Palaeomagnetism of NW Scotland syenites in relation to local and regional tectonics

Abstract

Summary. Spherical harmonic expansions are derived to represent arbitrary current densities and magnetic fields in a spherical region. The expansions can be viewed as a generalization of the spherical-harmonic, scalar-potential theory to include regions where spatially distributed current densities exist. The new expansions are found in terms of the eigenfunctions of the curl curl operator. It is found that four basic field forms may be present ; one of these is the well-known scalar potential expansion originated by Gauss. Electric and magnetic field boundary conditions appropriate to a conducting spherical shell including the case of anisotropic conductivity are presented. They are discussed in terms of their ability to couple the four field forms. It is pointed out that the four field forms can be expressed in five other orthogonal curvilinear coordinate systems.