Magnetometric problem for a 2-D body of polygonal cross-section buried in the unbounded magnetic halfspace

Abstract

We present the exact boundary integral formulae for calculation of the magnetic anomaly due to a two dimensional body whose permeability is μ_T and its cross-section is bounded by the closed general polygonal contour. This body is buried in a wide-spreaded halfspace (e.g. lava field) of magnetic permeability μ₁. The upper halfspace is non-magnetic, its permeability is μ₀. The boundary integral technique for this problem requires the application of two-term logarithmic potential. Numerical calculations on the basis of derived formulae revealed that the surface anomaly ΔT reflects the “topography” mainly of the upper boundary of the perturbing body. The derived algorithm and numerical program enables the calculation of a lot of interesting models: magnetic intrusions, polygonal valleys, polygonal mine galleries, etc.