Gravimagnetic anomaly formulas for polyhedra of spatially linear media

Abstract

Formulas for the gravity potential, field, and field gradient tensor are derived for a polyhedral target body of a spatially linear density medium. The formulas also define the magnetic potential and field in the case of a medium of spatially linear magnetization. This work generalizes existing solutions for the gravity field of a polyhedral target of linearly varying density. The formulas are analyzed for singularities and for numerical error growth. Error growth with increasing target distance is found to be higher than in the corresponding uniform polyhedral case. Examination of the error sources reveals that some error reduction is possible. On this basis, new algorithms of improved error control over existing algorithms are proposed for the linear medium. Computational results confirm the expected improvement.