Techniques for Separation of Plane Fields

This chapter is concerned with application of the body of the Cauchy-type integral to the solution of one of the oldest problems encountered in geopotential field theory, namely separation of the field into external and internal parts. This problem was first tackled as early as the last century in Gauss’ classical works on geomagnetism. Gauss was interested in the location of sources of the terrestrial magnetic field, whether they are found inside or outside the Earth. Having employed his own concept of spherical harmonic analysis, the great German mathematician demonstrated that the external part of the magnetic potential is negligible, compared to the internal part. The contributions of the magnetic field made by external and internal sources were analyzed once again toward the end of the nineteenth century by the German physicist and mathematician Schmiedt (Chapman and Bartels 1940). Having refined appropriately the technique of spherical harmonic analysis and employing more precise field data on the magnetic field, Schmiedt succeeded in evaluating the contribution of external sources into the terrestrial magnetic field, which proved to be negligible too.