Dipole model of the sources of the Earth's magnetic field and secular change

The magnitude, colatitude, longitude, and distance from the center for radial dipoles were adjusted by a least-squares procedure so as to reproduce the surface magnetic field synthesized from the Fineh-Leaton (F.L.) 1955 Spherical Harmonic Coefficients and for the 1965 International Geomagnetic Reference Field (IGRF). The rms residual was reduced to 28 γ using 21 dipoles for the 1955 field (6th degree and order) and to 25 γ using 35 dipoles for the IGRF (8th degree and order). These residuals include all components of the surface field. The dipole parameters were then varied using a least-squares method to approximate the secular change field. These solutions match the Z component of secular change field synthesized from Leaton's 1955 coefficients to a rms residual of 2.15 γ per year and the IGRF secular change field to a rms residual of 1.26 γ per year. In both cases the dipole sources were found to be approximately 0.2 earth radius from the center of the earth.