Reilly, W.I. 1972 Interpretation of gravity and magnetic anomalies in terms of the generalised inertia tensor of the source body. [s.l.]: [s.n.]. Report / Geophysics Division 79 23 p.
Abstract: The gravity or magnetic anomalies produced by a closed distribution of mass or of uniformly directed dipole moment can be analysed in terms of a spherical harmonic series whose coefficients are the moments of the distribution about its centre of gravity. The problem is most readily formulated in terms of the generalised inertia tensor of arbitrary order. The analysis yields the total mass, or total magnetic moment, of the source body, the coordinates of its centre of gravity, and the components of the inertia tensor of the second and higher orders. The expressions for the gravity or magnetic anomalies are non-linear functions of some of the unknown parameters, but may be replaced by linear approximations and solved by an iterative least-squares method using Gram-Schmidt orthogonalisation. Investigation of the method has so far been confined to the determination of the second order inertia tensor. Diagonalisation of this tensor yields a pair of differences between the three principal moments of inertia, as well as defining the three principal planes of symmetry of the source body. Assumption of a value of uniform density or magnetisation further permits interpretation of the source body in terms of a regular geometric solid with the symmetry of the orthorhombic crystallographic class (auth.)