Group-theoretical methods in geophysics

A group-theoretical technique is described whereby a linear system of tensor field equations of arbitrary rank and form, but with spherical or almost spherical boundary conditions, can be represented by an infinite-dimensional matrix equation. The matrix elements are in general radial operators, and formulae are given which enable them to be calculated explicitly. Particular reference is made to geophysical systems, where boundary perturbations, parameter fields and forcing fields may be expressed in terms of convergent series of spherical harmonics, and a truncated matrix of an appropriate finite dimension will represent the system to the desired accuracy.