Mathematical model of the geomagnetic field for 1965

A mathematical model of the geomagnetic field for 1965.0 is presented. The field is given by internal and external spherical harmonic coefficients to degree and order 12. This model was derived from approximately 425,000 measurements made since 1900. An important step in the derivation was the analytic smoothing of data, which produced the regularly spaced grid values used as input to a two-stage spherical harmonic analysis. Consequently it has been possible to construct the 1965 world magnetic charts (published by the United States Naval Oceanographic Office) from the model, instead of the reverse. On the whole, the smoothed surface field defined by the model (and by the charts exactly drawn from the model) is believed to be at least as faithful to nature as that defined by any previously published model or set of charts. Plans for future analyses include the use of a modified truncation of the series expression for the potential and an allowance for the earth's oblateness.