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Modelling magnetic fields due to steel drum accumulations
Author(s) -
Furness Peter
Publication year - 2007
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.2007.00635.x
Subject(s) - drum , dipole , computer science , integral equation , magnetic field , process (computing) , orientation (vector space) , centroid , field (mathematics) , magnetization , iterative method , geology , mechanics , statistical physics , algorithm , physics , mathematical analysis , mathematics , mechanical engineering , geometry , engineering , artificial intelligence , quantum mechanics , pure mathematics , operating system
Modelling the magnetic fields produced by accumulations of steel drums is a problem that is relevant to the detection and evaluation of disposal sites containing materials that are potentially hazardous to the environment. Accurate modelling is possible with existing integral equation techniques but these are numerically intensive due to the need to solve very large systems of linear equations. Use of an approximate iterative technique for the solution of the equations (system iteration) allows the integral equation technique to be extended to modelling the magnetic effect of substantially large accumulations, comprising up to several hundred drums, on very moderate computing facilities. However, even this process remains time‐consuming and suggests the use of more rapid, if less accurate, modifications. Several are available. Surprisingly, quite reasonable results can also be achieved with a very basic approximation that represents each drum by a discrete dipole located at its centroid. The dipole moments are found from the magnetic behaviour of single drums exposed to a uniform inducing field, which can be conveniently defined by a dyadic drum apparent susceptibility. The basic discrete dipole model for drum accumulations can be substantially improved by using a first‐order accommodation of the depolarizing effect produced by the shape of the accumulation. All of the above modelling techniques require details of individual drum locations and orientation. This information is generally unavailable to geophysical practitioners involved in environmental surveys and so prompts the idea of models that represent drum accumulations as a continuous distribution of magnetization. The convenience of neglecting details of drum location and orientation comes at the cost of some loss in accuracy of the modelled responses. However, for accumulations buried sufficiently deep and in which the drums are uniformly distributed, the total field magnetic anomaly is found to be reasonably approximated by the effect of a continuous magnetization, expressible in terms of an effective isotropic susceptibility. Again, the basic model can be improved by the accommodation of demagnetization effects due to the shape of the accumulation.