Inversion of Magnetic Anomalies Using Affine Transforms of Geometrical Source Models

A method of magnetic data inversion is proposed and implemented. The magnetic source body is represented by a basic geometrical figure that undergoes affine transforms. The latter produce a family of figures in the affine space and among them the optimal solution can be found. If the basic figure in a 2D inverse problem is given as a circular one, then the affine family contains ellipsoidal figures. They represent solutions useful as a first approximation to more complicated source models. The model tests show that ellipsoidal solutions allow the magnetization direction, depth of the upper source surface, sizes and slope of the source body to be estimated. The inverse problem solution is stable and unique due to the small number of unknowns (less than ten in 2D problems) and because of the geometrical restriction over the ellipsoidal convex model with homogeneous magnetization. Two field examples from a lend magnetic survey in the area of the Bulgarian Antarctic base station at Livingston Island and from aeromagnetic investigations in the area of SE Bulgarian Black Sea shelf illustrate the effectiveness of the proposed method of magnetic inversion.