Gravity gradient tensor due to a cylinder

Abstract

We have derived closed-form expressions for the gravity gradient tensor above a vertical semi-infinite cylinder. We first derived the solution in the cylindrical coordinate system where, due to the azimuthal symmetry of the cylinder, there are only three nontrivial independent components of the tensor. The expressions in the Cartesian coordinate system can then be obtained through a coordinate transformation. For general use, we have also developed a solution to the gravity gradient tensor due to a semi-infinite cylinder with an arbitrary orientation through rotation between a user-defined coordinate and the cylinder-affixed Cartesian system. We have verified the validity of the solutions numerically through comparison with the results from approximating the cylinder with a set of small prisms and by comparison with the analytical solution for a semi-infinite line source.