Thin planar sheets are useful gravitational and magnetic models of dykes and veins treated as twodimensionalgeophysical structures on the scale of the survey. Thus, the anomaly of a polygonal thin sheetof uniform surface density or magnetization in arbitrary orientation has practical interest. The limitingthin-sheet anomaly can be approached from the corresponding polyhedral parallelepiped under decreasingthickness, though the numerical limit cannot be reached this way on account of the floating point finiteprecision.We derive the analytical zero thickness limit 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 thepotential, field and field gradient in both gravity and magnetic cases, thereby generalising other studiesthat have obtained isolated polygonal thin-sheet anomaly solutions. We compare the anomalies computedby the new formulae to those of corresponding finite thickness targets, and to the finite differenceestimates of the field and field gradient obtainedfrom numerically differentiated thin-sheet potentials. In both cases a second order rate of approach to thelimit is observed, verifying the correctness of the new formulae.Thin-sheet solutions are attractive for their reduced computational burden compared to full parallelepipedsolutions, while the stacking of thin sheets may be used to simulate variable density or magnetizationtargets. It is anticipated that thin-sheet solutions presented here will find wide application in gravimagneticmodelling.
展开▼
