Computing three-dimensional gravitational fields with equivalent sources

Abstract

Existing techniques for computing the gravitational field due to a homogeneous polyhedron all transform the required volume integral, expressing the field due to a volume distribution of mass, into a surface integral, expressing the potential due to a surface mass distribution over the boundary of the source body. An alternative representation is also possible and results in a surface integral expressing the potential due to a variable-strength double layer located on the polyhedral source boundary. Manipulation of this integral ultimately allows the gravitational field component in an arbitrary direction to be expressed as a weighted sum of the potentials due to two basic source distributions. These are a uniform-strength double layer located on all faces and a uniform-strength line source located along all edges. The derivatives of the gravitational field components can also be expressed in a similar form as can the magnetic field components due to a homogeneous magnetic polyhedron. It follows that the present approach can be used to generate a universal program capable of modelling all the commonly used potential field responses due to 3D bodies of arbitrary shape.