Magnetic gradients produced by a 2D homogeneous polygonal source

We use a set of analytic equations for calculating horizontal and vertical gradients of the magnetic anomaly produced by a 2D homogeneous magnetic source with a polygonal cross section. The magnetization vector of the source is assumed to be constant and known, and the anomalous field is assumed to be much smaller than the ambient geomagnetic field in magnitude. The derivation begins from an expression of the magnetic potential; then we evaluate clockwise integrations to establish the equations. A comparison between this analytic approach and a numerical approach using the finite-difference method to compute gradients indicates the reliability of the equations. The proposed method is numerically efficient and does not present singularity on the edges of the polygon prism, except at the vertices where the gradients approach to infinity.