Calculation of magnetic anomalies caused by 2D bodies of arbitrary shape with consideration of demagnetization |
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| Authors: | Nick P Kostrov |
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| Institution: | 19–101 Popov Street, Nizhny Tagil, Sverdlovsk region, 622005 Russia |
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| Abstract: | Forward calculations of magnetic anomalies caused by two-dimensional bodies of any shape and magnetic properties may be performed either without considering demagnetization as in the equivalent source technique or taking demagnetization into account as in the volume integral equation (VIE) approach, in which, for this purpose, magnetized bodies are divided into a set of rectangular prismatic cells. Ignoring demagnetization may result in distortion of the shape and the amplitude of an anomaly, whereas rectangular cells may not be an optimal representation of the source. Moreover, an inaccurate form approximation in the VIE technique may lead to inconsistent results in the near-body region. In this paper, a method is proposed, based on the VIE approach but differing by applying triangular elementary cells. The method largely overcomes the above-mentioned limitations of the VIE technique. It allows us to delineate large and complex structures exactly and only requires the source to be divided into a few elementary cells to take demagnetization into account satisfactorily. These improvements have been attained through analytical calculation of the Green's function in the complex plane, using the theory of the Cauchy-type integral. Comparing numerical solutions with analytical solutions for homogeneous elliptic cylinders without remanence, the method is found to be consistent with the theory in the range of relative magnetic permeability of 2–20, not only far from but also at subcell distances from the body. The method is appropriate for modelling highly and inhomogeneously magnetized 2D bodies of any shape. It may be of value in interpreting underground measurements or topographic effects, as well as in modelling regional geomagnetic profiles, and it is also a convenient tool for testing questionable geological hypotheses. In the framework of the method, the gravitational anomaly for the same causative bodies can be easily calculated. However, at higher and geologically uncommon values of relative magnetic permeability, the algorithm may become unstable but may be stabilized with SVD regularization. The fact that discrepancies were found with the method employed is a basis for further research. |
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