Premium
Computing three‐dimensional gravitational fields with equivalent sources [Note 1. Received June 1999, revision accepted October 1999. ...]
Author(s) -
Furness Peter
Publication year - 2000
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1046/j.1365-2478.2000.00193.x
Subject(s) - surface integral , polyhedron , gravitational field , line integral , volume integral , gravitation , gravitational potential , physics , surface (topology) , boundary (topology) , field (mathematics) , geometry , homogeneous , mathematical analysis , classical mechanics , integral equation , mathematics , statistical physics , pure mathematics
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.