Asymptotic Anomalies of Uniform Thin Polygonal Sheets

Thin planar sheets are useful gravitational and magnetic models of dykes and veins, treated as two-dimensional geophysical structures on the survey scale of a 3D geological environment. We show that the thin-sheet anomaly formulae are numerically more stable than the corresponding formulae for a finitely thick poyhedral target. We also demonstrate the possibility of finding versions of the thin-sheet formulae that are absolutely stable with respect to increasing target distance to target size ratio, though this stability is obtained at the expense of extra numerical complexity.