Gravi-magnetic Anomalies of Uniform thin Polygonal Sheets

Thin planar sheets are useful gravitational and magnetic models of dykes and veins treated as two-dimensional limit cannot be reached this way on account of the floating point finite precision. We derive the analytical zero thickness for the gravity potential while maintaining finite total mass. We use the concept of gravi-magnetic similarity to extend the thin-sheet potential formula to include the potential, field and field gradient in both gravity and megnetic cases, thereby generalising other studies that have obtained isolated polygonal thin-sheet anomaly solutions. We compare the anomalies computed by the new formulae to those of corresponding finite thickness targets, and to the finite differences estimates of the field and field gradient obtained from numerically differentiated thin-sheet potentials. In both cases a second order rate of approach to the limit is observed, verifying the correctness of the new formulae. Thin-sheet solutions are attractive for their reduced computational burden compared to full parallelepiped solutions, while the stacking of thin sheets may be used to stimulate variable density or magnetization targets. It is anticipated than thin-sheet solutions presented here will find application in gravi-magnetic modelling.