SUMMARY Spherical harmonic analysis of the main magnetic field of the Earth and its daily variations is the numerical determination of coefficients of solid spherical harmonics in the mathematical expressions used for the magnetic scalar potential of fields of internal and external origin. The coefficients are determined from vector components of the field and their purpose is to represent the vector field, not to reconstruct the magnetic scalar potential. An alternative interpretation of the spherical harmonic analysis is presented: namely the determination of the coefficients of a series representation of the magnetic vector field on a spherical surface in orthonormal real vector spherical harmonics, which correspond to the internal and external fields, and an additional non‐potential toroidal field. The numerical values of the coefficients of an orthonormal vector spherical harmonic series have a direct physical significance, which is not obscured by some arbitrary normalization of the vector spherical harmonics. Therefore, we propose a Schmidt vector normalization to be used in conjunction with the Schmidt quasi‐normalization of associated Legendre functions. A property of orthonormalized functions is that the standard deviations of the coefficients determined by the method of least squares from ideal data, which are uniformly accurate and uniformly globally distributed, are constant for all coefficients. The real vector spherical harmonic analysis of the geomagnetic field is extended to a spherical shell and conditions that restrict the radial dependence of the vector spherical harmonic coefficients are examined. In particular, two hypotheses for the current systems deriving from the non‐potential toroidal component of the magnetic field over the surface of a sphere are presented, namely, Earth–air currents and field‐aligned currents.

[1] Previous studies of the longitudinal variation of the local noon electrojet have yielded doubtful results either because of the poor data quality or because the local times of equatorial crossings occurred in the early morning or late afternoon. The recent launch of the Ørsted satellite in a near-circular orbit with slow drift in local time of equatorial crossing has provided the opportunity for researchers to study the electrojet more accurately. Most studies remove the main field using a spherical harmonic model and then search the daytime equatorial passes for the distinctive electrojet trough in total intensity. The present study examines the electrojet for two consecutive 6-month periods and consequently two local time ranges. Pure signal processing is used to remove the main field directly. The residuals are binned separately for night and day passes on a 1°by 1°grid to enhance the signal to noise ratio and are bin centered by a least squares fitted linear model to compensate for the variations in satellite altitude. Thereafter, for each period the compensated night and day binned values are subtracted from each other to produce a difference set. Global plots of the subsequently spatially filtered difference sets reveal an almost constant electrojet 1/e half width of 3°, as seen at satellite altitude apart from a region in the western Pacific. There are four maxima in the electrojet amplitude at 0°-30°E, 90°-120°E, 180°-220°E, and 260°-290°E in each local time range.

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[1] We examine three methods of determining the latitude of the focus of the Sq current system using data from an array of more than 50 magnetometers operating on the Australian mainland from November 1989 to July 1990. The magnetometer array enables the location of the Sq focus with more certainty than usual. Chains of stations within the array are then used to test the various methods of determining the focus latitude. The most accurate method was that which first determined the time when the magnetic eastward component DY passes through zero and then used northward magnetic components DX at that time, in a least squares linear fit, to find that latitude at which DX went to zero. This was found preferable to an alternative method which uses maximum and minimum values of DX. The reliability of these methods was examined on days with some magnetic disturbance present and on days when the focus latitude lay outside the chain of stations being used. The third method uses a principal component analysis to determine eigenvector elements for the daily variations of each station in the chain and fits the associated coefficients of the eigenvector elements to a straight line. This method had several shortcomings, especially if the procedure for determining the focus position were to be automated. For all methods the value of the correlation coefficient associated with the linear fit gave a good indication of the reliability of the estimation.