Truncation Errors in the Spherical Harmonic Analysis of the Geomagnetic Field and the Problem of Downward Extrapolation

The problem of extrapolating the geomagnetic field to the core boundary is considered, and the problem of suppressing the concomitant amplification of errors is examined in some detail. It is proved that if the extrapolation is accomplished by spherical harmonic analysis, the familiar least squares (or χ2-minimization) process of deriving the harmonic coefficients is open to theoretical objections. An alternative method is proposed which evades these criticisms.