Gravity potential series expansion for homogeneous polyhedra

The aim is to develop a computationally efficient local representation of the gravity potential of a causative polyhedral body of homogeneous density. To achieve this objective we make use of the gravi-magnetic anomaly formulae for homogeneous polyhdra to express the exact expansion coefficients in a stabilised computational form. Series expansion methods in gravity anomaly calculations provide a convenient representation of the local anomaly that do not require the complexity of a full anomaly computation at every evaluation point within a region of interest around the expansion point. We give one approach to obtaining such an expansion, appropriate when the causative body is a homogeneous polyhedral target. We make use of the known gravi-magnetic anomaly formulae for such targets, to obtain computationally stabilised coefficients of the series exansion around an interest point. We develop the formulae for the gravity potential as a the series expansion, and show that the method can have efficiency advantages over gridded interpolation as a means of expressing the local variation in potential.