SINGULARITIES IN GRAVITY COMPUTATION FOR VERTICAL CYLINDERS AND PRISMS

An efficient formulation using conjugate complex variables is presented to compute the vertical gravity and its higher order derivatives for vertical cylindrical and prismatic bodies with uniform density at all points in space. The volume integrations over the bodies are reduced to line integrals around the bounding cross-sectional curves of the bodies. Residue theory and theory of singularities are used to treat the singularities in the integral formulae for computing gravity effects due to the bodies. The paper includes the considerations of the field point being inside, on the boundary or outside the bodies. Sample calculations are performed to obtain vertical gravity and its various gradient tensor elements for a vertical elliptic cylinder and a polygonal prism. The studies will be useful to simulate the gravity field effects due to mass disturbances caused by drilling and casing of a well bore in borehole gravimetry and gradiometry, and the quantitative interpretation of gravity anomalies.