demagnetisation is negligible and as such conventional numerical calculation methods give satisfactory results even with geometrically complex models. However, in cases where target bodies possess high magnetic susceptibilities, self-demagnetisation effects have a significant influence on the observed magnetic field. If the geometry of the modelled body is complex, the fact that the self-demagnetising field can only be calculated exactly for an equivalent ellipsoid may lead to significant errors in its numerical interpretation. This paper proposes a new generalised iterative three-dimensional numerical modelling routine that allows for detailed modelling of geometrically complex target bodies possessing high magnetic susceptibilities. The modelling routine also allows for a magnetic field that varies spatially due to the effects of self-demagnetisation. This is done by segmenting the model into a three-dimensional matrix of spheres and repeatedly calculating the magnetic field at the center of each sphere. Each iteration of the modelling routine consists of a two-pass calculation of the magnetic field for each sphere. The first pass calculates the magnetic field at the centre of each sphere for a given inducing magnetic field (e.g. IGRF) with respect to the surrounding spheres. The second pass calculates the magnetic field at the centre of each sphere (using the resultant magnetic field from the first pass), where the sphere is considered to be in free-space. Each iteration uses the resultant magnetic field from the previous iteration as the inducing magnetic field. For simple models the added contribution from magnetic interaction with the surrounding voxels becomes negligible after approximately four (4) iterations. The number of iterations required for convergence increases with increasing complexity of the model.