Electromagnetic core-mantle coupling: The fourier method for the solution of the induction equation

The Gauss coefficients of the geomagnetic field since 1903 are used as a time-dependent boundary condition for the poloidal field in the Earth's mantle. The coefficients are Fourier transformed, and the induction equation for the mantle field is solved in Fourier space. The phase advance of the poloidal field at the base of the mantle, and of the ensuing “poloidal” electromagnetic couple, is investigated as a function of the conductivity profile. Since, except for the phase shift, the couple behaves essentially as the one calculated by Stix and Roberts (1984) for each epoch separately, the “toroidal” part of the couple is calculated according to their instantaneous method. The phase shift is then obtained from a comparison with the couple required by the decade fluctuations in the length of the day. This permits a determination of the electrical conductivity of the mantle, which we find to be a rather flat function of radius.